At the beginning of the 20th century, the great mathematician Hilbert was asked why he did not try to prove Fermat's theorem, and he replied: "I must spend three years doing in-depth research before I can start working on it, and I don't have so much time to waste on something that might fail." ”

Wiles knew that in order to find a way to prove Fermat's theorem, he would have to devote himself to the problem, but unlike Hilbert, he was willing to take that risk.

Wiles made a heavy decision: to conduct research in complete independence and confidentiality.

"I realized that anything related to Fermat's theorem would be of interest to too many people," he said. You really can't concentrate yourself for many years unless your concentration is not distracted by others, and this will not be possible because there are too many bystanders. ”

Wiles gave up all work that had nothing directly related to proving Fermat's theorem, and whenever he could, he returned to work at home, and in his study on the top floor of the house he began the battle to prove Fermat's theorem through the Guò Taniyama-Shimura conjecture.

It was a protracted battle that lasted for seven years, during which only his wife knew that he was proving Fermat's theorem.

Speaking of Wiles. This life was in Cambridge, but when I was admitted to university, I was 2B, I was not admitted to Cambridge, I went to King's College, which is not far from home, and after graduation, I also went to Oxford University to study for a doctorate in mathematics, but I graduated at the age of 27.

As a mathematics practitioner, everyone knows that he only graduated with a doctorate at the age of 27, which is basically synonymous with "this person's IQ is also ordinary".

The Fields Medal, the highest award in mathematics, is only given to people under the age of 4o, and you don't graduate until you're 27. There's still a few years left to mix up in this business. Just as my mother always compares the neighbor's children, look at the god of Teren Sutao, who graduated with a doctorate at the age of 2o. At the age of 24, he is a tenured professor, and this is the only way to have a master.

Another example is Tao Zhexuan, who entered high school at the age of 7, entered university at the age of 9, participated in the International Mathematical Olympiad at the age of 1o, 11, and 12 and won the bronze, silver, and gold medals respectively, obtained a doctorate at the age of 2o, and became a professor at the age of 24. I'm afraid it's only a matter of a few years to win the Fields Medal.

And what is the 31-year-old Wiles doing, obscure. At the age of 33, Wiles finally decided he wanted to do something. Fate also happened to give him a chance. In 1985, the German mathematician Frey pointed out the relationship between the Taniyama-Shimura conjecture and Fermat's theorem, and in 1986, the American mathematician Libert proved this proposition.

Wiles realized his opportunity had come. Fermat's theorem went around in a big circle. It is related to the elliptic curve, which I am best at now, and I have to gamble. So, Wiles began a seven-year retreat and practice, of course, he had to let off his breath occasionally when he was practicing, because he was not good enough before, the professor's position was not secure, and he would be laid off if he didn't show his thesis.

After a bumpy few years after graduating, Wiles finally landed a teaching position at Princeton. Officially entered the ranks of pseudo-bosses. Everyone knows that the first seven years of mixed teaching in the United States are the most difficult. Because there are hard requirements for articles every year, if you don't come out, you will be laid off. After seven years, he is a tenured professor.

As soon as Wiles went to Princeton, he also played with his life and wrote articles day and night. But he did something earth-shattering, and he deducted a few well-written articles every year. What is this doing, waiting to be robbed by others? Of course not, as an uncle of sling, he is planning a grand counterattack plan.

This is his strategy of arguing in doubt, and he has done a little trick to divide many of his research achievements in the elliptic curve into small results one by one, 66 The continuation of the table, what does it mean?

In fact, in fact, he hid in a small building and stayed out of the garden for several years, specializing in the study of Fermat's theorem. Of course, this process is extremely difficult. When he was making his own plans, he once thought that I would spend at least three years reviewing all the existing research results in the field of elliptic curves and modeling, and of course the subsequent progress was better than he expected, but it also took 18 months, which was to review the original problem sea tactics, and I couldn't talk about solving the problem.

Later, when he looked back on this period of research, Wiles made an analogy, he said that the solution to Fermat's great theorem is to walk through one dark room after another, first I came to a dark room, and I couldn't see anything, I had to touch it, touch all the furniture in this room, all the furnishings, and when I was familiar with it, and I knew every texture of this room, I could find its light switch, I turned on the light switch, I knew where the door of the next room was, opened the door, and then entered the next room, and then started the process again, and I didn't know when it was a head。

So it took him seven years in this painful time.

On June 23, 1993, the Newton Institute held one of the most important lectures on mathematics of the 2o century. Two hundred mathematicians listened to the lecture, but only a quarter of them understood exactly what the Greek letters and algebraic expressions on the blackboard meant.

The rest of the people come here to witness a truly meaningful moment that they are looking forward to. The speaker was Andrew Wiles. Wiles decided to use the opportunity to announce his work to an outstanding audience. Another major reason he chose to announce at the Newton Institute was that Cambridge was his hometown, where he had been a graduate student.

Wiles later recalled: "Although there was a rumor about the speech in the press, it was fortunate that they did not come to hear it. But someone in the audience took a shot at the end of the presentation, and the director of the institute must have prepared a bottle of champagne beforehand. There was a particularly solemn silence in the room as I read the proof, and when I finished writing the proof of Fermat's theorem, I said, 'I think I'll end up here,' and there was a long round of applause. ”

The New York Times ran a front-page headline titled "Finally cheering, 'I'm here!'" , the long-ago mathematical riddle solved" reported the news that Fermat's theorem had been proved. Overnight, Wiles became the most famous mathematician in the world, and the only one. People magazine named Wiles, along with Princess Diana, among the "25 most charismatic people of the year." The most creative compliment came from a major international garment company, who invited the suave genius to model for their new menswear collection.

However, mathematicians are very rigorous in their approach to proofs, and once a mathematical proof is passed, it is always correct, and they must be accountable to future generations, so Wiles's paper needs to be rigorously reviewed. So a committee of experts was organized, and six top mathematicians began to work on Wiles's book-like paper for a long time, and this verification lasted for eight months, and the six mathematicians repeatedly asked questions around him, and he came to give answers, and the little details in the calculation process, everyone went to torture to ask questions.

At the age of eight months, something finally happened, there was a very, very small mistake, the director zhì his round of dominoes suddenly couldn't be pushed down, Wiles didn't take it seriously at first, I thought it was a small mistake, I corrected it a little, and it was over, but I never expected that this mistake was getting bigger and bigger, and the more I looked at it, the bigger it was, in fact, Wiles was about to collapse at this time.

A guy named Nick Katz has a loophole. Coincidentally, in front of Wiles's paper, I wanted to find someone to test it in, and it was Nick Katz, at that time, this guy didn't have a problem, this guy was public, but he found out the problem, which made Wiles embarrassed: Are you kidding me? In fact, this is a big problem, enough to destroy Wiles's proof.

At this point, Wiles's counterattack was frustrated, and if the loophole could not be fixed, no one would regret that there would be one more loser on the road to proving Fermat's theorem. Fortunately, Wiles has become a tenured professor at this time, so he doesn't have to worry about the risk of being laid off, just stay at home and study hard.

However, mathematicians are very face-loving, how shameful it is, a person with such a high posture to claim that he has solved Fermat's theorem, and the layman has begun to give him all kinds of honors, although the public does not know what he is studying, they know that this is a great mathematician, and at this time he suddenly loses face, maybe all his results are wrong, this is a huge pressure, enough for a mathematician to quit the mathematical world, or even commit suicide.

Beginning on August 23, 1993, Wiles began to remedy this small loophole, thinking that it was a small problem and that the remedy might be nearby, but more than 6 months have passed, the mistake has not been corrected, Wiles is facing a desperate situation, and he is ready to admit defeat.

He explains his situation to his colleague Zack, who hints to him that part of the difficulty is that he lacks someone he can discuss with and can trust. After much consideration, Wiles decided to invite Taylor, a lecturer at Cambridge University and his former student, to work with him at Princeton.

Taylor went to Princeton in January 1994, but by September, there was still no result, and they were ready to give up. Taylor encouraged them to hold on for another month. Wiles decided to have a final check-up at the end of September.

On September 19, 1994, a Monday morning, Wiles presented the answer to his question, recounting the moment: "All of a sudden, unbelievably I had an incredible present. It was the most important moment of my career, and I will never experience it again, the beauty is so indescribable, and it is so simple and beautiful. For more than 2o minutes I couldn't believe it. Then during the day I walked around the department and went back to the table to see if it was still there - it was still there. ”

After Kong Jidao finished this paragraph in one breath, he sighed deeply, as if this was what he had experienced, or what he was experiencing, he knew too well the feeling of finally grasping the truth through layers of fog.

Liu Meng is also excited, that is the truth, just like the cultivator in the fantasy novel who preaches the Tao and succeeds in converging, the truth will remain forever. (To be continued!)

PS: That's the truth, and it's worth a lifetime of pursuit.

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