Chapter 161: Wiles's Regret
Deligne first went through the paper from beginning to end, and then, he raised his head and said to Morse Eddie: "Eddie, you go out first, I'll read it slowly!" ”
"Oh, good!"
Eddie paused for a moment, turned out of Drenne's office, and quietly closed the door.
Deligne calmed down and began to reopen the paper, starting from the first page.
Soon, Deligne's brow furrowed.
In 1637, the French mathematician Fermat proposed Fermat's conjecture, that is, when the integer n>2, there is no positive integer solution for the equation x^n+y^n=z^n.
Since then, the Fermat conjecture has become one of the highest peaks in the minds of mathematicians around the world.
From the 17th century, Fermat gave the proof of the theorem of n=4 in his notes, to 1985, when the American mathematician Rosser used a mainframe computer to prove that the Fermat conjecture was true when n<41000000.
The international mathematical community has been spinning around how to generalize n to infinity.
It was not until 1986 that the German mathematician Gerhard Frey proposed that if the Taniyama-Shimura conjecture was proved, the Fermat conjecture would be indirectly proved.
Mathematicians realized that the Fermat conjecture could be translated into elliptic curve equations for study.
For the past seven years, Deligne's colleague Andrew Wiles, including Deligne's colleague, has been trying to prove the Fermat conjecture from the Taniyama-Shimura conjecture.
Deligne even vaguely heard Wiles mention that the other party has made a lot of progress on this road.
But this paper is completely different.
The authors of this paper propose a new theoretical framework to solve the Fermat conjecture.
Within this theoretical framework, Deligne even faintly saw the shadow of the far-abelian geometry proposed by his mentor Grothendieck.
However, this theory is not as abstract and complex as far abelian geometry, and its logical system is very concise and powerful.
"Interesting!"
Deligne muttered to himself and continued reading.
Minutes and seconds passed.
One hour ......
Two-hour ......
Three-hour ......
……
I don't know how long it was, but by the time Deligne had finished reading all the thirty-odd pages of the paper, it was already past two o'clock in the afternoon.
But Deligne didn't feel much tired, on the contrary, the high-intensity thinking still kept his brain nerves in a state of high excitement.
It's a feeling I haven't felt in a long time.
In this paper, Deligne seems to touch the boundaries of mathematical knowledge.
The feeling of being immersed in truth was something that Deligne had experienced when he proved Wey's conjecture.
The simplicity of the paper and the cold logic of the ice are something that Deligne has never seen before.
In particular, the new theoretical framework proposed in the paper made him faintly see the shadow of new mathematics.
This is a true masterpiece!
"I really didn't expect that after three hundred and fifty years, Fermat's conjecture was solved by a mathematician from China!"
Deligne muttered to himself.
At present, the most well-known Chinese mathematician in the international mathematical community is undoubtedly Chen Jingrun, whose paper "The Table of Large Even Numbers is the Sum of the Products of a Prime Number and a No More Than Two Prime Numbers" published in 1973 is the glorious peak of the theory of the large sieve method.
But Pang Xuelin's proof of Fermat's conjecture is much more important than Chen Jingrun's results.
Even throughout the twentieth century, the proof of Fermat's conjecture was one of the most important achievements in mathematics.
Drinje groaned for a moment with his chin down, then picked up the phone on his desk and dialed it.
Soon, the phone was picked up.
Deligne said, "Wiles, are you at home?" ”
"Yes, what's wrong?"
"Old man, prepare something for me to eat, I'll go look for you now, besides, there is something I will inform you in advance, Fermat guesses, it may be proven!"
"What?!"
On the other end of the phone, Wiles' voice was disfigured.
Deligne shook his head, understandably at Wyles' gaffe.
Over the years, Andrew Wiles has been working on the Fermat conjecture.
Although it has not succeeded so far, it is nearing the end of the road.
At this time, someone suddenly claimed to have proved Fermat's conjecture, which undoubtedly meant that Wiles's research over the past seven years had been completely wasted.
But in academia, this is not uncommon.
Mathematics is relatively better, and the competition between different research groups in other subject areas is much more intense.
……
Twenty minutes later, Deligne showed up at Andrew Wiles' home on time.
"Pierre, what the hell is going on, who proved Fermat's conjecture?"
As soon as they met, Wiles couldn't wait.
Deligne handed the paper to Wiles and said, "You read the paper first, do you have anything to eat at home?" ”
"There's pizza, Amy is making it in the kitchen!"
"Okay, then I'll eat first, you can see first!"
Twenty minutes later, a well-fed and well-fed Deligne walked into Andrew Wiles' attic.
Wiles was quickly flipping through Pang Xuelin's paper.
Deligne was not in a hurry, and waited patiently on the sidelines.
It wasn't until five o'clock in the afternoon that Wiles closed the paper, raised his head, as if with some regret, and as if relieved: "Pierre, I lost!" But to see such a wonderful paper can be regarded as convincing! ”
In fact, after seven years of research, Wiles had a vague sense that he had touched the edge of proving Fermat's conjecture.
But Pang Xuelin's paper gave him a blow in the face.
Compared to his method of proof, the paper is incredibly succinct.
However, its logical system is extremely rigorous.
In particular, the new framework that is vaguely reflected in this paper makes Wiles himself impressed.
"By the way, who is the author of this paper?"
Wilesdau.
Deligne shook his head and said: "I don't know either, my name is Xuelin Pang, a strange Chinese mathematician, but I think it won't be long before the name of this Chinese mathematician will resound throughout the world." ”
Wiles nodded and said, "Are you sure about the reviewer of this paper now?" ”
Deligne said: "You count one, I count one, in addition, I plan to find Peter Sanek, Nick Kates and John Coates and Richard Taylor of Cambridge as reviewers, if you think it's okay, go directly to the Annals of Mathematics next month......"
Wiles nodded, "Yes." ”
Needless to say, Peter Sanek is also a top mathematician from Princeton, and Nick Kates, John Coates, and Richard Taylor are also well-known figures in the field of number theory.
If you can get the approval of these people, there will be basically no problem with this paper.
Deligne said: "In addition, I am also going to send an invitation letter to invite Pang to come to Princeton to give a report, after all, such an important achievement, a single paper is definitely not enough, and the new theoretical framework used in this paper, I feel that there is still a lot to explore." ”