Chapter 227 Two Choices

As a firm and clear-hearted materialist warrior, Lu Zhou certainly does not believe in ghosts and gods.

After his eyes got used to the light in the corridor for a while, he asked in an uncertain tone relying on the only impression he had.

"Molina?"

Hearing Lu Zhou read her name, the French lady smiled a little: "I knew you would come here...why didn't you call me? I can drive to Philadelphia to pick you up."

Here's the problem again...

"I've already asked my brother... Where is No. 211?" Lu Zhou coughed dryly and quickly changed the subject.

"Go upstairs and turn left at the end of the corridor." Molina raised her index finger slightly, but Molina didn't bother with the phone, and said in a chatty tone, "By the way, speaking of it, have you chosen a mentor yet?"

Lu Zhou: "What's wrong?"

"What I mean is, if you don't choose well, I recommend my tutor Sophie Morell to you," Molina said, looking at Lu Zhou seriously, "My previous invitation is still valid, and our subject needs to you."

Sophie Morel?

Lu Zhou looked at her in surprise.

Molina raised her eyebrows and asked with a smile, "Are you surprised?"

"I'm really surprised..." Lu Zhou nodded.

One of the popular candidates for the Fields Award, a French female mathematician with both good looks and knowledge.

But what surprised him was not Sophie's name, but Princeton's ability to poach people.

Sure enough, it is the Yankee who "does whatever he wants" relying on the alumni association. It seems that the name of the Paris Mathematical Center was not stolen, it was simply bought...

Thinking of this, Lu Zhou suddenly understood the reason why Princeton and Jinling University, a small transparency in the mathematics world, reached an "unequal agreement", and his expression was a little subtle.

After a long time, it turned out that he was betting on the Fields Medal...

Folding her arms, Molina's mouth curled into a smile: "Then what is your choice?"

"Thank you for your invitation, but let me decline."

Passing by the stunned Molina, Lu Zhou dragged his suitcase and walked towards the room at the end of the corridor.

joke.

As a popular candidate with a 99% probability of winning, there is something wrong with finding a competitor with an 80% probability of winning as a mentor!

...

Lu Zhou originally planned to listen to a few classes and inquire more before choosing his own tutor. As a result, he far underestimated how "attractive" a 21-year-old Cole Prize winner and popular candidate for the Philippine Prize is to Princeton professors.

I don’t know where the invitations to the coffee meeting and the invitations to academic exchanges are nothing. When eating at eating clubs (eating-clubs), a certain young female teaching assistant took the initiative to strike up a conversation with him, and within ten In a few words, he talked about the issue of the mentor, and kept hinting that his own mentor was a good choice.

What was even more exaggerated was Senior Brother Luo, who obviously recommended so many people to him at the beginning, but changed his previous tone at dinner the next day and began to slam Professor Edward Witten. Later, they might have blown too much, and a Mexican boy who was sitting next to him who was engaged in condensed matter physics complained, "Is that sissy?", and the two almost fell out on the spot because of this incident.

Routine, all are routine.

Aside from the headache, Lu Zhou knew that he had to make a choice as soon as possible.

Going to Nassau Hall to ask for a roster of doctoral supervisors, Lu Zhou carefully studied the roster for an hour, and finally chose Professor Deligne as the target of the first interview.

As for why, the reason is simple.

Algebraic geometry is an important tool for studying analytic number theory, but this is Lu Zhou's shortcoming. In the past, he always wanted to find Grothendieck's original manuscripts for research, but when he got the electronic file from Academician Xiang, he found that he couldn't read French at all.

Professor Deligne is a student of Grothendieck and one of the leaders of the Grothendieck School. And in terms of awards alone, there are only two people in the history of mathematics who have won the Fields Medal, the Wolf Medal, and the Craford Medal. One of them is Qiu Chengtong, and the other is Deligne.

With Professor Deligne's knowledge, he must be able to learn a lot.

After making an appointment for the interview, Lu Zhou originally thought that this old professor, known for his rigor and strictness, would test him, even if it was formal. Unexpectedly, Deligne just glanced at his materials and announced that he passed the interview.

Standing up from the chair behind the desk, Deligne said while taking off his big gray trench coat and hat from the hanger.

"Welcome to join the Princeton family, and I will go through the relevant procedures for you now."

"My research group mainly studies the 'standard conjecture'. Of course, I have no hard requirements for you, and I will not restrict your development. According to my observation, you are a scholar who is good at independent research. But if you are willing to join my I welcome the topic. If you are not interested, you can also complete the tasks I give you like other doctoral students and prepare your graduation thesis at the same time, and you can get your doctorate in the same way."

Having said that, Deligne paused for a moment, looked at Lu Zhou and continued.

"Of course, I have higher expectations and requirements for you than others. Your graduation thesis must at least meet the standards of the "Annual Journal of Mathematics". If everything goes well, you may be able to get your doctorate next year. But if you Be too lax with yourself, waste your talent, and maybe never get it."

Lu Zhou: "I understand...I want to think about your suggestion again."

Deligne nodded and said, "Well...it's okay, I can understand, but it's better to hurry up. Try to give me an answer within three days, I don't want to wait too long for one thing."

Lu Zhou: "Definitely!"

...

The Riemann conjecture is different from a series of relatively independent mathematical problems such as the twin prime conjecture and the Polignac conjecture. Although it seems to be very simple to describe, even with a sentence "all non-trivial zeros of the Riemannζ function are located on the complex plane Re( s)=1/2" can be summarized.

But in fact, it is a huge project, similar to a building.

Just like the Poincaré conjecture, without Smail introducing it into the high-dimensional concept in the 1960s, and without the theory of "using nonlinear differential equations to study geometric structures" developed by Qiu Chengtong when he proved Calabi's conjecture, there would be no There will be Hamilton's breakthrough on the "Ricci flow" and the paper on singularity theory in 1993, let alone Perelman's final proof.

This is an objective law proved by a mathematical proposition at the level of a millennium puzzle. Even a genius and a loner like Perelman cannot skip all the previous work and directly conclude that the Poincaré conjecture is true.

Let alone eight years, even if Gauss is invited back, eighty years may not be enough for him.

The same is true for the Riemann conjecture, and this building is larger than the Poincaré conjecture.

It is like an isolated mountain, and all the mathematicians are standing on the mountainside, not even sure how high the mountain is.

The only thing confirmed is that there are as many problems as there are mountains in front of me, and no one has yet solved them. Who can solve all the problems leading to the ultimate proposition of the Riemann Hypothesis, ten Fields Medals are afraid to speak, five are definitely enough... The premise is that one person can receive so many times.

If someone thinks that skipping all unsolved problems and relying on a certain mathematical method to prove Riemann's conjecture, then most likely, like the professor in Nigeria at the end of 2015, he is a layman who can't even figure out what Riemann's conjecture is. .

Because this is tantamount to those people in time-travel novels who didn't even make a lithography machine, took a file back to the Qing Dynasty and wanted to make chips, completely divorced from reality. The Clay Institute collects a few baskets of similar papers every year, but they are no different from waste paper.

Of course, modern mathematicians are not without ideas. Whether it is the "40% zero point" of Kang Rui's critical line theorem, or the "introduction of the Riemann conjecture into a quantum mechanical system in a special case for explanation" recently proposed by three mathematicians such as Carl Bender ", can be regarded as a train of thought.

There is also algebraic geometry as an entry point.

For example, the Weil conjecture that has been proved by Deligne (one of the most brilliant achievements in the field of pure numbers in the 1970s), the popular description is the Riemann conjecture on the function field, which is often jokingly called the "cottage version" Riemann conjecture.

As for the "standard conjecture" mentioned by Professor Deligne and Lu Zhou, it is the general form of Weil's conjecture. It was proposed by Mr. Grothendieck, the "pope" of modern algebraic geometry, and was known as the crown of algebraic geometry.

If Professor Deligne hopes to fulfill his teacher's long-cherished wish and prove the Riemann Hypothesis, then as an expert in algebraic geometry, the standard conjecture is always something he must face.

After returning to the dormitory, Lu Zhou lay on the soft bed and seriously considered Professor Deligne's invitation.

Now, he faces two choices.

One is to join Professor Deligne's research group. Although it is possible to gain higher mathematical experience by targeting the standard conjecture, this will undoubtedly delay the progress of the system task, especially since he does not know where Professor Deligne has gone. How much work remains to be done.

The other is to do it alone, concentrate all your energy on overcoming Goldbach's conjecture, and then use it as your graduation thesis to complete your doctorate at Princeton...