Fermat never sent this challenge by letter and after his death his son Clément-Samuel found it and published it. Translated into mathematical formulas, that means that it is impossible to find a solution to any equation of the type x n + y n = z n(if we only use positive integers and n is also greater than 2). An example of Fermat’s provocative style is the famous annotation that Fermat wrote in 1637 in the margin of his copy of Diophantus’ Arithmetica: “I have discovered a truly marvellous proof of this proposition which this margin is too narrow to contain.” That sentence accompanied another handwritten statement by Fermat: “It is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second, into two like powers.” In an episode of ‘The Simpsons’ Homer appears to find a counterexample to Fermat’s Last Theorem, but the trick only works if tested on a regular hand held calculator. However, this French mathematical genius had the habit of not revealing his calculations or the proofs of his theorems, which frustrated his adversaries: Descartes came to call him a “braggart”, and the Englishman John Wallis referred to him as “that damn Frenchman”. He used mathematical logic to prove that no other number between zero and infinity meets that condition (x 2 + 1 = z = y 3 – 1), and he challenged his friends and rivals to prove it too. This is pure mathematics-a game of wits: for example, Fermat showed that 26 is the only number “trapped” between a square (5 2 = 25) and a cube (3 3 = 27). Pure mathematics, a game of witsīut the greatest contributions of Pierre de Fermat to mathematics were in another branch- number theory-which studies whole numbers, the relations between them and the patterns that follow. Pascal challenged Fermat to solve the problem and together they succeeded, thereby laying the foundation of probability theory.
#FERMAT INFINITESIMALS PROFESSIONAL#
Later, in 1654, a writer and professional gambler asked the mathematician Blaise Pascal for help in fairly distributing the money wagered on an interrupted game of dice, based on the scores obtained until then. The result of his quarrels through the post with the philosopher René Descartes inspired Newton and Leibniz to develop infinitesimal calculus. Stamp with the image of the mathematician Pierre de Fermat and his Last Theorem’s formulation. In this way, Fermat found mathematical problems with which he challenged by letter other intellectuals such as Descartes and Pascal. He studied the treatises of the scholars of classical Greece and combined those old ideas with the new methods of algebra by François Viète (1540-1603). In the afternoons, Fermat would put the law to one side and dedicate himself to deepening his mathematical investigations. The son of a wealthy leather merchant, Pierre de Fermat ( between 31 October and 6 December 1607 – 12 January 1665) studied civil law at the University of Orleans and progressed in his judicial career path until reaching a comfortable position in the Parliament of Toulouse, which allowed him to spend his spare time on his great love: mathematics. At the heart of that intense postal exchange was Pierre de Fermat, an enthusiast who became one of the most greatest mathematicians of all time, known both for his discoveries and for a final problem that he left unsolved and that for three centuries confounded everyone who tried to solve it-until a boy read the history of Fermat’s Last Theorem and dreamed of finding the solution. And from those letters and challenges were born new disciplines of that science, like the theory of probabilities or infinitesimal calculus. It was in France, at the beginning of the 17th century, when the habit of challenging oneself to solve problems and numerical puzzles spread among the intellectual elite. There was a time when mathematics flourished thanks to some passionate relationships by letter.
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