Ferma is French.

Pierre de Fremat

Fermat's Last Theorem

Fermat's Last Theorem originated more than three hundred years ago and has challenged mankind for three centuries. It shocked the whole world, exhausted the energy of many of mankind's most outstanding brains, and fascinated thousands of amateurs. It was finally conquered by Andrew Wiles in 1994. Diophantus of ancient Greece wrote the famous "Arithmetic". After going through the darkness of the Middle Ages and the Renaissance, the fragments of "Arithmetic" were rediscovered and studied.

In 1637, the French amateur mathematician Pierre de Fremat wrote a conjecture on the margin of "Arithmetic" about the Pythagorean problem: a b=c is impossible ( Here n is greater than 2; a, b, c, n are all non-zero integers). This conjecture later became known as Fermat's last theorem. Fermat also wrote, "I have a wonderful proof of this, but the margins are too narrow to fit it." It is generally accepted that he could not have had the correct proof at the time. After the conjecture was proposed, through the efforts of generations of geniuses such as Euler, only four cases of n = 3, 4, 5, and 7 were solved in 200 years. In 1847, Kumul founded "algebraic number theory", an important modern discipline, and proved Fermat's last theorem for many n (for example, within 100), which was a big leap.

Fermat's last theorem has been one of the climaxes and legends in history. His amazing charm once saved a suicidal young man from death at the last moment. He was Wolfskler of Germany. He later set a reward of 100,000 marks (equivalent to more than 1.6 million US dollars today) for Fermat's last theorem, which lasted from 1908 to 2007. Countless people have exhausted their efforts, leaving nothing but sighs. The most modern computers and mathematical techniques have verified N within 4 million, but this does not help the final proof. In 1983, Faltings of Germany proved that: for any fixed n, there are at most a finite number of a, b, c, which vibrated the world, and won the Fields Medal (the highest award in mathematics).

A new turning point in history occurred in the summer of 1986, when Berkeley Rippert proved that Fermat's Last Theorem was included in the "Taniyama Yutaka-Shimura Goro Conjecture". Wiles, who had been obsessed with this topic since childhood, immediately devoted himself to it in his study on the top floor for 7 years after hearing this. With many twists and turns, he gathered all the breakthrough results of number theory in the 20th century. Finally, at the end of the "Lecture of the Century" at the Newton Institute of Cambridge University on June 23, 1993, it was announced that Fermat's last theorem had been proved. It immediately shocked the world and everyone celebrated. Unfortunately, a few months later it was gradually discovered that this proof had flaws, and it became the focus of the world. This proof system is a logical network composed of thousands of profound mathematical reasonings connected to thousands of the most modern theorems, facts and calculations. Problems in any link will cause all previous efforts to be wasted. Wiles fought in a desperate situation with no way out. On the morning of Monday, September 19, 1994, Wiles suddenly found the lost key in a flash of thinking: the answer turned out to be in the ruins! Tears welled up in his eyes. Wiles's historic long article "Modular Elliptic Curves and Fermat's Last Theorem" was published in the 142nd volume of the American "Annals of Mathematics" in May 1995. It actually occupies the entire volume, the last five chapters, and 130 pages. On June 27, 1997, Wiles won the Wolfskler 100,000 mark reward. 10 years before the deadline, the dream of history has been fulfilled. He also received the Wolf Prize (1996.3), the National Academy of Sciences Award (1996.6), and the Fields Special Medal (1998.8).