NEWTON, ISAAC(Newton, Isaac) (1643–1727) - English mathematician, physicist, alchemist and historian, who laid the foundations of mathematical analysis, rational mechanics and all mathematical science, and also made a fundamental contribution to the development of physical optics.

Isaac (in English his name is pronounced Isaac) was born in the town of Woolsthorpe in Lincolnshire on Christmas Day, December 25, 1642 (January 4, 1643 in a new style) after the death of his father. Newton's childhood was spent in conditions of material prosperity, but was deprived of family warmth. The mother soon remarried - to an already middle-aged priest from a neighboring town - and moved in with him, leaving her son with his grandmother in Woolsthorpe. Over the next years, the stepfather had virtually no contact with his stepson. It is noteworthy that almost ten years after the death of his stepfather, nineteen-year-old Newton included in the confession he prepared for St. Day. Trinity has a long list of their sins and childhood threats to their stepfather and mother to burn down their house. Some modern researchers explain Newton's painful unsociability and bileness, which later manifested itself in his relationships with others, as a mental breakdown in childhood.

Newton received his primary education at the surrounding village schools, and then at the Grammar School, where he studied mainly Latin and the Bible. Due to the revealed abilities of her son, the mother abandoned her intention to make her son a farmer. In 1661 Newton entered St. College. Trinity (Trinity College) of the University of Cambridge and three years later received - thanks to the mysterious favor of fate that accompanied him throughout his life - one of 62 scholarships that entitled him to subsequent admission to Fellows of the college.

The early period of Newton's amazing creative activity occurred during his student years during the terrible plague years of 1665 and 1666, when classes at Cambridge were partially suspended. Newton spent a significant part of this time in the village. These years included the emergence of fundamental ideas from Newton, who had virtually no mathematical training before entering the university, that formed the basis for most of his subsequent great discoveries - from elements of series theory (including Newton's binomial) and mathematical analysis to new approaches in physical optics and dynamics, including the calculation of centrifugal force and the emergence of at least a guess about the law of universal gravitation.

In 1667 Newton became a bachelor and junior fellow of the college, and the following year - master and senior fellow of Trinity College. Finally, in the fall of 1669, he received one of the eight privileged royal chairs of Cambridge - the Lucasian Chair of Mathematics, inherited by him from Isaac (Isaac) Barrow, who left it.

According to the college's charter, its members were required to take the priesthood. This also awaited Newton. But by this time he had fallen into the most terrible heresy for a true Christian: Arianism: a member of the College of the Holy and Undivided Trinity doubted the fundamental dogma of the doctrine of the Trinity of God. Newton faced the grim prospect of leaving Cambridge. Even the king could not exempt a Trinity College member from ordination. But it was in his power to allow an exception for a professor who occupied the royal chair, and such an exception for the Lucasian chair (formally not for Newton) was legalized in 1675. Thus, the last obstacle to Newton’s career at the university was miraculously removed. He acquired a firm position without being burdened with almost any responsibilities. Newton's overly complex lectures were not popular with students, and in subsequent years the professor sometimes found no listeners in the audience.

The late 1660s and early 1670s saw Newton's manufacture of a reflecting telescope, for which he was elected to the Royal Society of London (1672). In the same year, he presented to the Society his research on a new theory of light and colors, which caused a heated debate with Robert Hooke (Newton’s pathological fear of public discussions, which developed with age, led, in particular, to the fact that he published Optics only 30 years later, after Hooke’s death). Newton owns ideas about monochromatic light rays and the periodicity of their properties, substantiated by the finest experiments, that underlie physical optics.

In those same years, Newton was developing the foundations of mathematical analysis, which became widely known from the correspondence of European scientists, although Newton himself did not publish a single line on this subject: Newton’s first publication on the foundations of analysis was published only in 1704, and a more complete manual - posthumously (1736).

Ten years later than Newton, G.V. Leibniz also came to the general ideas of mathematical analysis, and began publishing his works in this field in 1684. It should be noted that the subsequently generally accepted Leibniz notation system was more practical than Newton’s “method of fluxions”, becoming widespread in continental Western Europe already in the 1690s.

However, as it finally became clear only in the 20th century, the center of gravity of Newton’s interests lay in alchemy in the 1670–1680s. He was actively interested in metal transmutation and gold from the early 1670s.

Newton's seemingly monotonous life in Cambridge was shrouded in mystery. Perhaps the only serious disruption to its rhythm was the two and a half years devoted in the mid-1680s to writing Mathematical principles of natural philosophy(1687), which laid the foundation not only for rational mechanics, but also for the entire mathematical science. During this short period, Newton showed superhuman activity, concentrating on creating Began all the creative potential of the genius bestowed upon him. Beginnings contained the laws of dynamics, the law of universal gravitation with effective applications to the movement of celestial bodies, the origins of the study of the movement and resistance of liquids and gases, including acoustics. This work has remained for over three centuries the most remarkable creation of human genius.

History of creation Began remarkable. In the 1660s, Hooke also thought about the problem of universal gravitation. In 1674, he published his insightful ideas about the structure of the solar system, the movement of the planets in which consists of uniform rectilinear motion and motion under the influence of universal mutual attraction between bodies. Hooke soon became secretary of the Royal Society and in the late autumn of 1679, having consigned his previous disputes to oblivion, he invited Newton to speak about the laws of motion of bodies and, in particular, about the idea that “the celestial movements of the planets consist of direct tangential motion and motion due to attraction to the central body.” . Three days later, Newton confirmed to Hooke the receipt of his letter, but avoided giving a detailed answer under false pretexts. However, Newton made a rash statement, noting that bodies are deflected to the east when falling on Earth and move in a spiral converging towards its center. The triumphant Hooke respectfully pointed out to Newton that bodies do not fall in a spiral at all, but along some kind of ellipsoidal curve. Hooke then added that bodies on the rotating Earth fall not strictly to the east, but to the southeast. Newton responded with a letter that was striking for his irreconcilable character: “I agree with you,” he wrote, “that a body at our latitude will fall more to the south than to the east... And also with the fact that if we assume its gravity to be uniform, then it will not will descend in a spiral to the very center, but will spin with alternate rise and fall... But... the body will not describe an ellipsoidal curve.” According to Newton, the body will then describe a trajectory like a kind of trefoil, like an elliptical orbit with a rotating line of apses. Hooke, in his next letter, objected to Newton, pointing out that the apses of the orbit of a falling body would not shift. Newton did not answer him, but Hooke, using another pretext, added in his last letter from this cycle: “Now it remains to find out the properties of a curved line... caused by a central attractive force, under the influence of which the speed of evasion from a tangent or uniform rectilinear motion on all distances are inversely proportional to the squares of the distance. And I have no doubt that with the help of your wonderful method you will easily establish what kind of curve this should be and what its properties are...”

We don’t know exactly what happened and in what order over the next four years. Hooke's diaries over the years (as well as many of his other manuscripts) subsequently strangely disappeared, and Newton almost never left his laboratory. Frustrated by his oversight, Newton, of course, had to immediately take up the analysis of the problem clearly formulated by Hooke and, probably, soon received his main fundamental results, proving, in particular, the existence of central forces subject to the law of areas and the ellipticity of planetary orbits when the center of gravity is found in one of their tricks. At this point, Newton apparently considered the development of the principles he developed later in Beginnings the system of the world was complete for himself and calmed down on this.

At the beginning of 1684 in London, a historic meeting took place between Robert Hooke and the future royal astronomer Edmund Halley (who is usually called Halley in Russian) and the royal architect Christopher Wren, at which the interlocutors discussed the law of attraction ~ 1/ R 2 and set the task of deducing the ellipticity of orbits from the law of attraction. In August of that year, Halley visited Newton and asked him what he thought about this problem. In response, Newton said that he already had proof of the ellipticity of orbits, and promised to find his calculations.

Further events developed from cinematography to the 17th century. speed. At the end of 1684, Newton sent the first application text of an essay on the laws of motion to the Royal Society of London. Under pressure from Halley, he began to write a large treatise. He worked with all the passion and dedication of a genius, and in the end Beginnings were written in an amazingly short time - from one and a half to two and a half years. In the spring of 1686 Newton presented the text of the first book to London Began, which contained the formulation of the laws of motion, the doctrine of central forces in connection with the law of areas and the solution of various problems about motion under the influence of central forces, including motion along precessing orbits. In his presentation, he does not even mention the mathematical analysis he created and uses only the theory of limits he developed and the classical geometric methods of the ancients. No mention of the solar system, book one Began also does not contain. The Royal Society, which greeted Newton's work with enthusiasm, was, however, unable to finance its publication: printing Began Halley himself took over. Fearing controversy, Newton changed his mind about publishing a third book. Began, dedicated to the mathematical description of the Solar System. Still, Halley's diplomacy won. In March 1687, Newton sent to London the text of the second book, which expounded the doctrine of hydro-aerodynamic resistance of moving bodies and was silently directed against Descartes’ theory of vortices, and on April 4 Halley received the final third book Began- about the world system. On July 5, 1687, printing of the entire work was completed. The pace at which Halley carried out the publication Began three hundred years ago, can well be set as an example for modern publishing houses. Typesetting (from manuscript!), proofreading and printing of the second and third books Began, constituting slightly more than half of the entire composition, took exactly four months.

In preparation Began To print, Halley tried to convince Newton of the need to somehow note Hooke's role in establishing the law of universal gravitation. However, Newton limited himself to only a very ambiguous mention of Hooke, trying with his remark to also drive a wedge between Hooke, Halley and Wren.

Newton's point of view on the role of mathematical proofs in discovery is, in general, very peculiar, at least when it comes to his own priority. Thus, Newton not only did not recognize Hooke’s merits in the formulation of the law of universal gravitation and the formulation of the problem of planetary motion, but he believed that those two sentences that we call Kepler’s first two laws belonged to him - Newton, since it was he who received these laws as consequences from mathematical theory. Newton left only his third law to Kepler, which was only mentioned as Kepler’s law in Beginnings.

Nowadays, we still have to recognize the prominent role of Hooke as Newton's predecessor in understanding the mechanics of the solar system. S.I. Vavilov formulated this idea in the following words: “Write Beginnings in the 17th century no one except Newton could, but it cannot be disputed that the program, plan Began was first sketched by Hooke."

Having completed the publication Began, Newton, apparently, again isolated himself in his (al)chemical laboratory. His final years at Cambridge in the 1690s were marred by particularly severe mental depression. Someone then surrounded Newton with care, preventing the widespread spread of rumors about his illness, and as a result, little is known about the actual state of affairs.

In the spring of 1696, Newton received the post of Warden (Warden) of the Mint and moved from Cambridge to London. Here Newton immediately became intensively involved in organizational and administrative activities; under his leadership, in 1696–1698, enormous work was carried out to re-mint all English coins. In 1700 he was appointed to the highly paid position of Director (Master) of the Mint, which he held until his death. In the spring of 1703, Robert Hooke, an irreconcilable opponent and antipode of Newton, died. Hooke's death gave Newton complete freedom in the Royal Society of London, and at the next annual meeting, Newton was elected its president, occupying this chair for a quarter of a century.

In London he approached the court. In 1705, Queen Anne elevated him to the rank of knighthood. Soon Sir Isaac Newton became the generally recognized national pride of England. Discussion of the advantages of his philosophical system over Cartesian and his priority in relation to Leibniz in the discovery of infinitesimal calculus became an indispensable element of conversation in educated society.

In the last years of his life, Newton himself devoted a lot of time to theology and ancient and biblical history.

He died on March 31, 1727, a bachelor at the age of 85, in his country house, secretly refusing the sacrament and leaving a very significant fortune. A week later, his ashes were solemnly placed in a place of honor in Westminster Abbey.

A relatively complete collection of Newton's works was published in London in five volumes (1779–1785). However, his works and manuscripts began to be studied more deeply only in the mid-20th century, when 7 volumes of his correspondence were published ( Correspondence, 1959–1977) and 8 volumes of mathematical manuscripts ( Mathematical Papers, 1967–1981). Published in Russian Mathematical principles of natural philosophy Newton (first edition - 1915/1916, last - 1989), his Optics(1927) and Lectures on optics(1945), selected Mathematical work(1937) and Notes on the book« Prophet Daniel and the Apocalypse of St. Joanna"(1916).

Gleb Mikhailov

NEWTON, Isaac

English mathematician, physicist, alchemist and historian Isaac Newton was born in the town of Woolsthorpe in Lincolnshire into a farmer's family. Newton's father died shortly before his birth; the mother soon remarried a priest from a neighboring town and moved in with him, leaving her son with his grandmother in Woolsthorpe. Some researchers explain Newton's painful unsociability and bileness, which later manifested itself in his relationships with others, as a mental breakdown in childhood.

At the age of 12, Newton began studying at Grantham School, and in 1661 he entered St. Trinity College (Trinity College) of the University of Cambridge as a subsidizer (the so-called poor students who performed the duties of servants in the college to earn money), where his teacher was the famous mathematician I. Barrow. After graduating from the university, Newton received a bachelor's degree in 1665. In 1665-1667, during the plague epidemic, he was in his home village of Woolsthorpe; These years were the most productive in Newton's scientific work. Here he developed mainly those ideas that led him to the creation of differential and integral calculus, to the invention of a reflecting telescope (made by him with his own hands in 1668), the discovery of the law of universal gravitation, and here he conducted experiments on the decomposition of light.

In 1668, Newton was awarded a master's degree, and in 1669, Barrow transferred to him the chair of physics and mathematics, which Newton occupied until 1701. In 1671, Newton built a second reflecting telescope - larger in size and of better quality. The demonstration of the telescope made a strong impression on his contemporaries, and soon after, in January 1672, Newton was elected a member of the Royal Society of London (he became its president in 1703). In the same year, he presented to the Society his research on the new theory of light and colors, which caused a sharp controversy with Robert Hooke (Newton’s inherent pathological fear of public discussions led to the fact that he published “Optics”, prepared in those years, only 30 years later, after Hooke's death). Newton owns ideas about monochromatic light rays and the periodicity of their properties, substantiated by the finest experiments, that underlie physical optics.

In those same years, Newton was developing the foundations of mathematical analysis, which became widely known from the correspondence of European scientists, although Newton himself did not publish a single line on this subject: Newton’s first publication on the foundations of analysis was published only in 1704, and a more complete one leadership – posthumously (1736).

In 1687, Newton published his grandiose work “Mathematical Principles of Natural Philosophy” (briefly – “Principles”), which laid the foundation not only for rational mechanics, but also for the entire mathematical science. The “Principles” contained the laws of dynamics, the law of universal gravitation with effective applications to the movement of celestial bodies, the origins of the study of the movement and resistance of liquids and gases, including acoustics.

In 1695, Newton received the position of Superintendent of the Mint (this was apparently facilitated by the fact that Newton was actively interested in alchemy and the transmutation of metals in the 1670s and 1680s). Newton was entrusted with the leadership of the re-minting of all English coins. He managed to put the disordered coinage of England in order, for which in 1699 he received the highly paid lifelong title of Director of the Mint. In the same year, Newton was elected a foreign member of the Paris Academy of Sciences. In 1705, Queen Anne elevated him to a knighthood for his scientific works. In the last years of his life, Newton devoted a lot of time to theology and ancient and biblical history. Newton was buried in the English national pantheon - Westminster Abbey.

Sir Isaac Newton (December 25, 1642 – March 20, 1727) was the most famous English mathematician, physicist and astronomer throughout the world. He is considered the founder and ancestor of classical physics, since in one of his works - “Mathematical Principles of Natural Philosophy” - Newton outlined the three laws of mechanics and proved the law of universal gravitation, which helped classical mechanics move far forward.

Childhood

Isaac Newton was born on December 25 in the small town of Woolsthorpe, located in the county of Lincolnshire. His father was an average but very successful farmer who did not live to see the birth of his own son and died a couple of months before this event from a severe form of consumption.

It was in honor of the father that the child was named Isaac Newton. This was the decision of the mother, who mourned her deceased husband for a long time and hoped that her son would not repeat his tragic fate.

Despite the fact that Isaac was born at his due date, the boy was very sick and weak. According to some records, it was precisely because of this that they did not dare to baptize him, but when the child grew a little older and stronger, the baptism still took place.

There were two versions about the origin of Newton. Previously, bibliographers were sure that his ancestors were nobles who lived in England in those distant times.

However, the theory was refuted later when manuscripts were found in one of the local settlements, from which the following conclusion was drawn: Newton had absolutely no aristocratic roots; rather, on the contrary, he came from the poorest part of the peasants.

The manuscripts said that his ancestors worked for wealthy landowners and later, having accumulated enough money, bought a small plot of land, becoming yeomen (full landowners). Therefore, by the time Newton's father was born, the position of his ancestors was slightly better than before.

In the winter of 1646, Newton's mother, Anna Ayscough, marries a widower for the second time, and three more children are born. Since the stepfather communicates little with Isaac and practically does not notice him, after a month a similar attitude towards the child can already be discerned in his mother.

She also becomes cold towards her own son, which is why the already sullen and closed boy becomes even more alienated, not only in the family, but also with the classmates and friends around him.

In 1653, Isaac's stepfather dies, leaving his entire fortune to his newfound family and children. It would seem that now the mother should begin to devote much more time to the child, but this does not happen. Rather, on the contrary, now her husband’s entire household is in her hands, as well as children who require care. And despite the fact that part of the fortune still goes to Newton, he, as before, does not receive attention.

Youth

In 1655, Isaac Newton goes to Grantham School, located near his home. Since he has virtually no relationship with his mother during this period, he becomes close to the local pharmacist Clark and moves in with him. But he is not allowed to calmly study and tinker with various mechanisms in his free time (by the way, this was Isaac’s only passion). Six months later, his mother forcibly takes him from school, returns him to the estate and tries to transfer to him some of her own responsibilities for managing the household.

She believed that this way she could not only provide her son with a decent future, but also make her own life much easier. But the attempt was a failure - management was not interesting to the young man. On the estate, he only read, invented new mechanisms and tried to compose poems, showing with all his appearance that he was not going to interfere with the farm. Realizing that she won’t have to wait for help from her son, the mother allows him to continue his studies.

In 1661, after graduating from Grantham School, Newton entered Cambridge and successfully passed the entrance exams, after which he was enrolled in Trinity College as a “sizer” (a student who does not pay for his education, but earns it by providing services the institution itself or its wealthier students).

Quite little is known about Isaac’s university education, so it has been extremely difficult for scientists to reconstruct this period of his life. What is known is that the unstable political situation had a negative impact on the university: teachers were fired, student payments were delayed, and the educational process was partially absent.

Beginning of scientific activity

Until 1664, Newton, according to his own notes in his workbooks and personal diary, did not see any benefit or prospects in his university education. However, it was 1664 that became a turning point for him. First, Isaac compiles a list of problems of the surrounding world, consisting of 45 points (by the way, similar lists will appear more than once in the future on the pages of his manuscripts).

Then he meets a new mathematics teacher (and subsequently best friend) Isaac Barrow, thanks to whom he develops a special love for mathematical science. At the same time, he makes his first discovery - he creates a binomial expansion for an arbitrary rational exponent, with the help of which he proves the existence of an expansion of a function in an infinite series.

In 1686, Newton created the theory of universal gravitation, which later, thanks to Voltaire, acquired a certain mysterious and slightly humorous character. Isaac was on friendly terms with Voltaire and shared almost all his theories with him. One day they were sitting after lunch in the park under a tree, talking about the essence of the universe. And at this very moment, Newton suddenly admits to a friend that the theory of universal gravitation came to him at exactly the same moment - during rest.

“The afternoon weather was so warm and good that I definitely wanted to go out into the fresh air, under the apple trees. And at that moment, when I was sitting, completely immersed in my thoughts, a large apple fell from one of the branches. And I wondered why all the objects fall vertically down?”.

Isaac Newton's further scientific work was more than just fruitful. He was in constant correspondence with many famous scientists, mathematicians, astronomers, biologists and physicists. He authored such works as “A New Theory of Light and Colors” (1672), “Motion of Bodies in Orbit” (1684), “Optics or a Treatise on Reflections, Refractions, Bendings and Colors of Light” (1704), “Enumeration of the Lines of the Third order" (1707), "Analysis by means of equations with an infinite number of terms" (1711), "Method of differences" (1711) and many others.

early years

Isaac Newton, the son of a small but prosperous farmer, was born in the village of Woolsthorpe, Lincolnshire, on the eve of the Civil War. Newton's father did not live to see his son born. The boy was born prematurely and was sickly, so they did not dare to baptize him for a long time. Yet he survived, was baptized (January 1), and named Isaac in honor of his late father. Newton considered the fact of being born on Christmas a special sign of fate. Despite poor health in infancy, he lived to be 84 years old.

Newton sincerely believed that his family went back to the Scottish nobles of the 15th century, but historians discovered that in 1524 his ancestors were poor peasants. By the end of the 16th century, the family became rich and became yeomen (landowners). Newton's father left an inheritance of a large sum of 500 pounds sterling at that time and several hundred acres of fertile land occupied by fields and forests.

In January 1646, Newton's mother, Hannah Ayscough, remarried. She had three children with her new husband, a 63-year-old widower, and began to pay little attention to Isaac. The boy's patron was his maternal uncle, William Ayscough. As a child, Newton, according to contemporaries, was silent, withdrawn and isolated, loved to read and make technical toys: a sundial and water clock, a mill, etc. All his life he felt lonely.

His stepfather died in 1653, part of his inheritance went to Newton’s mother and was immediately registered by her in Isaac’s name. The mother returned home, but focused most of her attention on the three youngest children and the extensive household; Isaac was still left to his own devices.

In 1655, 12-year-old Newton was sent to study at a nearby school in Grantham, where he lived in the house of the pharmacist Clark. Soon the boy showed extraordinary abilities, but in 1659 his mother Anna returned him to the estate and tried to entrust part of the management of the household to her 16-year-old son. The attempt was not successful - Isaac preferred reading books, writing poetry, and especially designing various mechanisms to all other activities. At this time, Stokes, Newton's school teacher, approached Anna and began to persuade her to continue the education of her unusually gifted son; This request was joined by Uncle William and Isaac's Grantham acquaintance (relative of the pharmacist Clark) Humphrey Babington, a member of Trinity College Cambridge. With their combined efforts, they eventually achieved their goal. In 1661, Newton successfully graduated from school and went to continue his education at Cambridge University.

Trinity College (1661-1664)

In June 1661, 18-year-old Newton arrived in Cambridge. According to the charter, he was given an examination of his knowledge of the Latin language, after which he was informed that he had been accepted into Trinity College (College of the Holy Trinity) at the University of Cambridge. More than 30 years of Newton’s life are associated with this educational institution.

The college, like the entire university, was going through a difficult time. The monarchy had just been restored in England (1660), King Charles II often delayed payments due to the university, and dismissed a significant part of the teaching staff appointed during the revolution. In total, 400 people lived at Trinity College, including students, servants and 20 beggars, to whom, according to the charter, the college was obliged to give alms. The educational process was in a deplorable state.

Newton was included in the category of “sizar” students from whom tuition fees were not charged (probably on Babington’s recommendation). Very little documentary evidence and memories of this period of his life have survived. During these years, Newton's character was finally formed - the desire to get to the bottom, intolerance to deception, slander and oppression, indifference to public fame. He still had no friends.

In April 1664, Newton, having passed the exams, moved to a higher student category of “scholars”, which gave him the right to a scholarship and continuation of his studies at college.

Despite Galileo's discoveries, science and philosophy at Cambridge were still taught according to Aristotle. However, Newton's surviving notebooks already mention Galileo, Copernicus, Cartesianism, Kepler and Gassendi's atomic theory. Judging by these notebooks, he continued to make (mainly scientific instruments), and was enthusiastically engaged in optics, astronomy, mathematics, phonetics, and music theory. According to the memoirs of his roommate, Newton devoted himself wholeheartedly to his studies, forgetting about food and sleep; probably, despite all the difficulties, this was exactly the way of life that he himself desired.

The year 1664 in Newton's life was rich in other events. Newton experienced a creative surge, began independent scientific activity and compiled a large-scale list (of 45 points) of unsolved problems in nature and human life (Questionnaire, lat. Questiones quaedam philosophicae). In the future, similar lists appear more than once in his workbooks. In March of the same year, lectures began at the college's newly founded (1663) mathematics department by a new teacher, 34-year-old Isaac Barrow, a major mathematician, Newton's future friend and teacher. Newton's interest in mathematics increased sharply. He made the first significant mathematical discovery: binomial expansion for an arbitrary rational exponent (including negative ones), and through it he came to his main mathematical method - the expansion of a function into an infinite series. Finally, at the very end of the year, Newton became a bachelor.

The scientific support and inspiration for Newton's work were the physicists: Galileo, Descartes and Kepler. Newton completed their work by combining them into a universal system of the world. Other mathematicians and physicists had a lesser but significant influence: Euclid, Fermat, Huygens, Wallis and his immediate teacher Barrow. In Newton's student notebook there is a program phrase:

"The Plague Years" (1665-1667)

On Christmas Eve 1664, red crosses began to appear on London houses - the first marks of the Great Plague Epidemic. By summer, the deadly epidemic had expanded significantly. On 8 August 1665, classes at Trinity College were suspended and the staff disbanded until the end of the epidemic. Newton went home to Woolsthorpe, taking with him the main books, notebooks and instruments.

These were disastrous years for England - a devastating plague (a fifth of the population died in London alone), a devastating war with Holland, and the Great Fire of London. But Newton made a significant part of his scientific discoveries in the solitude of the “plague years.” From the surviving notes it is clear that the 23-year-old Newton was already fluent in the basic methods of differential and integral calculus, including series expansion of functions and what was later called the Newton-Leibniz formula. After conducting a series of ingenious optical experiments, he proved that white color is a mixture of the colors of the spectrum. Newton later recalled these years:

But his most significant discovery during these years was the law of universal gravitation. Later, in 1686, Newton wrote to Halley:

The inaccuracy mentioned by Newton is caused by the fact that Newton took the dimensions of the Earth and the magnitude of the acceleration of gravity from Galileo’s Mechanics, where they are given with a significant error. Later, Newton received more accurate data from Picard and was finally convinced of the truth of his theory.

There is a well-known legend that Newton discovered the law of gravity by observing an apple falling from a tree branch. For the first time, “Newton’s apple” was briefly mentioned by Newton’s biographer William Stukeley (book “Memoirs of the Life of Newton”, 1752):

The legend became popular thanks to Voltaire. In fact, as can be seen from Newton's workbooks, his theory of universal gravitation developed gradually. Another biographer, Henry Pemberton, gives Newton's reasoning (without mentioning the apple) in more detail: "by comparing the periods of the several planets and their distances from the sun, he found that ... this force must decrease in quadratic proportion as the distance increases." In other words, Newton discovered that from Kepler’s third law, which relates the orbital periods of planets to the distance to the Sun, it follows precisely the “inverse square formula” for the law of gravity (in the approximation of circular orbits). Newton wrote out the final formulation of the law of gravitation, which was included in textbooks, later, after the laws of mechanics became clear to him.

These discoveries, as well as many of the later ones, were published 20-40 years later than they were made. Newton did not pursue fame. In 1670 he wrote to John Collins: “I see nothing desirable in fame, even if I were capable of earning it. This would perhaps increase the number of my acquaintances, but this is exactly what I try most to avoid.” He did not publish his first scientific work (October 1666), which outlined the fundamentals of analysis; it was found only 300 years later.

Beginning of scientific fame (1667-1684)

In March-June 1666, Newton visited Cambridge. However, in the summer a new wave of plague forced him to go home again. Finally, early in 1667, the epidemic subsided, and Newton returned to Cambridge in April. On October 1 he was elected a fellow of Trinity College, and in 1668 he became a master. He was allocated a spacious separate room to live in, assigned a salary (2 pounds per year) and was given a group of students with whom he conscientiously studied standard academic subjects for several hours a week. However, neither then nor later did Newton become famous as a teacher; his lectures were poorly attended.

Having strengthened his position, Newton traveled to London, where shortly before, in 1660, the Royal Society of London was created - an authoritative organization of prominent scientific figures, one of the first Academies of Sciences. The publication of the Royal Society was the journal Philosophical Transactions.

In 1669, mathematical works using expansions in infinite series began to appear in Europe. Although the depth of these discoveries could not be compared with Newton's, Barrow insisted that his student fix his priority in this matter. Newton wrote a brief but fairly complete summary of this part of his discoveries, which he called “Analysis by Equations with an Infinite Number of Terms.” Barrow sent this treatise to London. Newton asked Barrow not to reveal the name of the author of the work (but he still let it slip). “Analysis” spread among specialists and gained some fame in England and abroad.

In the same year, Barrow accepted the king's invitation to become a court chaplain and left teaching. On 29 October 1669, the 26-year-old Newton was elected as his successor, professor of mathematics and optics at Trinity College, with a high salary of £100 per annum. Barrow left Newton an extensive alchemical laboratory; During this period, Newton became seriously interested in alchemy and conducted a lot of chemical experiments.

At the same time, Newton continued experiments in optics and color theory. Newton studied spherical and chromatic aberration. To reduce them to a minimum, he built a mixed reflecting telescope: a lens and a concave spherical mirror, which he made and polished himself. The project for such a telescope was first proposed by James Gregory (1663), but this plan was never realized. Newton's first design (1668) was unsuccessful, but the next one, with a more carefully polished mirror, despite its small size, provided a 40-fold magnification of excellent quality.

Rumors about the new instrument quickly reached London, and Newton was invited to show his invention to the scientific community. At the end of 1671 - beginning of 1672, a demonstration of the reflector took place before the king, and then at the Royal Society. The device received universal rave reviews. The practical importance of the invention probably also played a role: astronomical observations served to accurately determine time, which in turn was necessary for navigation at sea. Newton became famous and in January 1672 was elected a member of the Royal Society. Later, improved reflectors became the main tools of astronomers, with their help the planet Uranus, other galaxies, and red shift were discovered.

At first, Newton valued his communication with colleagues from the Royal Society, which included, in addition to Barrow, James Gregory, John Wallis, Robert Hooke, Robert Boyle, Christopher Wren and other famous figures of English science. However, tedious conflicts soon began, which Newton really did not like. In particular, a noisy controversy erupted over the nature of light. It began when, in February 1672, Newton published a detailed description of his classical experiments with prisms and his theory of color in the Philosophical Transactions. Hooke, who had previously published his own theory, stated that he was not convinced by Newton's results; he was supported by Huygens on the grounds that Newton's theory "contradicts generally accepted views." Newton responded to their criticism only six months later, but by this time the number of critics had increased significantly.

An avalanche of incompetent attacks left Newton irritated and depressed. He regretted that he had trustingly disclosed his discoveries to his fellow scientists. Newton asked the secretary of the Oldenburg Society not to send him any more critical letters and made a vow for the future: not to get involved in scientific disputes. In his letters, he complains that he is faced with a choice: either not to publish his discoveries, or to spend all his time and energy repelling unfriendly amateurish criticism. In the end he chose the first option and announced his resignation from the Royal Society (8 March 1673). It was not without difficulty that Oldenburg persuaded him to stay. However, scientific contacts with the Society are now reduced to a minimum.

Two important events occurred in 1673. First: by royal decree, Newton's old friend and patron, Isaac Barrow, returned to Trinity, now as a leader (“master”). Second: Leibniz, known at that time as a philosopher and inventor, became interested in Newton’s mathematical discoveries. Having received Newton's 1669 work on infinite series and studied it deeply, he then independently began to develop his own version of analysis. In 1676, Newton and Leibniz exchanged letters in which Newton explained a number of his methods, answered Leibniz's questions, and hinted at the existence of even more general methods, not yet published (meaning general differential and integral calculus). The Secretary of the Royal Society, Henry Oldenburg, persistently asked Newton to publish his mathematical discoveries on analysis for the glory of England, but Newton replied that he had been working on another topic for five years and did not want to be distracted. Newton did not respond to Leibniz's next letter. The first brief publication on Newton's version of analysis appeared only in 1693, when Leibniz's version had already spread widely throughout Europe.

The end of the 1670s was sad for Newton. In May 1677, 47-year-old Barrow died unexpectedly. In the winter of the same year, a strong fire broke out in Newton's house, and part of Newton's manuscript archive burned down. In September 1677, the secretary of the Royal Society, Oldenburg, who favored Newton, died, and Hooke, who was hostile to Newton, became the new secretary. In 1679, mother Anna became seriously ill; Newton, leaving all his affairs, came to her, took an active part in caring for the patient, but the mother’s condition quickly deteriorated, and she died. Mother and Barrow were among the few people who brightened up Newton's loneliness.

"Mathematical principles of natural philosophy" (1684-1686)

The history of the creation of this work, along with Euclid's Elements, one of the most famous in the history of science, began in 1682, when the passage of Halley's comet caused a rise in interest in celestial mechanics. Edmond Halley tried to persuade Newton to publish his “general theory of motion,” which had long been rumored in the scientific community. Newton refused. He was generally reluctant to be distracted from his research for the painstaking task of publishing scientific works.

In August 1684, Halley came to Cambridge and told Newton that he, Wren and Hooke had discussed how to derive the ellipticity of the orbits of planets from the formula for the law of gravitation, but did not know how to approach the solution. Newton reported that he already had such a proof, and in November he sent Halley the finished manuscript. He immediately appreciated the significance of the result and the method, immediately visited Newton again and this time managed to persuade him to publish his discoveries. On December 10, 1684, a historical entry appeared in the minutes of the Royal Society:

Work on the book took place in 1684-1686. According to the recollections of Humphrey Newton, a relative of the scientist and his assistant during these years, at first Newton wrote “Principia” in between alchemical experiments, to which he paid the main attention, then he gradually became carried away and enthusiastically devoted himself to working on the main book of his life.

The publication was supposed to be carried out with funds from the Royal Society, but at the beginning of 1686 the Society published a treatise on the history of fish that was not in demand, and thereby depleted its budget. Then Halley announced that he would bear the costs of publication himself. The Society gratefully accepted this generous offer and, as partial compensation, provided Halley with 50 free copies of a treatise on the history of fish.

Newton's work - perhaps by analogy with Descartes' "Principles of Philosophy" (1644) - was called "Mathematical Principles of Natural Philosophy" (lat. Philosophiae Naturalis Principia Mathematica), that is, in modern language, "Mathematical Foundations of Physics".

On April 28, 1686, the first volume of "Mathematical Principles" was presented to the Royal Society. All three volumes, after some editing by the author, were published in 1687. The circulation (about 300 copies) was sold out in 4 years - very quickly for that time.

Both the physical and mathematical level of Newton's work are completely incomparable with the work of his predecessors. It lacks Aristotelian or Cartesian metaphysics, with its vague reasoning and vaguely formulated, often far-fetched “first causes” of natural phenomena. Newton, for example, does not proclaim that the law of gravity operates in nature; he strictly proves this fact based on the observed picture of the motion of the planets and their satellites. Newton's method is to create a model of a phenomenon, “without inventing hypotheses,” and then, if there is enough data, to search for its causes. This approach, which began with Galileo, meant the end of old physics. A qualitative description of nature has given way to a quantitative one - a significant part of the book is occupied by calculations, drawings and tables.

In his book, Newton clearly defined the basic concepts of mechanics, and introduced several new ones, including such important physical quantities as mass, external force and momentum. Three laws of mechanics are formulated. A rigorous derivation from the law of gravity of all three Kepler laws is given. Note that hyperbolic and parabolic orbits of celestial bodies unknown to Kepler were also described. The truth of Copernicus's heliocentric system is not directly discussed by Newton, but implied; it even estimates the deviation of the Sun from the solar system's center of mass. In other words, the Sun in Newton’s system, unlike Keplerian’s, is not at rest, but obeys the general laws of motion. The general system also included comets, the type of orbits of which caused great controversy at that time.

The weak point of Newton's theory of gravity, according to many scientists of that time, was the lack of explanation of the nature of this force. Newton outlined only the mathematical apparatus, leaving open questions about the cause of gravity and its material carrier. For the scientific community, brought up on the philosophy of Descartes, this was an unusual and challenging approach, and only the triumphant success of celestial mechanics in the 18th century forced physicists to temporarily reconcile with Newtonian theory. The physical basis of gravity became clear only more than two centuries later, with the advent of the General Theory of Relativity.

Newton built the mathematical apparatus and general structure of the book as close as possible to the then standard of scientific rigor - Euclid's Elements. He deliberately did not use mathematical analysis almost anywhere - the use of new, unusual methods would have jeopardized the credibility of the results presented. This caution, however, devalued Newton's method of presentation for subsequent generations of readers. Newton's book was the first work on new physics and at the same time one of the last serious works using old methods of mathematical research. All of Newton's followers already used the powerful methods of mathematical analysis he created. The largest direct successors of Newton's work were D'Alembert, Euler, Laplace, Clairaut and Lagrange.

Administrative activities (1687-1703)

The year 1687 was marked not only by the publication of the great book, but also by Newton’s conflict with King James II. In February, the king, consistently pursuing his line for the restoration of Catholicism in England, ordered the University of Cambridge to give a master's degree to the Catholic monk Alban Francis. The university leadership hesitated, not wanting to irritate the king; Soon, a delegation of scientists, including Newton, was summoned for reprisals to the Lord Chief Justice, George Jeffreys, known for his rudeness and cruelty. Newton opposed any compromise that would impair university autonomy and persuaded the delegation to take a principled stand. As a result, the vice-chancellor of the university was removed from office, but the king’s wish was never fulfilled. In one of his letters these years, Newton outlined his political principles:

In 1689, after the overthrow of King James II, Newton was first elected to Parliament from Cambridge University and sat there for little more than a year. The second election took place in 1701-1702. There is a popular anecdote that he took the floor to speak in the House of Commons only once, asking that the window be closed to avoid a draft. In fact, Newton carried out his parliamentary duties with the same conscientiousness with which he treated all his affairs.

Around 1691, Newton became seriously ill (most likely, he was poisoned during chemical experiments, although there are other versions - overwork, shock after a fire, which led to the loss of important results, and age-related ailments). Those close to him feared for his sanity; the few surviving letters of his from this period do indicate mental disorder. Only at the end of 1693 did Newton's health fully recover.

In 1679, Newton met at Trinity an 18-year-old aristocrat, a lover of science and alchemy, Charles Montagu (1661-1715). Newton probably made a strong impression on Montagu, because in 1696, having become Lord Halifax, President of the Royal Society and Chancellor of the Exchequer (that is, the Minister of the Exchequer of England), Montagu proposed to the King that Newton be appointed Warden of the Mint. The king gave his consent, and in 1696 Newton took this position, left Cambridge and moved to London. From 1699 he became the manager (“master”) of the Mint.

To begin with, Newton thoroughly studied the technology of coin production, put the paperwork in order, and redid the accounting over the past 30 years. At the same time, Newton energetically and skillfully contributed to Montagu's monetary reform, restoring confidence in the English monetary system, which had been thoroughly neglected by his predecessors. In England during these years, almost exclusively inferior coins were in circulation, and in considerable quantities counterfeit coins were in circulation. Trimming the edges of silver coins became widespread. Now the coins began to be produced on special machines and there was an inscription along the rim, so that criminal grinding of the metal became impossible. Over the course of 2 years, the old, inferior silver coin was completely withdrawn from circulation and re-minted, the production of new coins increased to keep up with the need for them, and their quality improved. Previously, during such reforms, the population had to change old money by weight, after which the volume of cash decreased both among individuals (private and legal) and throughout the country, but interest and loan obligations remained the same, which is why the economy began stagnation. Newton proposed exchanging money at par, which prevented these problems, and the inevitable shortage of funds after this was made up for by taking loans from other countries (most of all from the Netherlands), inflation dropped sharply, but the external public debt grew by the middle of the century to unprecedented levels in the history of England sizes. But during this time, there was noticeable economic growth, because of which tax payments to the treasury increased (equal in size to those of France, despite the fact that France was inhabited by 2.5 times more people), due to this, the national debt was gradually paid off.

However, an honest and competent person at the head of the Mint did not suit everyone. From the very first days, complaints and denunciations rained down on Newton, and inspection commissions constantly appeared. As it turned out, many denunciations came from counterfeiters, irritated by Newton's reforms. Newton, as a rule, was indifferent to slander, but never forgave if it affected his honor and reputation. He was personally involved in dozens of investigations, and more than 100 counterfeiters were tracked down and convicted; in the absence of aggravating circumstances, they were most often sent to the North American colonies, but several leaders were executed. The number of counterfeit coins in England has decreased significantly. Montagu, in his memoirs, highly appreciated the extraordinary administrative abilities shown by Newton and ensured the success of the reform. Thus, the reforms carried out by the scientist not only prevented an economic crisis, but also, decades later, led to a significant increase in the country’s well-being.

In April 1698, the Russian Tsar Peter I visited the Mint three times during the “Great Embassy”; Unfortunately, the details of his visit and communication with Newton have not been preserved. It is known, however, that in 1700 a monetary reform similar to the English one was carried out in Russia. And in 1713, Newton sent the first six printed copies of the 2nd edition of the Principia to Tsar Peter in Russia.

Newton's scientific triumph was symbolized by two events in 1699: the teaching of Newton's world system began at Cambridge (from 1704 at Oxford), and the Paris Academy of Sciences, the stronghold of his Cartesian opponents, elected him as a foreign member. All this time Newton was still listed as a member and professor of Trinity College, but in December 1701 he officially resigned from all his posts at Cambridge.

In 1703, the President of the Royal Society, Lord John Somers, died, having attended the meetings of the Society only twice during the 5 years of his presidency. In November, Newton was elected as his successor and ruled the Society for the rest of his life - more than twenty years. Unlike his predecessors, he was personally present at all meetings and did everything to ensure that the British Royal Society took an honorable place in the scientific world. The number of members of the Society grew (among them, in addition to Halley, one can highlight Denis Papin, Abraham de Moivre, Roger Coates, Brooke Taylor), interesting experiments were carried out and discussed, the quality of journal articles improved significantly, financial problems were mitigated. The society acquired paid secretaries and its own residence (on Fleet Street); Newton paid the moving expenses out of his own pocket. During these years, Newton was often invited as a consultant to various government commissions, and Princess Caroline, the future Queen of Great Britain, spent hours talking with him in the palace on philosophical and religious topics.

Last years

In 1704, the monograph “Optics” was published (first in English), which determined the development of this science until the beginning of the 19th century. It contained an appendix “On the quadrature of curves” - the first and fairly complete presentation of Newton’s version of mathematical analysis. In fact, this is Newton's last work on the natural sciences, although he lived for more than 20 years. The catalog of the library he left behind contained books mainly on history and theology, and it was to these pursuits that Newton devoted the rest of his life. Newton remained the manager of the Mint, since this post, unlike the position of superintendent, did not require much activity from him. Twice a week he went to the Mint, once a week to a meeting of the Royal Society. Newton never traveled outside of England.

In 1705, Queen Anne knighted Newton. From now on he is Sir Isaac Newton. For the first time in English history, the title of knight was awarded for scientific merit; the next time it happened was more than a century later (1819, in reference to Humphry Davy). However, some biographers believe that the queen was guided not by scientific, but by political motives. Newton acquired his own coat of arms and a not very reliable pedigree.

In 1707, a collection of Newton's mathematical works, Universal Arithmetic, was published. The numerical methods presented in it marked the birth of a new promising discipline - numerical analysis.

In 1708, an open priority dispute with Leibniz began (see below), in which even the reigning persons were involved. This feud between two geniuses cost science dearly - the English mathematical school soon withered for a whole century, and the European school ignored many of Newton’s outstanding ideas, rediscovering them much later. Even the death of Leibniz (1716) did not extinguish the conflict.

The first edition of Newton's Principia has long been sold out. Newton's many years of work to prepare the 2nd edition, revised and expanded, was crowned with success in 1710, when the first volume of the new edition was published (the last, third - in 1713). The initial circulation (700 copies) turned out to be clearly insufficient; there were additional printings in 1714 and 1723. When finalizing the second volume, Newton, as an exception, had to return to physics to explain the discrepancy between theory and experimental data, and he immediately made a major discovery - hydrodynamic compression of the jet. The theory now agreed well with experiment. Newton added an Instruction to the end of the book with a scathing critique of the “vortex theory” with which his Cartesian opponents tried to explain the motion of the planets. To the natural question “how is it really?” the book follows the famous and honest answer: “I still have not been able to deduce the cause... of the properties of the force of gravity from phenomena, and I do not invent hypotheses.”

In April 1714, Newton summarized his experience of financial regulation and submitted his article “Observations Concerning the Value of Gold and Silver” to the Treasury. The article contained specific proposals for adjusting the cost of precious metals. These proposals were partially accepted, and this had a beneficial effect on the British economy.

Shortly before his death, Newton became one of the victims of a financial scam by a large trading company, the South Sea Company, which was supported by the government. He purchased the company's securities for a large sum, and also insisted on their acquisition by the Royal Society. On September 24, 1720, the company bank declared itself bankrupt. Niece Catherine recalled in her notes that Newton lost more than 20,000 pounds, after which he declared that he could calculate the movement of celestial bodies, but not the degree of madness of the crowd. However, many biographers believe that Catherine did not mean a real loss, but a failure to receive the expected profit. After the company's bankruptcy, Newton offered to compensate the Royal Society for the losses from his own pocket, but his offer was rejected.

Newton devoted the last years of his life to writing the Chronology of Ancient Kingdoms, which he worked on for about 40 years, and preparing the third edition of the Elements. The third edition was published in 1726; Unlike the second, the changes in it were minor - mainly the results of new astronomical observations, including a fairly complete guide to comets observed since the 14th century. Among others, the calculated orbit of Halley's comet was presented, the reappearance of which at the indicated time (1758) clearly confirmed the theoretical calculations of the (by then deceased) Newton and Halley. The circulation of the book for a scientific publication of those years could be considered huge: 1250 copies.

In 1725, Newton's health began to deteriorate noticeably, and he moved to Kensington near London, where he died at night, in his sleep, on March 20 (31), 1727. He did not leave a written will, but shortly before his death he transferred a significant part of his large fortune to his closest relatives. By order of the king, he was buried in Westminster Abbey.

Personal qualities

Character traits

It is difficult to draw up a psychological portrait of Newton, since even people who sympathize with him often attribute various qualities to Newton. We have to take into account the cult of Newton in England, which forced the authors of memoirs to endow the great scientist with all conceivable virtues, and the real contradictions in his nature. In addition, by the end of his life, Newton’s character acquired such traits as good nature, condescension and sociability, which were previously not characteristic of him.

In appearance, Newton was short, strongly built, with wavy hair. He was almost never sick, and until old age he retained his thick hair (already completely gray since he was 40) and all his teeth except one. I never (according to other sources, almost never) used glasses, although I was slightly myopic. He almost never laughed or got irritated; there is no mention of his jokes or other manifestations of his sense of humor. In financial transactions he was careful and thrifty, but not stingy. Never married. He was usually in a state of deep internal concentration, which is why he often showed absent-mindedness: for example, once, having invited guests, he went to the pantry to get wine, but then some scientific idea dawned on him, he rushed to the office and never returned to the guests . He was indifferent to sports, music, art, theater, and travel, although he knew how to draw well. His assistant recalled: “He did not allow himself any rest or respite ... he considered every hour not devoted to [science] to be lost ... I think he was quite saddened by the need to waste time on eating and sleeping.” With all that has been said, Newton was able to combine everyday practicality and common sense, clearly manifested in his successful management of the Mint and the Royal Society.

Brought up in Puritan traditions, Newton established for himself a number of strict principles and self-restraints. And he was not inclined to forgive others what he would not forgive himself; this is the root of many of his conflicts (see below). He treated his relatives and many colleagues warmly, but had no close friends, did not seek the company of other people, and remained aloof. At the same time, Newton was not heartless and indifferent to the fate of others. When, after the death of his half-sister Anna, her children were left without a means of support, Newton assigned an allowance to the minor children, and later took Anna’s daughter, Katherine, into his care. He constantly helped other relatives. “Being economical and prudent, he was at the same time very free with money and was always ready to help a friend in need, without being intrusive. He is especially noble towards young people.” Many famous English scientists - Stirling, Maclaurin, astronomer James Pound and others - recalled with deep gratitude the help provided by Newton at the beginning of their scientific careers.

Conflicts

In the history of science, Robert Hooke is marked not only by remarkable discoveries and inventions, but also by constant priority disputes. He accused his first patron, Robert Boyle, of having appropriated Hooke's improvements to the air pump. He quarreled with the Society's secretary, Oldenburg, saying that, with the help of Oldenburg, Huygens had stolen the idea of ​​a clock with a spiral spring from Hooke. His friend and biographer Richard Waller wrote in the preface to Hooke's posthumous collection of works: "His character was melancholy, distrustful and jealous, which became more and more noticeable over the years." S.I. Vavilov writes:

In 1675, Newton sent the Society his treatise with new research and speculation on the nature of light. Hooke stated at the meeting that everything that was valuable in the treatise was already contained in Hooke’s previously published book “Micrography”. In private conversations, he accused Newton of plagiarism: “I showed that Mr. Newton used my hypotheses about impulses and waves” (from Hooke’s diary). Hooke disputed the priority of all of Newton's discoveries in the field of optics, except those with which he did not agree. Oldenburg immediately informed Newton about these accusations, and he regarded them as insinuations. This time the conflict was resolved, and the scientists exchanged letters of conciliation (1676). However, from that moment until Hooke’s death (1703), Newton did not publish any work on optics, although he accumulated a huge amount of material, which he systematized in the classic monograph “Optics” (1704).

When Newton was preparing his Principia for publication, Hooke demanded that Newton stipulate in the preface Hooke's priority regarding the law of gravitation. Newton countered that Bulliald, Christopher Wren, and Newton himself arrived at the same formula independently and before Hooke. A conflict broke out, which greatly poisoned the lives of both scientists. S.I. Vavilov writes:

Subsequently, Newton's relationship with Hooke remained tense. For example, when Newton presented the Society with a new design for a sextant, Hooke immediately stated that he had invented such a device more than 30 years ago (although he had never built a sextant). Nevertheless, Newton was aware of the scientific value of Hooke’s discoveries and in his “Optics” he mentioned his now deceased opponent several times.

Newton is sometimes accused of destroying the only portrait of Hooke that was once kept at the Royal Society. In reality, there is not a single piece of evidence to support such an accusation.

John Flamsteed, an outstanding English astronomer, met Newton in Cambridge (1670), when Flamsteed was still a student and Newton a master. However, already in 1673, almost simultaneously with Newton, Flamsteed also became famous - he published astronomical tables of excellent quality, for which the king awarded him a personal audience and the title “Royal Astronomer”. Moreover, the king ordered the construction of an observatory in Greenwich near London and transfer it to Flamsteed. However, the king considered the money to equip the observatory to be an unnecessary expense, and almost all of Flamsteed’s income went to the construction of instruments and the economic needs of the observatory.

At first, Newton and Flamsteed's relationship was cordial. Newton was preparing the second edition of the Principia and was in dire need of accurate observations of the Moon to construct and (as he hoped) confirm his theory of its motion; In the first edition, the theory of the motion of the Moon and comets was unsatisfactory. This was also important for the establishment of Newton’s theory of gravitation, which was sharply criticized by the Cartesians on the continent. Flamsteed willingly gave him the requested data, and in 1694 Newton proudly informed Flamsteed that a comparison of calculated and experimental data showed their practical agreement. In some letters, Flamsteed urgently asked Newton, in the case of using observations, to stipulate his, Flamsteed's, priority; this primarily applied to Halley, whom Flamsteed did not like and suspected of scientific dishonesty, but it could also mean a lack of trust in Newton himself. Flamsteed's letters begin to show resentment:

The open conflict began with a letter from Flamsteed, in which he apologetically reported that he had discovered a number of systematic errors in some of the data provided to Newton. This jeopardized Newton's theory of the Moon and forced the calculations to be redone, and confidence in the remaining data was also shaken. Newton, who hated dishonesty, was extremely irritated and even suspected that Flamsteed had deliberately introduced the errors.

In 1704, Newton visited Flamsteed, who by this time had received new, extremely accurate observational data, and asked him to convey this data; in return, Newton promised to help Flamsteed in publishing his main work, the Great Star Catalog. Flamsteed, however, began to delay for two reasons: the catalog was not yet completely ready, and he no longer trusted Newton and was afraid of theft of his priceless observations. Flamsteed used the experienced calculators provided to him to complete the work to calculate the positions of the stars, while Newton was primarily interested in the Moon, planets and comets. Finally, in 1706, printing of the book began, but Flamsteed, suffering from agonizing gout and becoming increasingly suspicious, demanded that Newton not open the sealed copy until printing was completed; Newton, who urgently needed the data, ignored this prohibition and wrote down the necessary values. The tension grew. Flamsteed confronted Newton for attempting to personally correct minor errors. The printing of the book was extremely slow.

Due to financial difficulties, Flamsteed failed to pay his membership fee and was expelled from the Royal Society; a new blow was dealt by the queen, who, apparently at Newton’s request, transferred control functions over the observatory to the Society. Newton gave Flamsteed an ultimatum:

Newton also threatened that further delays would be considered disobedience to Her Majesty's orders. In March 1710, Flamsteed, after heated complaints about injustice and the machinations of enemies, nevertheless handed over the final pages of his catalog, and at the beginning of 1712 the first volume, entitled “Heavenly History,” was published. It contained all the data Newton needed, and a year later, a revised edition of the Principia, with a much more accurate theory of the Moon, also quickly appeared. The vindictive Newton did not include gratitude to Flamsteed in the edition and crossed out all references to him that were present in the first edition. In response, Flamsteed burned all the unsold 300 copies of the catalog in his fireplace and began preparing its second edition, this time to his own taste. He died in 1719, but through the efforts of his wife and friends this wonderful publication, the pride of English astronomy, was published in 1725.

From surviving documents, historians of science have found out that Newton discovered differential and integral calculus back in 1665-1666, but did not publish it until 1704. Leibniz developed his version of the calculus independently (from 1675), although the initial impetus for his thought probably came from rumors that Newton already had such a calculus, as well as through scientific conversations in England and correspondence with Newton. Unlike Newton, Leibniz immediately published his version, and later, together with Jacob and Johann Bernoulli, widely propagated this epoch-making discovery throughout Europe. Most scientists on the continent had no doubt that Leibniz had discovered analysis.

Having heeded the persuasion of friends who appealed to his patriotism, Newton, in the 2nd book of his “Principles” (1687), said:

After the first detailed publication of Newton's analysis (mathematical appendix to Optics, 1704) appeared in Leibniz's journal Acta eruditorum, an anonymous review appeared with insulting allusions to Newton. The review clearly indicated that the author of the new calculus was Leibniz. Leibniz himself strongly denied that he had written the review, but historians were able to find a draft written in his handwriting. Newton ignored Leibniz's paper, but his students responded indignantly, after which a pan-European priority war broke out, "the most shameful squabble in the entire history of mathematics."

On January 31, 1713, the Royal Society received a letter from Leibniz containing a conciliatory formulation: he agreed that Newton arrived at the analysis independently, “on general principles similar to ours.” An angry Newton demanded the creation of an international commission to clarify priority. The commission did not need much time: after a month and a half, having studied Newton’s correspondence with Oldenburg and other documents, it unanimously recognized Newton’s priority, and in wording, this time offensive to Leibniz. The commission's decision was published in the proceedings of the Society with all supporting documents attached. In response, from the summer of 1713, Europe was flooded with anonymous pamphlets that defended Leibniz's priority and argued that "Newton arrogates to himself the honor that belongs to another." The pamphlets also accused Newton of stealing the results of Hooke and Flamsteed. Newton's friends, for their part, accused Leibniz himself of plagiarism; According to their version, during his stay in London (1676), Leibniz at the Royal Society became acquainted with Newton’s unpublished works and letters, after which Leibniz published the ideas expressed there and passed them off as his own.

The war continued unabated until December 1716, when Abbé Conti informed Newton: “Leibniz is dead—the dispute is over.”

Scientific activity

A new era in physics and mathematics is associated with Newton's work. He completed the creation of theoretical physics, begun by Galileo, based, on the one hand, on experimental data, and on the other, on a quantitative and mathematical description of nature. Powerful analytical methods are emerging in mathematics. In physics, the main method of studying nature is the construction of adequate mathematical models of natural processes and intensive research of these models with the systematic use of the full power of the new mathematical apparatus. Subsequent centuries have proven the exceptional fruitfulness of this approach.

Philosophy and scientific method

Newton resolutely rejected the approach of Descartes and his Cartesian followers, popular at the end of the 17th century, which prescribed that when constructing a scientific theory, one must first use the “discernment of the mind” to find the “root causes” of the phenomenon under study. In practice, this approach often led to the formulation of far-fetched hypotheses about “substances” and “hidden properties” that were not amenable to experimental verification. Newton believed that in “natural philosophy” (that is, physics), only such assumptions (“principles”, now prefer the name “laws of nature”) are permissible that directly follow from reliable experiments and generalize their results; He called hypotheses assumptions that were not sufficiently substantiated by experiments. “Everything... that is not deduced from phenomena should be called a hypothesis; hypotheses of metaphysical, physical, mechanical, hidden properties have no place in experimental philosophy.” Examples of principles are the law of gravity and the 3 laws of mechanics in Principia; the word “principles” (Principia Mathematica, traditionally translated as “mathematical principles”) is also contained in the title of his main book.

In a letter to Pardiz, Newton formulated the “golden rule of science”:

This approach not only placed speculative fantasies outside of science (for example, the Cartesians’ reasoning about the properties of “subtle matters” that allegedly explained electromagnetic phenomena), but was more flexible and fruitful because it allowed mathematical modeling of phenomena for which the root causes had not yet been discovered. This is what happened with gravity and the theory of light - their nature became clear much later, which did not interfere with the successful centuries-old use of Newtonian models.

The famous phrase “I do not invent hypotheses” (lat. Hypotheses non fingo), of course, does not mean that Newton underestimated the importance of finding “first causes” if they are clearly confirmed by experience. The general principles obtained from the experiment and the consequences from them must also undergo experimental testing, which can lead to an adjustment or even a change in the principles. “The whole difficulty of physics... consists in recognizing the forces of nature from the phenomena of motion, and then using these forces to explain other phenomena.”

Newton, like Galileo, believed that mechanical motion underlies all natural processes:

Newton formulated his scientific method in his book “Optics”:

In the 3rd book of the Elements (starting from the 2nd edition), Newton placed a number of methodological rules directed against the Cartesians; The first of them is a variant of Occam's razor:

Newton's mechanistic views turned out to be incorrect - not all natural phenomena arise from mechanical motion. However, his scientific method became established in science. Modern physics successfully explores and applies phenomena whose nature has not yet been clarified (for example, elementary particles). Since Newton, natural science has developed with the firm belief that the world is knowable because nature is organized according to simple mathematical principles. This confidence became the philosophical basis for the tremendous progress of science and technology.

Mathematics

Newton made his first mathematical discoveries back in his student years: the classification of algebraic curves of the 3rd order (curves of the 2nd order were studied by Fermat) and the binomial expansion of an arbitrary (not necessarily integer) degree, from which Newton’s theory of infinite series began - a new and powerful tool of analysis . Newton considered series expansion to be the main and general method of analyzing functions, and in this matter he reached the heights of mastery. He used series to calculate tables, solve equations (including differential ones), and study the behavior of functions. Newton was able to obtain expansions for all the functions that were standard at that time.

Newton developed differential and integral calculus simultaneously with G. Leibniz (a little earlier) and independently of him. Before Newton, actions with infinitesimals were not linked into a single theory and were in the nature of disparate ingenious techniques (see Method of Indivisibles). The creation of a systemic mathematical analysis reduces the solution of relevant problems, to a large extent, to the technical level. A complex of concepts, operations and symbols appeared, which became the starting point for the further development of mathematics. The next century, the 18th century, was a century of rapid and extremely successful development of analytical methods.

Perhaps Newton came to the idea of ​​analysis through difference methods, which he studied a lot and deeply. True, in his “Principles” Newton almost did not use infinitesimals, adhering to ancient (geometric) methods of proof, but in other works he used them freely.

The starting point for differential and integral calculus were the works of Cavalieri and especially Fermat, who already knew how (for algebraic curves) to draw tangents, find extrema, inflection points and curvature of a curve, and calculate the area of ​​its segment. Among other predecessors, Newton himself named Wallis, Barrow and the Scottish scientist James Gregory. There was no concept of a function yet; he interpreted all curves kinematically as trajectories of a moving point.

Already as a student, Newton realized that differentiation and integration are mutually inverse operations. This fundamental theorem of analysis had already emerged more or less clearly in the works of Torricelli, Gregory and Barrow, but only Newton realized that on this basis it was possible to obtain not only individual discoveries, but a powerful systemic calculus, similar to algebra, with clear rules and gigantic possibilities.

For almost 30 years Newton did not bother to publish his version of the analysis, although in letters (in particular to Leibniz) he willingly shared much of what he had achieved. Meanwhile, Leibniz's version had been spreading widely and openly throughout Europe since 1676. Only in 1693 did the first presentation of Newton's version appear - in the form of an appendix to Wallis's Treatise on Algebra. We have to admit that Newton’s terminology and symbolism are rather clumsy in comparison with Leibniz’s: fluxion (derivative), fluenta (antiderivative), moment of magnitude (differential), etc. Only Newton’s notation “o” for an infinitesimal dt has been preserved in mathematics (however , this letter was used earlier by Gregory in the same sense), and even a dot above the letter as a symbol of the derivative with respect to time.

Newton published a fairly complete statement of the principles of analysis only in the work “On the Quadrature of Curves” (1704), attached to his monograph “Optics”. Almost all of the material presented was ready back in the 1670-1680s, but only now Gregory and Halley persuaded Newton to publish the work, which, 40 years late, became Newton’s first printed work on analysis. Here, Newton introduced derivatives of higher orders, found the values ​​of the integrals of various rational and irrational functions, and gave examples of solving 1st order differential equations.

In 1707, the book “Universal Arithmetic” was published. It presents a variety of numerical methods. Newton always paid great attention to the approximate solution of equations. Newton's famous method made it possible to find the roots of equations with previously unimaginable speed and accuracy (published in Wallis' Algebra, 1685). Newton's iterative method was given its modern form by Joseph Raphson (1690).

In 1711, after 40 years, Analysis by Equations with an Infinite Number of Terms was finally published. In this work, Newton explores both algebraic and “mechanical” curves (cycloid, quadratrix) with equal ease. Partial derivatives appear. In the same year, “The Method of Differences” was published, where Newton proposed an interpolation formula for drawing through (n + 1) given points with equally spaced or unequally spaced abscissas of an nth-order polynomial. This is a difference analogue of Taylor's formula.

In 1736, the final work, “The Method of Fluxions and Infinite Series,” was published posthumously, significantly advanced compared to “Analysis by Equations.” It provides numerous examples of finding extrema, tangents and normals, calculating radii and centers of curvature in Cartesian and polar coordinates, finding inflection points, etc. In the same work, quadratures and straightenings of various curves were performed.

It should be noted that Newton not only developed the analysis quite fully, but also made an attempt to strictly substantiate its principles. If Leibniz was inclined to the idea of ​​actual infinitesimals, then Newton proposed (in the Principia) a general theory of passage to limits, which he somewhat floridly called the “method of first and last relations.” The modern term “limit” (Latin limes) is used, although there is no clear description of the essence of this term, implying an intuitive understanding. The theory of limits is set out in 11 lemmas in Book I of the Elements; one lemma is also in book II. There is no arithmetic of limits, there is no proof of the uniqueness of the limit, and its connection with infinitesimals has not been revealed. However, Newton rightly points out the greater rigor of this approach compared to the “rough” method of indivisibles. Nevertheless, in Book II, by introducing “moments” (differentials), Newton again confuses the matter, in fact considering them as actual infinitesimals.

It is noteworthy that Newton was not at all interested in number theory. Apparently, physics was much closer to mathematics to him.

Mechanics

Newton's merit lies in the solution of two fundamental problems.

• Creation of an axiomatic basis for mechanics, which actually transferred this science to the category of strict mathematical theories.
• Creation of dynamics that connects the behavior of the body with the characteristics of external influences (forces) on it.

In addition, Newton finally buried the idea, rooted since ancient times, that the laws of motion of earthly and celestial bodies are completely different. In his model of the world, the entire Universe is subject to uniform laws that can be formulated mathematically.

Newton's axiomatics consisted of three laws, which he himself formulated as follows.

The first law (the law of inertia), in a less clear form, was published by Galileo. It should be noted that Galileo allowed free movement not only in a straight line, but also in a circle (apparently for astronomical reasons). Galileo also formulated the most important principle of relativity, which Newton did not include in his axiomatics, because for mechanical processes this principle is a direct consequence of the equations of dynamics (Corollary V in the Principia). In addition, Newton considered space and time to be absolute concepts, common to the entire Universe, and clearly indicated this in his Principia.

Newton also gave strict definitions of such physical concepts as momentum (not quite clearly used by Descartes) and force. He introduced into physics the concept of mass as a measure of inertia and, at the same time, gravitational properties. Previously, physicists used the concept of weight, but the weight of a body depends not only on the body itself, but also on its environment (for example, on the distance to the center of the Earth), so a new, invariant characteristic was needed.

Euler and Lagrange completed the mathematization of mechanics.

Universal gravity

The very idea of ​​the universal force of gravity was repeatedly expressed before Newton. Previously, Epicurus, Gassendi, Kepler, Borelli, Descartes, Roberval, Huygens and others thought about it. Kepler believed that gravity is inversely proportional to the distance to the Sun and extends only in the ecliptic plane; Descartes considered it the result of vortices in the ether. There were, however, guesses with a correct dependence on distance; Newton mentions Bulliald, Wren and Hooke in his Principia. But before Newton, no one was able to clearly and mathematically conclusively connect the law of gravity (a force inversely proportional to the square of the distance) and the laws of planetary motion (Kepler's laws). Only with the works of Newton does the science of dynamics begin, including as applied to the movement of celestial bodies.

• law of gravitation;
• law of motion (Newton's second law);
• system of methods for mathematical research (mathematical analysis).

Taken together, this triad is sufficient for a complete study of the most complex movements of celestial bodies, thereby creating the foundations of celestial mechanics. Before Einstein, no fundamental amendments to this model were needed, although the mathematical apparatus turned out to be necessary to significantly develop.

The first argument in favor of the Newtonian model was the rigorous derivation of Kepler's empirical laws on its basis. The next step was the theory of the movement of comets and the Moon, set out in the “Principles”. Later, with the help of Newtonian gravity, all observed movements of celestial bodies were explained with high accuracy; This is a great merit of Euler, Clairaut and Laplace, who developed perturbation theory for this. The foundation of this theory was laid by Newton, who analyzed the motion of the Moon using his usual method of series expansion; On this path, he discovered the causes of the then known irregularities (inequalities) in the movement of the Moon.

The law of gravity made it possible to solve not only problems of celestial mechanics, but also a number of physical and astrophysical problems. Newton indicated a method for determining the mass of the Sun and planets. He discovered the cause of tides: the attraction of the Moon (even Galileo considered tides to be a centrifugal effect). Moreover, having processed many years of data on the height of tides, he calculated the mass of the Moon with good accuracy. Another consequence of gravity was the precession of the earth's axis. Newton found out that due to the oblateness of the Earth at the poles, the earth's axis undergoes a constant slow displacement with a period of 26,000 years under the influence of the attraction of the Moon and the Sun. Thus, the ancient problem of “anticipation of the equinoxes” (first noted by Hipparchus) found a scientific explanation.

Newton's theory of gravitation caused many years of debate and criticism of the concept of long-range action adopted in it. However, the outstanding successes of celestial mechanics in the 18th century confirmed the opinion about the adequacy of the Newtonian model. The first observed deviations from Newton's theory in astronomy (a shift in the perihelion of Mercury) were discovered only 200 years later. These deviations were soon explained by the general theory of relativity (GR); Newton's theory turned out to be an approximate version of it. General relativity also filled the theory of gravitation with physical content, indicating the material carrier of the force of attraction - the metric of space-time, and made it possible to get rid of long-range action.

Optics and theory of light

Newton made fundamental discoveries in the ancient science of optics. He built the first mirror telescope (reflector), in which, unlike purely lens telescopes, there was no chromatic aberration. He also studied the dispersion of light in detail, showed that white light is decomposed into the colors of the rainbow due to the different refraction of rays of different colors when passing through a prism, and laid the foundations for a correct theory of colors. Newton created the mathematical theory of interference rings discovered by Hooke, which have since been called “Newton’s rings.” In a letter to Flamsteed, he outlined a detailed theory of astronomical refraction. But his main achievement was the creation of the foundations of physical (not only geometric) optics as a science and the development of its mathematical basis, the transformation of the theory of light from an unsystematic set of facts into a science with rich qualitative and quantitative content, experimentally well substantiated. Newton's optical experiments became a model of deep physical research for decades.

During this period there were many speculative theories of light and color; Basically, they fought between the points of view of Aristotle (“different colors are a mixture of light and darkness in different proportions”) and Descartes (“different colors are created when light particles rotate at different speeds”). Hooke, in his Micrographia (1665), proposed a variant of Aristotelian views. Many believed that color is an attribute not of light, but of an illuminated object. The general discord was aggravated by a cascade of discoveries in the 17th century: diffraction (1665, Grimaldi), interference (1665, Hooke), double refraction (1670, Erasmus Bartholin, studied by Huygens), estimation of the speed of light (1675, Roemer). There was no theory of light compatible with all these facts.

In his speech to the Royal Society, Newton refuted both Aristotle and Descartes, and convincingly proved that white light is not primary, but consists of colored components with different angles of refraction. These components are primary - Newton could not change their color with any tricks. Thus, the subjective sensation of color received a solid objective basis - the refractive index.

In 1689, Newton stopped publishing in the field of optics (although he continued research) - according to a widespread legend, he vowed not to publish anything in this field during Hooke's lifetime. In any case, in 1704, the year after Hooke’s death, the monograph “Optics” was published (in English). The preface to it contains a clear hint of a conflict with Hooke: “Not wanting to be drawn into disputes on various issues, I delayed this publication and would have delayed it further if not for the persistence of my friends.” During the author's lifetime, Optics, like Principia, went through three editions (1704, 1717, 1721) and many translations, including three in Latin.

• Book one: principles of geometric optics, the study of light dispersion and the composition of white color with various applications, including the theory of the rainbow.
• Book two: interference of light in thin plates.
• Book three: diffraction and polarization of light.

Historians distinguish two groups of then-current hypotheses about the nature of light.

• Emissive (corpuscular): light consists of small particles (corpuscles) emitted by a luminous body. This opinion was supported by the straightness of light propagation, on which geometric optics is based, but diffraction and interference did not fit well into this theory.
• Wave: light is a wave in the invisible world ether. Newton's opponents (Hooke, Huygens) are often called supporters of the wave theory, but it must be borne in mind that by wave they did not mean a periodic oscillation, as in modern theory, but a single impulse; for this reason, their explanations of light phenomena were hardly plausible and could not compete with Newton’s (Huygens even tried to refute diffraction). Developed wave optics appeared only at the beginning of the 19th century.

Newton is often considered a proponent of the corpuscular theory of light; in fact, as usual, he “did not invent hypotheses” and readily admitted that light could also be associated with waves in the ether. In a treatise presented to the Royal Society in 1675, he writes that light cannot be simply vibrations of the ether, since then it could, for example, travel through a curved pipe, as sound does. But, on the other hand, he suggests that the propagation of light excites vibrations in the ether, which gives rise to diffraction and other wave effects. Essentially, Newton, clearly aware of the advantages and disadvantages of both approaches, puts forward a compromise, particle-wave theory of light. In his works, Newton described in detail the mathematical model of light phenomena, leaving aside the question of the physical carrier of light: “My teaching about the refraction of light and colors consists solely in establishing certain properties of light without any hypotheses about its origin.” Wave optics, when it appeared, did not reject Newton's models, but absorbed them and expanded them on a new basis.

Despite his dislike of hypotheses, Newton included at the end of Optics a list of unsolved problems and possible answers to them. However, in these years he could already afford this - Newton’s authority after “Principia” became indisputable, and few people dared to bother him with objections. A number of hypotheses turned out to be prophetic. Specifically, Newton predicted:

• deflection of light in a gravitational field;
• the phenomenon of light polarization;
• interconversion of light and matter.

Other works in physics

Newton was the first to derive the speed of sound in a gas, based on the Boyle-Mariotte law. He discovered the law of viscous friction and hydrodynamic compression of the jet. In “Principles” he expressed and argued the correct assumption that a comet has a solid core, the evaporation of which under the influence of solar heat forms an extensive tail, always directed in the direction opposite to the Sun.

Newton predicted the oblateness of the Earth at the poles, estimating it to be approximately 1:230. At the same time, Newton used a homogeneous fluid model to describe the Earth, applied the law of universal gravitation and took into account centrifugal force. At the same time, similar calculations were performed by Huygens, who did not believe in long-range gravitational force and approached the problem purely kinematically. Accordingly, Huygens predicted a compression less than half that of Newton, 1:576. Moreover, Cassini and other Cartesians argued that the Earth is not compressed, but bulged at the poles like a lemon. Subsequently, although not immediately (the first measurements were inaccurate), direct measurements (Clerot, 1743) confirmed Newton’s correctness; actual compression is 1:298. The reason this value differs from that proposed by Newton in favor of Huygens’s is that the model of a homogeneous liquid is still not entirely accurate (density increases noticeably with depth). A more accurate theory, explicitly taking into account the dependence of density on depth, was developed only in the 19th century.

Students

Strictly speaking, Newton had no direct students. However, a whole generation of English scientists grew up reading his books and communicating with him, so they themselves considered themselves Newton’s students. Among them the most famous are:

• Edmund Halley
• Roger Cotes
• Colin Maclaurin
• Abraham de Moivre
• James Stirling
• Brooke Taylor

Other areas of activity

Chemistry and alchemy

In parallel with the research that laid the foundation of the current scientific (physical and mathematical) tradition, Newton (like many of his colleagues) devoted a lot of time to alchemy, as well as theology. Books on alchemy made up a tenth of his library. He did not publish any works on chemistry or alchemy, and the only known result of this long-term hobby was the serious poisoning of Newton in 1691. When Newton's body was exhumed, dangerous levels of mercury were found in his body.

Stukeley recalls that Newton wrote a treatise on chemistry, “explaining the principles of this mysterious art from experimental and mathematical proofs,” but the manuscript, unfortunately, was destroyed by fire, and Newton made no attempt to restore it. Surviving letters and notes suggest that Newton was pondering the possibility of some kind of unification of the laws of physics and chemistry into a single system of the world; He placed several hypotheses on this topic at the end of Optics.

B. G. Kuznetsov believes that Newton’s alchemical studies were attempts to reveal the atomic structure of matter and other types of matter (for example, light, heat, magnetism):

This assumption is confirmed by Newton’s own statement: “Alchemy does not deal with metals, as the ignorant believe. This philosophy is not one of those that serves vanity and deception; it rather serves benefit and edification, and the main thing here is the knowledge of God.”

Theology

Being a deeply religious man, Newton viewed the Bible (like everything in the world) from a rationalistic position. Newton's rejection of the Trinity of God is apparently connected with this approach. Most historians believe that Newton, who worked for many years at Trinity College, did not believe in the Trinity himself. Students of his theological works have found that Newton's religious views were close to heretical Arianism (see Newton's article "A Historical Tracing of Two Notable Corruptions of the Holy Scriptures").

The degree of closeness of Newton's views to various heresies condemned by the church is assessed differently. The German historian Fisenmayer suggested that Newton accepted the Trinity, but closer to the Eastern, Orthodox understanding of it. American historian Stephen Snobelen, citing a number of documentary evidence, decisively rejected this point of view and classified Newton as a Socinian.

Outwardly, however, Newton remained loyal to the state Anglican Church. There was a good reason for this: the 1698 legislation “The Act for the Suppression of Blasphemy and Profaneness” provided for the loss of civil rights for denying any of the persons of the Trinity, and if the crime was repeated - imprisonment . For example, Newton's friend William Whiston was stripped of his professorship and expelled from Cambridge University in 1710 for his claims that the creed of the early Church was Arian. However, in letters to like-minded people (Locke, Halley, etc.) Newton was quite frank. In addition to anti-trinitarianism, elements of deism are seen in Newton’s religious worldview. Newton believed in the material presence of God at every point in the Universe and called space the “sensorium of God” (lat. sensorium Dei).

Newton published (partially) the results of his theological research late in his life, but it began much earlier, no later than 1673. Newton proposed his own version of biblical chronology, left work on biblical hermeneutics, and wrote a commentary on the Apocalypse. He studied the Hebrew language, studied the Bible using scientific methods, using astronomical calculations related to solar eclipses, linguistic analysis, etc. to substantiate his point of view. According to his calculations, the end of the world will come no earlier than 2060.

Newton's theological manuscripts are now kept in Jerusalem, in the National Library.

Ratings

The inscription on Newton's grave reads:

The statue erected to Newton in 1755 at Trinity College bears the following verses from Lucretius:

Newton himself assessed his achievements more modestly:

Lagrange said: “Newton was the happiest of mortals, for there is only one Universe, and Newton discovered its laws.”

The Old Russian pronunciation of Newton's surname is "Nevton". He, along with Plato, is respectfully mentioned by M. V. Lomonosov in his poems:

According to A. Einstein, “Newton was the first who tried to formulate elementary laws that determine the time course of a wide class of processes in nature with a high degree of completeness and accuracy” and “... had with his works a deep and strong influence on the entire worldview as a whole.”

Named after Newton:

• SI unit of force;
• many scientific laws, theorems and concepts, see List of objects named after Isaac Newton;
• craters on the Moon and Mars.

• At the turn of 1942-1943, during the most dramatic days of the Battle of Stalingrad, Newton’s 300th anniversary was widely celebrated in the USSR. A collection of articles and a biographical book by S.I. Vavilov were published. As a token of gratitude to the Soviet people, the Royal Society of Great Britain presented the Academy of Sciences of the USSR with a rare copy of the first edition of Newton’s “Principles of Mathematics” (1687) and a draft of Newton’s letter to Alexander Menshikov, which informed the latter of his election as a member of the Royal Society of London.
• There is a common legend that Newton made two holes in his door - one larger, the other smaller, so that his two cats, large and small, could enter the house on their own. In fact, Newton never owned cats or other pets.
• Newton is sometimes credited with an interest in astrology. If there was one, it quickly gave way to disappointment.

Proceedings

• "A New Theory of Light and Colors", 1672 (communication to the Royal Society)
• “Motion of Bodies in Orbit” (lat. De Motu Corporum in Gyrum), 1684
• “Mathematical principles of natural philosophy” (lat. Philosophiae Naturalis Principia Mathematica), 1687
• “Optics or a treatise of the reflections, refractions, inflections and colors of light”, 1704
  • “On the quadrature of curves” (lat. Tractatus de quadratura curvarum), appendix to “Optics”
  • “Enumeration of lines of the third order” (lat. Enumeratio linearum tertii ordinis), appendix to “Optics”
• “Universal Arithmetic” (lat. Arithmetica Universalis), 1707
• “Analysis by means of equations with an infinite number of terms” (lat. De analysi per aequationes numero terminorum infinitas), 1711
• "Method of Differences", 1711

Published posthumously

• "Lectures on Optics" (eng. Optical Lectures), 1728
• “The System of the World” (Latin: De mundi systemate), 1728
• The Chronology of Ancient Kingdoms, 1728
• “Notes on the Book of the Prophet Daniel and the Apocalypse of St. John" (eng. Observations Upon the Prophecies of Daniel and the Apocalypse of St. John), 1733, written around 1690
• “Method of Fluxions” (Latin Methodus fluxionum, English Method of Fluxions), 1736, written in 1671
• An Historical Account of Two Notable Corruptions of Scripture, 1754, written 1690

Canonical editions

Classic complete edition of Newton's works in 5 volumes in the original language:

• Isaac Newtoni. Opera quae existant omnia. - Commentariis illustravit Samuel Horsley. - Londini, 1779-1785.

Selected correspondence in 7 volumes:

• Turnbull, H. W. (Ed.), The Correspondence of Sir Isaac Newton. - Cambridge: Cambr. Univ. Press, 1959-1977.

Translations into Russian

• Newton I. Notes on the book of the prophet Daniel and the Apocalypse of St. John. - Petrograd: New Time, 1915.
• Newton I. Corrected chronology of ancient kingdoms. - M.: RIMIS, 2007. - 656 p. - ISBN 5-9650-0034-0

Isaac Newton, the son of a small but prosperous farmer, was born in the village of Woolsthorpe (Lincolnshire), in the year of Galileo's death and on the eve of the Civil War. Newton's father did not live to see his son born. The boy was born sickly, prematurely, but still survived and lived for 84 years. Newton considered the fact of being born on Christmas a special sign of fate.

The boy's patron was his maternal uncle, William Ayscough. After graduating from school (1661), Newton entered Trinity College (College of the Holy Trinity) at the University of Cambridge. Even then, his powerful character took shape - scientific meticulousness, the desire to get to the bottom of things, intolerance to deception and oppression, indifference to public fame. As a child, Newton, according to contemporaries, was withdrawn and isolated, loved to read and make technical toys: a clock, a mill, etc.

Apparently, the scientific support and inspiration for Newton’s work were largely the physicists: Galileo, Descartes and Kepler. Newton completed their work by combining them into a universal system of the world. Other mathematicians and physicists had a lesser but significant influence: Euclid, Fermat, Huygens, Mercator, Wallis. Of course, the enormous influence of his immediate teacher Barrow cannot be underestimated.

It seems that Newton made a significant part of his mathematical discoveries while still a student, during the “plague years” of 1664-1666. At the age of 23, he was already fluent in the methods of differential and integral calculus, including series expansion of functions and what was later called the Newton-Leibniz formula. At the same time, according to him, he discovered the law of universal gravitation, or rather, he was convinced that this law follows from Kepler’s third law. In addition, during these years Newton proved that white color is a mixture of colors, derived the formula of “Newton’s binomial” for an arbitrary rational exponent (including negative ones), etc.

1667: The plague subsides and Newton returns to Cambridge. Elected a fellow of Trinity College, and in 1668 he became a master.

In 1669, Newton was elected professor of mathematics, Barrow's successor. Barrow sent to London Newton's "Analysis by Equations of Infinite Number of Terms", which contained a condensed summary of some of his most important discoveries in analysis. It gained some fame in England and abroad. Newton is preparing a complete version of this work, but is still unable to find a publisher. It was published only in 1711.

Experiments in optics and color theory continue. Newton studies spherical and chromatic aberration. To reduce them to a minimum, he builds a mixed reflecting telescope (lens and concave spherical mirror, which he polishes himself). He is seriously interested in alchemy and conducts a lot of chemical experiments.

1672: Demonstration of the reflector in London - universally rave reviews. Newton becomes famous and is elected a member of the Royal Society (British Academy of Sciences). Later, improved reflectors of this design became the main tools of astronomers, with their help other galaxies, red shifts, etc. were discovered.

A controversy breaks out over the nature of light with Hooke, Huygens and others. Newton makes a vow for the future: not to get involved in scientific disputes.

1680: Newton receives a letter from Hooke with the formulation of the law of universal gravitation, which, according to the former, served as the reason for his work on determining planetary motions (though then postponed for some time), which formed the subject of the Principia. Subsequently, Newton, for some reason, perhaps suspecting Hooke of illegally borrowing some earlier results of Newton himself, does not want to recognize any of Hooke’s merits here, but then agrees to do so, although rather reluctantly and not completely.

1684-1686: work on “Mathematical principles of natural philosophy” (the entire three-volume work was published in 1687). The Cartesians gained worldwide fame and fierce criticism: the law of universal gravitation introduces long-range action that is incompatible with the principles of Descartes.

1696: By royal decree, Newton was appointed Warden of the Mint (from 1699 - Director). He vigorously pursues monetary reform, restoring confidence in the British monetary system, which had been thoroughly neglected by his predecessors.

1699: the beginning of an open priority dispute with Leibniz, in which even the reigning persons were involved. This absurd quarrel between two geniuses cost science dearly - the English mathematical school soon withered for a whole century, and the European school ignored many of Newton’s outstanding ideas, rediscovering them much later. On the continent, Newton was accused of stealing the results of Hooke, Leibniz and the astronomer Flamsteed, as well as of heresy. Even the death of Leibniz (1716) did not extinguish the conflict.

1703: Newton is elected president of the Royal Society, which he rules for twenty years.

1705: Queen Anne knights Newton. From now on he is Sir Isaac Newton. For the first time in English history, the title of knight was awarded for scientific merit.

Newton devoted the last years of his life to writing the Chronology of Ancient Kingdoms, which he worked on for about 40 years, and preparing the third edition of the Elements.

In 1725, Newton's health began to deteriorate noticeably (stone disease), and he moved to Kensington near London, where he died at night, in his sleep, on March 20 (31), 1727.

The inscription on his grave reads:

Here lies Sir Isaac Newton, the nobleman who, with an almost divine mind, was the first to prove with the torch of mathematics the motion of the planets, the paths of comets, and the tides of the oceans.

He investigated the difference in light rays and the various properties of colors that appeared at the same time, which no one had previously suspected. A diligent, wise and faithful interpreter of nature, antiquity and Holy Scripture, he affirmed with his philosophy the greatness of Almighty God, and with his disposition he expressed evangelical simplicity.

Let mortals rejoice that such an adornment of the human race existed.

Named after Newton:

craters on the Moon and Mars;

SI unit of force.

The statue erected to Newton in 1755 at Trinity College bears the following verses from Lucretius:

Qui genus humanum ingenio superavit (He was superior to the human race in intelligence)

Scientific activity

A new era in physics and mathematics is associated with Newton's work. Powerful analytical methods appear in mathematics, and there is a breakthrough in the development of analysis and mathematical physics. In physics, the main method of studying nature is the construction of adequate mathematical models of natural processes and intensive research of these models with the systematic use of the full power of the new mathematical apparatus. Subsequent centuries have proven the exceptional fruitfulness of this approach.

According to A. Einstein, “Newton was the first who tried to formulate elementary laws that determine the time course of a wide class of processes in nature with a high degree of completeness and accuracy” and “... had with his works a deep and strong influence on the entire worldview as a whole.”

Mathematical analysis

Newton developed differential and integral calculus simultaneously with G. Leibniz (a little earlier) and independently of him.

Before Newton, operations with infinitesimals were not linked into a single theory and had the character of isolated ingenious techniques (see Method of indivisibles), at least there was no published systematic formulation and the power of analytical techniques for solving such complex problems as the problems of celestial mechanics in their entirety. The creation of mathematical analysis reduces the solution of relevant problems, to a large extent, to a technical level. A complex of concepts, operations and symbols appeared, which became the starting point for the further development of mathematics. The next century, the 18th century, was a century of rapid and extremely successful development of analytical methods.

Apparently, Newton came to the idea of ​​analysis through difference methods, which he studied extensively and deeply. True, in his “Principles” Newton almost did not use infinitesimals, adhering to ancient (geometric) methods of proof, but in other works he used them freely.

The starting point for differential and integral calculus were the works of Cavalieri and especially Fermat, who already knew how (for algebraic curves) to draw tangents, find extrema, inflection points and curvature of a curve, and calculate the area of ​​its segment. Among other predecessors, Newton himself named Wallis, Barrow and the Scottish astronomer James Gregory. There was no concept of a function yet; he interpreted all curves kinematically as trajectories of a moving point.

Already as a student, Newton realized that differentiation and integration are mutually inverse operations (apparently, the first published work containing this result in the form of a detailed analysis of the duality of the area problem and the tangent problem belongs to Newton's teacher Barrow).

For almost 30 years Newton did not bother to publish his version of the analysis, although in letters (in particular to Leibniz) he willingly shared much of what he had achieved. Meanwhile, Leibniz's version had been spreading widely and openly throughout Europe since 1676. Only in 1693 did the first presentation of Newton's version appear - in the form of an appendix to Wallis's Treatise on Algebra. We have to admit that Newton’s terminology and symbolism are rather clumsy in comparison with Leibniz’s: fluxion (derivative), fluenta (antiderivative), moment of magnitude (differential), etc. Only Newton’s notation “o” for an infinitesimal dt has been preserved in mathematics (however , this letter was used earlier by Gregory in the same sense), and even a dot above the letter as a symbol of the derivative with respect to time.

Newton published a fairly complete statement of the principles of analysis only in the work “On the Quadrature of Curves” (1704), an appendix to his monograph “Optics”. Almost all of the material presented was ready back in the 1670-1680s, but only now Gregory and Halley persuaded Newton to publish the work, which, 40 years late, became Newton’s first printed work on analysis. Here, Newton introduced derivatives of higher orders, found the values ​​of the integrals of various rational and irrational functions, and gave examples of solving 1st order differential equations.

1711: "Analysis by Equations with an Infinite Number of Terms" is finally published, after 40 years. Newton explores both algebraic and “mechanical” curves (cycloid, quadratrix) with equal ease. Partial derivatives appear, but for some reason there is no rule for differentiating a fraction and a complex function, although Newton knew them; however, Leibniz had already published them at that time.

In the same year, “The Method of Differences” was published, where Newton proposed an interpolation formula for drawing through (n + 1) given points with equally spaced or unequally spaced abscissas of a parabolic curve of the nth order. This is a difference analogue of Taylor's formula.

1736: The final work, “The Method of Fluxions and Infinite Series,” is published posthumously, significantly advanced compared to “Analysis by Equations.” Numerous examples are given of finding extrema, tangents and normals, calculating radii and centers of curvature in Cartesian and polar coordinates, finding inflection points, etc. In the same work, quadratures and straightenings of various curves were performed.

It should be noted that Newton not only developed the analysis quite fully, but also made an attempt to strictly substantiate its principles. If Leibniz was inclined to the idea of ​​actual infinitesimals, then Newton proposed (in the Principia) a general theory of passage to limits, which he somewhat floridly called the “method of first and last relations.” The modern term “limes” is used, although there is no clear description of the essence of this term, implying an intuitive understanding.

The theory of limits is set out in 11 lemmas in Book I of the Elements; one lemma is also in book II. There is no arithmetic of limits, there is no proof of the uniqueness of the limit, and its connection with infinitesimals has not been revealed. However, Newton rightly points out the greater rigor of this approach compared to the “rough” method of indivisibles.

Nevertheless, in Book II, by introducing moments (differentials), Newton again confuses the matter, in fact considering them as actual infinitesimals.

Other mathematical achievements

Newton made his first mathematical discoveries back in his student years: the classification of algebraic curves of the 3rd order (curves of the 2nd order were studied by Fermat) and the binomial expansion of an arbitrary (not necessarily integer) degree, from which Newton’s theory of infinite series began - a new and powerful tool of analysis . Newton considered series expansion to be the main and general method of analyzing functions, and in this matter he reached the heights of mastery. He used series to calculate tables, solve equations (including differential ones), and study the behavior of functions. Newton was able to obtain expansions for all the functions that were standard at that time.

In 1707, the book “Universal Arithmetic” was published. It presents a variety of numerical methods.

Newton always paid great attention to the approximate solution of equations. Newton's famous method made it possible to find the roots of equations with previously unimaginable speed and accuracy (published in Wallis' Algebra, 1685). Newton's iterative method was given its modern form by Joseph Raphson (1690).

It is noteworthy that Newton was not at all interested in number theory. Apparently, physics was much closer to mathematics to him.

Theory of gravity

The very idea of ​​the universal force of gravity was repeatedly expressed before Newton. Previously, Epicurus, Kepler, Descartes, Huygens, Hooke and others thought about it. Kepler believed that gravity is inversely proportional to the distance to the Sun and extends only in the ecliptic plane; Descartes considered it the result of vortices in the ether. There were, however, guesses with the correct formula (Bulliald, Wren, Hooke), and even quite seriously substantiated (using the correlation of Huygens' formula for centrifugal force and Kepler's third law for circular orbits). But before Newton, no one was able to clearly and mathematically conclusively connect the law of gravity (a force inversely proportional to the square of the distance) and the laws of planetary motion (Kepler's laws).

It is important to note that Newton did not simply publish a proposed formula for the law of universal gravitation, but actually proposed a complete mathematical model in the context of a well-developed, complete, explicit and systematic approach to mechanics:

law of gravitation;

law of motion (Newton's 2nd law);

system of methods for mathematical research (mathematical analysis).

Taken together, this triad is sufficient for a complete study of the most complex movements of celestial bodies, thereby creating the foundations of celestial mechanics. Before Einstein, no fundamental amendments to this model were needed, although the mathematical apparatus was very significantly developed.

Newton's theory of gravity caused many years of debate and criticism of the concept of long-range action.

The first argument in favor of the Newtonian model was the rigorous derivation of Kepler's empirical laws on its basis. The next step was the theory of the movement of comets and the Moon, set out in the “Principles”. Later, with the help of Newtonian gravity, all observed movements of celestial bodies were explained with high accuracy; This is a great merit of Clairaut and Laplace.

The first observable corrections to Newton's theory in astronomy (explained by general relativity) were discovered only more than 200 years later (shift of the perihelion of Mercury). However, they are also very small within the solar system.

Newton also discovered the cause of tides: the gravity of the Moon (even Galileo considered tides to be a centrifugal effect). Moreover, having processed many years of data on the height of tides, he calculated the mass of the Moon with good accuracy.

Another consequence of gravity was the precession of the earth's axis. Newton found out that due to the oblateness of the Earth at the poles, the earth's axis undergoes a constant slow displacement with a period of 26,000 years under the influence of the attraction of the Moon and the Sun. Thus, the ancient problem of “anticipation of the equinoxes” (first noted by Hipparchus) found a scientific explanation.

Optics and theory of light

Newton made fundamental discoveries in optics. He built the first mirror telescope (reflector), in which, unlike purely lens telescopes, there was no chromatic aberration. He also discovered the dispersion of light, showed that white light is decomposed into the colors of the rainbow due to the different refraction of rays of different colors when passing through a prism, and laid the foundations of the correct theory of colors.

During this period there were many speculative theories of light and color; Basically, they fought between the points of view of Aristotle (“different colors are a mixture of light and darkness in different proportions”) and Descartes (“different colors are created when light particles rotate at different speeds”). Hooke, in his Micrographia (1665), proposed a variant of Aristotelian views. Many believed that color is an attribute not of light, but of an illuminated object. The general discord was aggravated by a cascade of discoveries in the 17th century: diffraction (1665, Grimaldi), interference (1665, Hooke), double refraction (1670, Erasmus Bartholin, studied by Huygens), estimation of the speed of light (1675, Roemer), significant improvements in telescopes. There was no theory of light compatible with all these facts.

In his speech to the Royal Society, Newton refuted both Aristotle and Descartes, and convincingly proved that white light is not primary, but consists of colored components with different angles of refraction. These components are primary - Newton could not change their color with any tricks. Thus, the subjective sensation of color received a solid objective basis - the refractive index.

Newton created the mathematical theory of interference rings discovered by Hooke, which have since been called “Newton’s Rings.”

In 1689, Newton stopped research in the field of optics - according to a widespread legend, he vowed not to publish anything in this area during the life of Hooke, who constantly pestered Newton with criticism that was painful for the latter. In any case, in 1704, the next year after Hooke’s death, the monograph “Optics” was published. During the author’s lifetime, “Optics,” like “Principles,” went through three editions and many translations.

Book one of the monograph contained the principles of geometric optics, the doctrine of light dispersion and the composition of white color with various applications.

Book two: interference of light in thin plates.

Book three: diffraction and polarization of light. Newton explained polarization during birefringence closer to the truth than Huygens (a supporter of the wave nature of light), although the explanation of the phenomenon itself was unsuccessful, in the spirit of the emission theory of light.

Newton is often considered a proponent of the corpuscular theory of light; in fact, as usual, he “did not invent hypotheses” and readily admitted that light could also be associated with waves in the ether. In his monograph, Newton described in detail the mathematical model of light phenomena, leaving aside the question of the physical carrier of light.

Other works in physics

Newton was the first to derive the speed of sound in a gas, based on the Boyle-Mariotte law.

He predicted the oblateness of the Earth at the poles, approximately 1:230. At the same time, Newton used a homogeneous fluid model to describe the Earth, applied the law of universal gravitation and took into account centrifugal force. At the same time, Huygens performed similar calculations on similar grounds; he considered gravity as if its source was in the center of the planet, since, apparently, he did not believe in the universal nature of the force of gravity, that is, ultimately he did not take into account the gravity of the deformed surface layer of the planet. Accordingly, Huygens predicted a compression less than half that of Newton, 1:576. Moreover, Cassini and other Cartesians argued that the Earth is not compressed, but bulged at the poles like a lemon. Subsequently, although not immediately (the first measurements were inaccurate), direct measurements (Clerot, 1743) confirmed Newton’s correctness; actual compression is 1:298. The reason this value differs from that proposed by Newton in favor of Huygens’s is that the model of a homogeneous liquid is still not entirely accurate (density increases noticeably with depth). A more accurate theory, explicitly taking into account the dependence of density on depth, was developed only in the 19th century.

Other works

In parallel with the research that laid the foundation of the current scientific (physical and mathematical) tradition, Newton devoted a lot of time to alchemy, as well as theology. He did not publish any works on alchemy, and the only known result of this long-term hobby was the serious poisoning of Newton in 1691.

It is paradoxical that Newton, who worked for many years at the College of the Holy Trinity, apparently himself did not believe in the Trinity. Researchers of his theological works, such as L. More, believe that Newton's religious views were close to Arianism.

Newton proposed his own version of biblical chronology, leaving behind a significant number of manuscripts on these issues. In addition, he wrote a commentary on the Apocalypse. Newton's theological manuscripts are now kept in Jerusalem, in the National Library.

The Secret Works of Isaac Newton

As is known, shortly before the end of his life, Isaac refuted all the theories put forward by himself and burned the documents that contained the secret of their refutation: some had no doubt that everything was exactly like that, while others believe that such actions would be simply absurd and claim that the archive complete with documents, but only belongs to a select few...