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BIOGRAPHIES OF GREAT SCIENTISTS
Farm Pierre. Biography of a scientist
Directory / Biographies of great scientists
One of Pierre de Fermat's obituaries said: "He was one of the most remarkable minds of our century, such a universal genius and so versatile that if all scientists did not pay tribute to his extraordinary merits, it would be difficult to believe all the things that need to be said about him. to say so as not to miss anything in our eulogy." Unfortunately, not much is known about the life of the great scientist. Pierre de Fermat was born in the south of France in the small town of Beaumont-de-Lomagne, where his father, Dominique Fermat, was a "second consul", that is, something like an assistant to the mayor. The metric record of his baptism dated August 20, 1601 reads: "Pierre, son of Dominique Fermat, bourgeois and second consul of the city of Beaumont." Pierre's mother, Claire de Longe, came from a family of lawyers. Dominique Fermat gave his son a very solid education. In the college of his native city, Pierre acquired a good knowledge of languages: Latin, Greek, Spanish, Italian. Subsequently, he wrote poetry in Latin, French and Spanish "with such grace, as if he lived in the time of Augustus and spent most of his life at the court of France or Madrid." Fermat was famous as a fine connoisseur of antiquity, he was consulted about difficult places in the editions of the Greek classics. Of the ancient writers, he commented on Athenaeus, Polyunus, Sinezus, Theon of Smyrna and Frontinus, corrected the text of Sextus Empiricus. By all accounts, he could have made a name for himself in the field of Greek philology. But Fermat directed all the strength of his genius to mathematical research. Yet mathematics did not become his profession. Scientists of his time did not have the opportunity to devote themselves entirely to their beloved science. The farm elects jurisprudence. A bachelor's degree was awarded to him in Orleans. Since 1630, Fermat moved to Toulouse, where he received a position as an adviser in parliament (i.e., the court). About his legal activities, it is said in a "commendable word" that he performed it "with great conscientiousness and such skill that he was famous as one of the best lawyers of his time." In 1631, Fermat married his distant relative from the maternal side, Louise de Long. Pierre and Louise had five children, of whom the eldest, Samuel, became a poet and scientist. We owe to him the first collected works of Pierre Fermat, published in 1679. Unfortunately, Samuel Fermat did not leave any memories of his father. During Fermat's lifetime, his mathematical work became known mainly through the extensive correspondence he had with other scientists. The collected works, which he repeatedly tried to write, were never created by him. Yes, this is not surprising given the hard work in court that he had to perform. None of his writings were published during his lifetime. However, he gave several treatises a completely finished look, and they became known in manuscript to most of his contemporary scholars. In addition to these treatises, his extensive and extremely interesting correspondence remained. In the XNUMXth century, when there were no special scientific journals, correspondence between scientists played a special role. It set tasks, reported on methods for solving them, and discussed acute scientific issues. Fermat's correspondents were the greatest scientists of his time: Descartes, Etienne and Blaise Pascali, de Bessy, Huygens, Torricelli, Wallis. Letters were sent either directly to the correspondent, or to Paris to the Abbé Mersenne (a fellow student of Descartes in college); the latter multiplied them and sent them to those mathematicians who dealt with similar questions. But letters are almost never just short mathematical memoirs. The live feelings of the authors slip through them, which help to recreate their images, learn about their character and temperament. Usually Fermat's letters were imbued with friendliness. One of the first mathematical works of Fermat was the restoration of two lost books of Apollonius "On Flat Places". Fermat's great service to science is usually seen in his introduction of an infinitesimal quantity into analytic geometry, just as Kepler did a little earlier with regard to the geometry of the ancients. He took this important step in his works on the largest and smallest quantities dating back to 1629, works that opened up that series of studies by Fermat, which is one of the largest links in the history of the development of not only higher analysis in general, but also the analysis of infinitesimals in particular. At the end of the twenties, Fermat discovered methods for finding extremums and tangents, which, from a modern point of view, come down to finding a derivative. In 1636, the completed exposition of the method was handed over to Mersenne and everyone could get acquainted with him. In 1637-1638, Fermat had a heated controversy with Descartes about the "Method of Finding Highs and Lows". The latter did not understand the method and subjected it to harsh and unfair criticism. In one of his letters, Descartes even claimed that Fermat's method "contains a paralogism." In June 1638, Fermat sent Mersenne a new, more detailed exposition of his method to send to Descartes. His letter is restrained, but not without internal irony. He writes: “Thus, it turns out that either I explained poorly, or Mr. Descartes misunderstood my Latin work. I will nevertheless send him what I have already written, and he will undoubtedly find things there that will help him opinion that I discovered this method by chance and its true foundations are unknown to me. The farm never changes its calm tone. He feels his profound superiority as a mathematician, therefore he does not enter into petty polemics, but patiently tries to explain his method, as a teacher would do to a student. Before Fermat, the Italian scientist Cavalieri developed systematic methods for calculating areas. But already in 1642, Fermat discovered a method for calculating areas bounded by any "parabolas" and any "hyperbolas". He showed that the area of an unbounded figure can be finite. Fermat was one of the first to tackle the problem of straightening curves, that is, calculating the length of their arcs. He managed to reduce this problem to the calculation of some areas. Thus, Fermat's concept of "area" acquired a very abstract character. Problems of straightening curves were reduced to the determination of areas, he reduced the calculation of complex areas with the help of substitutions to the calculation of simpler areas. There was only a step left to pass from the area to the even more abstract concept of "integral". The further success of the methods for determining "areas", on the one hand, and the "methods of tangents and extrema", on the other, consisted in establishing the interconnection of these methods. There are indications that Fermat had already seen this connection, knew that "tasks on the area" and "tasks on tangents" are mutually inverse. But nowhere did he develop his discovery in any detail. Therefore, his honor is rightfully attributed to Barrow, Newton and Leibniz, to whom this discovery made it possible to create differential and integral calculus. Despite the lack of evidence (of which only one has survived), it is difficult to overestimate the importance of Fermat's work in the field of number theory. He alone managed to single out from the chaos of problems and particular questions that immediately arise before the researcher when studying the properties of integers, the main problems that became central to the entire classical theory of numbers. He also owns the discovery of a powerful general method for proving number-theoretic propositions - the so-called method of indefinite or infinite descent, which will be discussed below. Therefore, Fermat can rightfully be considered the founder of number theory. In a letter to de Bessy dated October 18, 1640, Fermat made the following statement: if the number In the problem of the second book of his Arithmetic, Diophantus set the task of representing a given square as a sum of two rational squares. In the margins, against this task, Fermat wrote: “On the contrary, it is impossible to decompose neither a cube into two cubes, nor a biquadrate into two biquadrates, and in general to any power greater than a square, into two powers with the same exponent. I have discovered a truly wonderful proof for this, but these fields are too narrow for him.” This is the famous Great Theorem. This theorem had an amazing fate. In the last century, her research has led to the construction of the most subtle and beautiful theories relating to the arithmetic of algebraic numbers. It can be said without exaggeration that it played no less a role in the development of number theory than the problem of solving equations in radicals. The only difference is that the latter has already been solved by Galois, and the Great Theorem still encourages mathematicians to research. On the other hand, the simplicity of the formulation of this theorem and the cryptic words about its "miraculous proof" led to the widespread popularity of the theorem among non-mathematicians and the formation of a whole corporation of "fermatists" who, in the words of Davenport, "have courage far beyond their mathematical abilities." Therefore, the Great Theorem is in first place in terms of the number of incorrect proofs given to it. Fermat himself left a proof of the Great Theorem for the fourth powers. Here he applied the "method of indefinite or infinite descent", which he described in his letter to Karkawi (August 1659) as follows: "If there were some right-angled triangle in integers, which would have an area equal to the square, then there would be another triangle, smaller than this, which would have the same property. If there were a second, smaller than the first, which would have the same property, then there would exist, by reasoning like this, a third less than the second, which would have the same property, and finally a fourth, fifth descending to infinity. whence it is concluded that there is no right-angled triangle with a square area." It was by this method that many propositions of number theory were proved, and, in particular, with its help, Euler proved the Great Theorem for In the last century, Kummer, while working on Fermat's Last Theorem, built arithmetic for algebraic integers of a certain kind. This allowed him to prove the Great Theorem for a certain class of prime exponents We also note that the Great Theorem is connected not only with algebraic number theory, but also with algebraic geometry, which is now being intensively developed. Fermat has many other accomplishments. He first came to the idea of coordinates and created analytical geometry. He also dealt with the problems of probability theory. But Fermat was not limited to mathematics alone, he also studied physics, where he owns the discovery of the law of propagation of light in media. Fermat proceeded from the assumption that light travels from any point in one medium to some point in another medium in the shortest possible time. Applying his method of maxima and minima, he found the path of light and established, in particular, the law of refraction of light. At the same time, Fermat expressed the following general principle: "Nature always acts in the shortest ways," which can be considered an anticipation of the Maupertuis-Euler principle of least action. One of the last letters of the scientist to Karkavy was called "Fermat's testament". Here are his final lines: “Perhaps posterity will be grateful to me for showing them that the ancients did not know everything, and this may penetrate the consciousness of those who come after me to pass the torch to their sons, as the great chancellor of England says, following whose feelings I I will add: "Many will come and go, but science is enriched." Pierre Fermat died on January 12, 1665 during one of his business trips. Author: Samin D.K.
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