Fermat was born in the south of France. He studied law at university, later became a lawyer and was elected as a member of parliament. Fermat spent all his spare time reading books, reading everything about philosophy, literature, history and law. I fell in love with mathematics at the age of 30 until I died at the age of 64, and I made many important discoveries in my life. However, he rarely publishes papers and works in public, and mainly reveals his thoughts through correspondence with friends. Many of his achievements were sorted out by his son after his death by sorting out his notes and annotations. Fortunately, Fermat has a habit of "no pen and ink, no reading". Every book he has read has his circles and sketches, and there are his comments in the margin. He delved into mathematics in his spare time and achieved fruitful results. Later mathematicians benefited a lot from his many conjectures and bold creations, and praised him as "the king of amateur mathematicians". ?
Fermat's contributions to mathematics include: establishing analytic geometry with Descartes; He created the tangent curve method, which was regarded as the pioneer of calculus by Newton, one of the inventors of calculus. By putting forward valuable conjectures, the development direction of integer theory & number theory is pointed out. He also studied the winning and losing law of dice gambling, thus becoming one of the founders of classical probability theory.
One of the most famous is Fermat's Last Theorem, which was called Fermat's Last Theorem in China. The real name of "finally" in the field of western mathematics means that all other conjectures have been confirmed. Is this the last one? (Fermat's last theorem: n>2 is an integer, then the equation x n+y n = z n does not have an integer solution satisfying xyz≠0. This is an indefinite equation, which has been proved by the British mathematician wiles (1995), and the process of proof is quite difficult! )。 This conjecture first appeared in Fermat's marginal note. When Fermat read the Latin translation of Diophantine Arithmetic, he wrote next to the eighth proposition in Volume 1 1: "Divide a cubic number by the sum of two cubic numbers, or divide a quartic power by the sum of two quartic powers, or generally divide a power higher than quadratic by two. I believe I have found a good proof? Unfortunately, the space here is too small to write. " (Latin original:? "Trish? rei？ Demonstrations? Milla Bilm? Rational? Detsey. ? Hanc？ Maguiness? exiguitas？ No? Caperet。” After all, Fermat didn't write down the proof, and his other conjectures made great contributions to mathematics, which aroused many mathematicians' interest in this conjecture. The related work of mathematicians enriches the content of number theory and promotes its development. Although Fermat also showed that he had found a wonderful proof, and there was not enough space in the margin to write it down, it took mathematicians more than three centuries to turn a conjecture into a theorem. In order to get a positive or negative proof of it, generations of the best mathematicians have studied it several times in history, and even using modern electronic computers can only prove that Fermat's Last Theorem is correct when n is less than or equal to 465,438+0 million. In the process of impacting the century-long problem of number theory, whether it is incomplete proof or final complete proof, it will bring great influence to the mathematical community; Many mathematical achievements and even branches of mathematics were born in this process, including elliptic curves and modular forms in algebraic geometry, Galois theory and Heck algebra. This also makes people wonder whether Fermat really found the correct proof at the beginning. Andrew wiles won the Shaw Prize in 2005 for successfully proving this theorem.
An amateur mathematician, who usually reads and writes a sentence, has been studied by later professional mathematicians for more than three centuries! Many people doubt whether the proof method he originally thought of really exists. The following picture shows that Google changed the logo of Fermat's Last Theorem on August 1 17, 2065438 to commemorate the 4th10 anniversary of Fermat's birth: