As a determined materialist warrior with a clear conscience, Lu Zhou certainly does not believe in ghosts and gods. *With* Dream *Small* Say .lā

His eyes adjusted to the light of the corridor for a moment, and he asked in an uncertain tone with the only impression he had.

"Molina?"

Hearing Lu Zhou pronounce her name, the corners of the French lady's mouth hooked up with a smile: "I knew you would come here...... Why don't you call me? I can drive you to Philadelphia to pick you up. ”

It's the same question again......

"I've already asked my senior brother...... Where's No. 2? Lu Zhou coughed dryly and quickly diverted the topic.

"Go upstairs and turn left at the end of the corridor," the index finger was raised slightly, but Molina didn't dwell on the phone matter, and said in a casual tone, "By the way, speaking of which, have you chosen a mentor?" ”

Lu Zhou: "What's wrong?" ”

"I mean, if you don't choose well, I recommend my mentor Sophie Morel to you," looking at Lu Zhou seriously, Molina said, "My previous invitation is still valid, we need you for our project." ”

Sophie Morel (Sphie Rel)?

Lu Zhou looked at her with some 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 Medal, a French female mathematician with both good looks and knowledge.

But it wasn't the name Sophie that surprised him, but Princeton's ability to poach people.

Sure enough, it is the Yankees who rely on the alumni association to "do whatever they want", and it seems that the name of the Paris Mathematics Center was not robbed, but simply bought......

Thinking of this, Lu Zhou suddenly understood the reason why Princeton and Jinling University, a small transparent university in the mathematical community, reached an "inequality agreement", and his expression couldn't help but be a little subtle.

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

Holding her arms together, the corners of Molina's mouth hooked up with a smile: "What about your choice?" ”

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

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

Joke.

As a popular candidate with a 99% probability of winning the award, 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, inquire more and then choose his own tutor. As a result, he far underestimated how "tempting" a two-year-old Cole Prize winner and a popular candidate for the Philippine Prize was for a professor at Princeton.

Invitations to coffee parties and academic exchanges were no longer a big deal, but while eating at the eating-lubs, a young female teaching assistant took the initiative to strike up a conversation with him, and in less than ten sentences he talked about his mentor, and kept suggesting that his own mentor was a good choice.

What's even more excessive is Senior Brother Luo, who obviously recommended so many people to him at the beginning, but at dinner the next day, he changed his previous tone and began to blow Professor Edward Witten. Later, it may have blown too much, and was complained by a Mexican guy who was sitting next to him who was engaged in condensed matter physics, "Just that sissy?" The two almost turned their faces on the spot because of this.

Routines, all routines.

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

I went to Nassau Hall to ask for a roster of doctoral supervisors, and 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 the study of analytic number theory, but this is the shortcoming of Lu Zhou. He had been trying to study Grothendieck's manuscript, but when he got the electronic file from the academician, he found that he could not read French at all.

Professor Deligne was a pupil of Grothendieck and one of the leading figures of the Grothendieck school. Moreover, there are only two people in the history of mathematics who have won the Fields Medal, the Wolf Medal, and the Cafford Prize, one of whom is Qiu Chengtong and the other is Delinene.

With Professor Deligne's knowledge, he will definitely learn a lot.

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

Standing up from the chair behind his desk, Deligne said as he removed his large gray trench coat and hat from the hanger.

"Welcome to the Princeton family, I'm going to help you with the formalities now."

"My research group is mainly engaged in the study of 'standard conjectures', and of course, I have no hard requirements for you and will not restrict your development. From what I've observed, you're a scholar who excels at independent research. But if you'd like to join me in my project, I'd love to hear from you. If you are not interested, you can also complete the tasks I gave you and prepare your dissertation at the same time as other doctoral students, and you can also get your PhD. ”

Speaking of this, Deligne paused for a moment, looked at Lu Zhou and continued.

"Of course, I have higher expectations and requirements for you than others. Your dissertation must at least meet the standards of the Annals of Mathematics. If all goes well, maybe you'll be able to get your PhD next year. But if you are too lax with yourself and waste your talents, you may never get it. ”

Lu Zhou: "I see...... As for your suggestion, I would like to think again. ”

Deligne nodded, "Hmm...... It's fine, I can understand, but it's better to be faster. Try to get back to me within three days, I don't want to wait too long for one thing. ”

Lu Zhou: "Definitely! ”

……

The Riemann conjecture is different from the twin prime conjecture, the Polygnac conjecture and a series of relatively independent mathematical problems, although it seems simple to describe, and can even be summarized with the sentence "All non-trivial zeros of the Rieannζ function are located on a straight line of Re(s)=/2 on the complex plane".

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

Just like the Poincaré conjecture, without Smale's introduction of the concept of higher dimensions in the sixties, and without the theory of "studying geometric structures with nonlinear differential equations" developed by Qiu Chengtong when proving the Calabi conjecture, there would have been Hamilton's breakthrough in the "Rii flow" and the paper on the singularity theory in '93, let alone Perelman's final proof.

This is an objective law of the proof of mathematical propositions at the level of a millennial problem, and even a genius and a recluse person like Perelman cannot skip all the previous work and directly arrive at the Poincaré conjecture.

Not to mention eight years, even if you invite Gauss back, eighty years may not be enough to give him.

The same is true of the Riemann conjecture, and this edifice is larger than the Poincaré conjecture.

It resembles an isolated mountain, and all mathematicians stand halfway up the mountain, not even sure how high the mountain will be.

The only thing that is confirmed is that there are as many problems as the mountains in front of us, and no one has solved them yet. Whoever can solve all the problems that lead to the ultimate proposition of the Riemann conjecture, ten Fields Medals dare not speak, five is certainly enough...... The premise is that one person can receive it so many times.

If anyone thinks that the Riemann hypothesis can be proved by some mathematical method by skipping all the unsolved problems, then he is probably the same layman as the professor in Nigeria at the end of five years, who does not even understand what the Riemann hypothesis is.

Because this is tantamount to those who didn't even make a lithography machine in the crossing, and when they returned to the Qing Dynasty with a file, they wanted to make chips, which was completely out of 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 Conreus's critical line theorem, or Karl Bend's (Arl· Bender et al. recently proposed by mathematicians to introduce the Riemann hypothesis into a quantum mechanical system in a special case for interpretation, which can be regarded as a line of thought.

There is also algebraic geometry as a starting point.

For example, the Wey conjecture (one of the most brilliant achievements in the field of pure numbers in the 70s), which has been proved by Deligne, is popularly described as the Riemann conjecture on the functional domain, and is often jokingly referred to as the "copycat" Riemann conjecture.

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

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

After returning to the dormitory, Lu Zhou lay on the fluffy bed, seriously considering Professor Deligne's invitation.

Now, he is faced with two choices.

One is to join Professor Deligne's group, although it is possible to gain more mathematical experience by aiming for the standard conjecture, but this will undoubtedly delay the progress of the system task, especially since he does not know where Professor Deligne has reached and how much work is still to be done.

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