The Science Fiction World of Xueba

Schultz said: "Actually, the last time you held a report meeting in Jiangcheng, I received an invitation letter. At that time, I was thinking about the past, but I couldn't make it because I had something to do. Fortunately, I didn't miss the award ceremony!"

Pang Xuelin smiled and said, "Haha, if I don't see you this time, I plan to visit you in Germany!"

"Welcome, next time you have time to come to Germany, you must remember to come to the University of Bonn to find me!"

Although the two met for the first time, they quickly chatted like friends who have been friends for many years.

Mathematicians are generally lonely, and few people can chat with them. Therefore, mathematicians with comparable strength can generally become friends with each other.

Just like Deligne and Faltings, although these two old men often spray each other, they are the kind of old friends who talk about everything in private.

In the past, Pang Xuelin really did not have the confidence to compete with Schultz in terms of academic ability, but after years of thinking and research in the Martian world and the world of Wandering Earth, his own strength is no less than Schultz How much, even in terms of grasping the framework of the new mathematical theory, it is still slightly beyond.

"I heard that you have been studying Hodge's conjecture for the past few years. Two years ago, you proved a corollary of partially characterizable algebraic cohomology classes on non-singular projective complex algebraic varieties very beautifully. How is the progress now?"

Schultz shook his head, and said helplessly: "Now we have only progressed to prove the similarity of cohomology elements, and we are still far from proving Hodge's conjecture!"

The Hodge conjecture, like the ABC conjecture, is one of the seven millennium puzzles.

Schultz previously systematized a series of basic theories initiated by Faltings and others, and opened up a new framework in the field of arithmetic algebraic geometry, so he won the Fields Medal, known as both Faltings and German A new generation of leaders in post-Ligne mathematics.

But so far, he has not completed a proof of a heavyweight mathematical conjecture.

You must know that Deligne and Faltings completed the proofs of Weil's conjecture and Model's conjecture respectively when they were his age, so he has been holding back his energy and wants to make a breakthrough in Hodge's conjecture.

"What about you, after the BSD conjecture is proved, do you have any new goals?"

Pang Xuelin smiled slightly and said, "ABC guess!"

Schultz couldn't help being taken aback: "ABC conjecture? You also think there are problems in Mochizuki's paper?"

Pang Xuelin nodded and said: "Mochizuki Shinichi's choice of direction is no problem. On the basis of Far Abelian geometry, to establish a new mathematical framework, and then to solve the problem of the ABC conjecture, but the generalized Teich-Miller theory he established is not There are certain problems. A brand-new mathematical system should have universal significance, but Mochizuki Shinichi’s generalized Teich-Miller theory seems to have been created only to solve the ABC conjecture, and has not shown value in other aspects. He has gone In a dead end!"

Schultz nodded and said: "It is true. Last year, Professor Jacob Stix from Goethe University and I went to Japan to find him and told him about the flaws in the paper. We communicated with Shinichi Mochizuki in Japan for a week, and finally No one has been able to convince anyone. I always feel that that guy is a little bewildered, and I hope he can come out by himself! By the way, do you have an idea for proving the ABC conjecture now?"

Pang Xuelin said: "Probably has a research direction, similar to Mochizuki Shinichi's approach, starting from far Abelian geometry, but I don't know when it will be proved."

The mechanism of modern mathematics research has become mature. A problem is always proposed based on previous work and understanding of related problems, and the mechanism for solving problems is mostly a variant of known methods.

In 2003, Perelman proved the Poincaré conjecture that unified human understanding of the three-dimensional universe, using the research method "curvature flow" introduced by Hamilton in the 1980s in differential geometry.

Hundreds of years ago, Fermat claimed that the space was too narrow to write Fermat's last theorem of the proof process,

When Sir Wiles proved the conjecture in the 1990s, he also used the modular form theory of high-order elliptic curves established in the 1950s.

Ponzi's geometric theory has been established, but this is just a new set of mathematical tools. To prove the ABC conjecture, it depends on whether Pang Xuelin can use this set of tools well.

During this time, Pang Xuelin has been thinking about the ABC conjecture.

Through the Ponzi geometry theory, he faintly felt that he was close to the essence of the ABC conjecture, but he always felt that something was missing, as if there was still a thin film between him and the ABC conjecture.

It depends on whether he can pierce this film with a flash of inspiration one day.

Schultz was not surprised by Pang Xuelin's rhetoric. He would be surprised if Pang Xuelin really had a solution to this level of conjecture.

Schultz said: "The ABC conjecture is one of the most important problems in the Diophantine equation. Its importance in the field of number theory is second only to the Riemann conjecture. If it can be solved, it can partially prove the Fermat-Cattelan (Fermat-Cattelan) problem. ) conjecture, the Schinzel-Tijdeman conjecture can also be fully proved. Professor Pang, if you can really solve the ABC conjecture, maybe you can free Mochizuki Shinichi from that dazed state..."

Pang Xuelin smiled, but did not speak.

Schultz added: "Speaking of the ABC conjecture, last time I went to the French Institute for Advanced Study, some of Grothendieck's manuscripts are still kept in their library. There is not much content, and it may be placed in the Institute for Advanced Study in Princeton."

Pang Xuelin was slightly taken aback, and said, "Does the French Institute for Advanced Study have some of Grothendieck's manuscripts?"

Schultz nodded and said: "Yes, they can only be read in their library and cannot be borrowed. I think you should go there. In the manuscripts I saw last time, there are many Although we have already learned the contents of the two maps, Grothendieck's way of thinking about a proposition is very worth learning..."

Pang Xuelin stood there dumbfounded and did not respond to Schultz's words.

Bely function, bipartite map, Cattelan conjecture...

The key words mentioned by Schultz sounded like a thunderclap in Pang Xuelin's ears

Pang Xuelin closed his eyes, and the noisy banquet hall seemed to quiet down instantly, and everyone disappeared, leaving only himself and the number theory universe composed of countless numbers and formulas.

In the void, a ray of light seemed to light up in the universe of the theory of numbers, like a supernova explosion, instantly illuminating the dim starry sky.

A flash of inspiration flashed.

Pang Xuelin instantly put his hands deep in his hands and grasped it firmly!

"I see!"

Pang Xuelin opened his eyes, and ecstasy flashed in his eyes.

He stuffed the champagne glass into Schultz's hand, patted him on the shoulder, and laughed, "Thank you, brother!"

With that said, he turned around and left the banquet hall.

Schultz stared blankly at Pang Xuelin's back, and it took him a long time to react, and he muttered to himself, "This guy, did he think of something extraordinary?"