Scholar’s Advanced Technological System

As a determined and well-deserved materialist warrior, the Ark certainly does not believe in ghosts.

His eyes adapted for a while to the light of the corridor, and he asked in an uncertain tone, relying on his only impression.

“Molina? ”

When I heard the boat say its name, the French lady's mouth snapped a smile: “I knew you would come here... why didn't you call me? I can drive to Philadelphia to pick you up. ”

Again…

“I've asked my brother... where's 211?” The ark coughed dry and quickly turned the subject off.

“Turn left upstairs at the end of the hallway," the index finger lifted gently, but Molina didn't get tangled up about the phone thing and said in a chitchat, "By the way, have you chosen a mentor? ”

Ark: “What's wrong? ”

“I mean, if you don't choose, I recommend my mentor, Sophie Morell,” looking seriously at the ark, Molina said, "my previous invitation is still valid and our subject needs you. ”

Sophie Morel?

The ark looked at her with some surprise.

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

“Surprised indeed…” the ark nodded.

One of the most popular candidates for the Fields Prize, a French woman mathematician with values and knowledge.

But it wasn't the name Sophie that surprised him, it was Princeton's ability to dig.

It turns out it was the American who fought the alumni club "do what you want”. The name of the Paris Mathematics Center didn't seem to have been stolen, it was bought away...

Thinking about it, the Ark suddenly understood the reasons for the “Inequality Agreement” between Princeton and Little Transparent Golden Ring University in mathematics, and the expression was somewhat subtle.

After half a day, it turned out to be the Baofields Award...

With her arms in her arms, Molina's mouth snapped a smile: “What's your choice? ”

“Thank you for your invitation, but allow me to decline. ”

Rub your shoulders past the staring Molina and drag your suitcase to the room at the end of the hallway.

Just kidding.

What's wrong with finding a competitor with an 80% chance of winning an award as a popular candidate with a 99% chance of winning an award?

……

The Ark was originally intended to listen to several classes, ask more and choose your own mentor. As a result, he underestimated the popular candidacy of a 21-year-old Cole Prize winner and the Phil Prize, and how “tempting” it was for Professor Princeton.

I don't know where to send invitations to coffee parties and academic exchanges anymore. When eating at a food club (eating-clubs), a young assistant professor spontaneously talked to him, and then spoke less than 10 sentences about the mentor's problem, suggesting constantly that his own mentor was a good choice.

Even more excessive was Brother Luo, who had initially recommended so many people to him, and the next evening, at dinner, he changed his previous tone and started blowing Professor Edward Witten. Then it might blow too hard, and some Mexican dude sitting next to him with aggressive physics spat, "Just that pussy?” Two people almost turned their faces on the spot because of it.

The routine, it's all routine.

After a headache, the ship knew it had to make choices as soon as possible.

Going to Nassau Hall asked for a roster of doctoral mentors, and the Ark studied the roster for an hour, eventually choosing Professor Deligne as the goal of the first interview.

As for why, the reason is simple.

Algebraic geometry is an important tool for analyzing mathematics, but this is a short board for an ark. He had always wanted to study Grotendik's manuscript, but when he got the electronic file from the academician, he realized he didn't understand French at all.

Professor Deligne is a student of Grotendik and one of the leaders of the Grotendik school. And only two people in mathematical history have won the awards, including the Fields, Wolf and Crawford awards, one for Chengtong Qiu and the other for Delinière.

With Professor Deligne's knowledge, you must learn a lot.

After the interview was scheduled, Ark thought the old professor, who was famous for his rigour and rigour, would put him to the test, even formally. It turned out that Delinière had just looked at his material and announced that he had passed the interview.

Standing up from the chair behind the desk, Deligne took off his grey trench coat and hat from the hanger and said.

“Welcome to Princeton's extended family, and I'm on my way to help you through the process. ”

“My project group is focused on researching 'standard guesses', of course I have no hard requirements for you and will not constrain your development. According to my observations, you are an independent researcher. But if you'd like to join my subject, I'd love to. If you are not interested, you can also complete the tasks I have given you, like other doctoral students, and prepare your dissertation, as well as get your doctorate. ”

Speaking of which, Deligne paused for a moment and looked at the ark and continued.

“Of course, my expectations and demands for you are higher than others. Your graduation thesis must at least meet the standards of the Mathematical Yearbook. If all goes well, maybe next year you'll get your PhD. But if you are too lax with yourself and waste your talent, you may never get it. ”

Ark: “I see… I would like to reconsider your suggestion. ”

Deligne nodded, "Well... it's okay, I understand, but it's better to hurry. Try to get back to me within three days, and I don't want to wait too long for one thing. ”

Ark: “Absolutely! ”

……

Lehman speculation differs from a series of relatively independent mathematical questions, such as twin number speculation, Polynesian speculation, etc., although it seems simple to describe, and can even be summarized with the phrase "All the extraordinary zeros of the Riemannzeta function are in the straight line of Re (s) = 12 on the composite plane”.

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

Like Pongale's guess, without Smail's introduction of the Gao Dimension concept in the 1960s, without the theory of "studying geometry with non-linear differential equations” developed by Chengtong Qiu in proving Karabi's guess, there would be no subsequent breakthrough in Hamilton's "Ricci stream” and the '93 paper on singularity theory, let alone Perelman's final proof.

This is an objective pattern evidenced by a millennial-level mathematical proposition, and even genius, isolated like Perelman, cannot skip all the work ahead and come directly to the conclusion of the Pongalese conjecture.

Don't say it's eight years, it's not necessarily enough to invite Gaussian back, give him 80 years.

Same goes for Lehman's guess, and this building is bigger than Pongale's.

It's like an isolated mountain, where all the mathematicians stand on the waist, not even sure how tall the mountain is.

The only confirmation is that there are just as many problems in front of us, and no one has solved them yet. Who can solve all the problems leading up to Lehman's assumption of this ultimate proposition, ten Fields Awards won't dare speak, and five is certainly enough… provided that one person receives it so many times.

If one thinks that one can prove Lehman's guess by some mathematical means by skipping all the unresolved problems, then most of them, like the Nigerian professor at the end of 15 years, are outsiders who don't even know what Lehman's guess is.

Because this is like going through people in a novel who didn't even get a light engraver, and coming back to Daqing with a file wants to make a chip, completely out of reality. Similar papers The Clay Institute collects several baskets each year, but they are no different than scrap paper.

Of course, modern mathematicians don't have any ideas. Whether it's Conrad's "40% zero” on the threshold theorem, or "introducing Lehman speculation into a quantum mechanics system under a special circumstance" recently proposed by mathematicians such as Carl Bender, is a thought.

There is also algebraic geometry as the entry point.

For example, Way speculation, which has been proven by Deligne (one of the greatest achievements in the field of pure numbers in the 1970s), is commonly described as a Lehman speculation in the functional domain, often referred to as a “mountain version” of Lehman speculation.

As for what Professor Deligne and the Ark called "standard presumption”, it was the general form of Way's presumption, which was presented by Mr. Grotendik, the "pope” of modern algebraic geometry, and hailed as the crown of the algebraic geometry world.

If Professor Deligne wishes to complete his teacher's wishes and prove Lehman's assumptions, then, as an expert in algebraic geometry, standard assumptions are always something he must face.

Upon returning to the dormitory, the ark lay on a soft bed and carefully considered Professor Deligne's invitation.

Now he faces two choices.

One is to join Professor Deligne's cluster, which, while it is possible to gain higher mathematical experience targeting standard assumptions, will undoubtedly delay the progress of the system's tasks, especially since he does not know what step Professor Deligne has now taken and how much work remains to be done.

The other is to do it alone, focus all of your energy on the Goldbach conjecture, and then use it as your graduation thesis to complete your PhD in Princeton...