There is a fairy in the myth. She has a magical cornucopia, which can be turned into gold when filled with stones. There is a fairy in the fairy tale. She has a magical finger that can turn stone into gold. ..... These are, of course, imaginary stories made up by people.

However, in the kingdom of mathematics, there really is a magical hen that can lay golden eggs. ...

That was France more than 300 years ago.

At that time, there was a lawyer named Pierre in Paris? Fermat is a math lover. He spent all his spare time studying mathematics and made pioneering contributions in many fields of mathematics, and was called "the king of amateur mathematicians".

Fermat is quiet and doesn't like writing books and publishing papers, but he likes to write questions and notes in the margins of the pages at any time when studying other people's works.

1637, Fermat bought the Latin translation of arithmetic written by the ancient Greek mathematician Dipandu in Paris. He wrote a passage in the margin next to "Divide a square number into two squares" in Volume 2 of this book: "It is impossible to divide a cubic number into two cubic numbers, to divide a quartic power into two quartic powers, and to generally divide a power higher than quadratic into two powers of the same power. Regarding this conclusion, I am sure that I have found a wonderful proof method, but unfortunately the blank here is too small to write down. "

Of course, this passage was discovered when people looked up the books edited and arranged by Fermat after his death.

However, no one has seen this "wonderful proof". Fermat's son sorted out all his manuscripts and letters, but he couldn't find a "wonderful proof".

The conclusion that later generations wrote Fermat in the margin is called Fermat conjecture or Fermat problem, but it is more popular to say Fermat's last theorem. Expressing Fermat's last theorem in mathematical terms is: "When n is an integer greater than 2, the equation Xn+Yn = Zn has no non-zero integer solution."

The proof of Fermat's last theorem has aroused the interest of many mathematicians. Gauss ("Prince of Mathematics") and Euler (1the best mathematician in the 8th century) both made great efforts to prove it, but neither of them solved it. People exclaimed: it is really difficult to prove Fermat's last theorem! It's a challenge to human intelligence!

In order to encourage people to solve this problem, many national academies of science have set up various bonuses. At the end of 17, scientists and citizens in a German city raised 100000 goldmark, intending to reward those who solved this problem, but no results were achieved. /kloc-in the 0/9th century, the French Academy of Sciences set up a prize of 3,000 francs twice, but nothing came of it. 1908, the Academy of Sciences in G? ttingen, Germany, set up a prize of 65,438+one million marks, with a term of 100, and collected the proof of Fermat's Last Theorem from all over the world. Up to now, we haven't seen a complete proof!

For more than 300 years, generations of mathematicians have been constantly creating new mathematical methods to show human wisdom and reveal the mathematical truth behind difficult problems, and inadvertently created and developed new branches of mathematics, which promoted the development of the whole mathematics. This meaning goes far beyond the solution of this difficult problem itself.

1900 On August 6th, the 2nd International Congress of Mathematicians opened in Paris. On August 9th, Hilbert, a great German mathematician, put forward 23 questions to more than 200 mathematicians attending the meeting and also to the international mathematical community. Of course, these problems are very, very difficult and should be solved by mathematicians in the new century. People curiously ask Hilbert why there is no Fermat's Last Theorem in these 23 questions. Hilbert said meaningfully, "If I can solve this problem, I will avoid it and deliberately not solve it, because we should be more careful not to kill this hen who often lays golden eggs for us."

Hilbert compared Fermat's Last Theorem to "a hen that often lays golden eggs for us", indicating that the pursuit of solving a difficult problem often leads people to break into new fields. For example, German mathematician Kumar (18 10 ~ 1893) created an important mathematical concept-ideal number in the process of studying Fermat's last theorem, and at the same time created a brand-new branch of mathematics-algebraic number theory (1884). In modern mathematics, algebraic number theory

"Time flies, the sun and the moon fly." In the 1990s, the work of proving Fermat's Last Theorem made continuous progress. Too late, too early. The historical pointer points to A.D. 1993, and it is only 108 years before the German Academy of Sciences offered a reward 1908 to prove Fermat's Last Theorem. At this time, in the process of marching towards Fermat's Last Theorem, the news that shocked the world came out:1On June 23rd, 993, at a small mathematical academic conference held in Cambridge University, England, Dr. AWiles, who was in his forties, announced at the end of his academic report for three consecutive days that he had proved Fermat's Last Theorem! Within a few hours, the news that Fermat's Last Theorem was proved spread all over the world and shocked the international academic circles.

Wells was born in Oxford, England. After hearing the story of "A hen lays golden eggs" as a child, he was fascinated by Fermat's last theorem and determined to conquer the peak of this unparalleled mathematical kingdom. It was this wonderful theorem that led him to the palace of mathematics, and he chose "mathematics" as his career. The childhood dream, though with a gorgeous aura, is a dazzling light for Dr. Wells, who has become a mathematician. He drew up a feasible research scheme to realize his childhood dream of proving Fermat's Last Theorem. However, all these studies are conducted in a highly confidential situation. Even at the academic conference where he announced the proof of Fermat's last theorem, people didn't realize the ultimate goal of his report at first.

After the publication of Wells' work, it was quickly welcomed by some of the most famous mathematicians in the world. Most people think that Wells is a serious mathematician, and his proof foundation is reliable.

People eagerly look forward to the last moment when Fermat's Last Theorem is proved!

However, on February 4th, 1993, 1993, Professor Wells announced that there was a "loophole" in his proof of Fermat's Last Theorem in June. So Fermat's last theorem is still being proved! (See chinese mathematical society Newsletter No.2 1994) Readers, what do you think after reading this story?

Let's listen to the words of Hilbert, a master of mathematics: "Just like every career of human beings pursues a certain goal, mathematical research also needs its own problems." It is through the solution of these problems that researchers exercise iron-like will and strength, develop new methods and new ideas, and reach a broader and more free realm. "

We know the history and significance of some mathematical problems, which can improve our understanding of mathematics, motivate ourselves to study as tenaciously as our predecessors and make contributions to the cause of human progress.