The Science Fiction World of Xueba

Peter Sarneck asked Deligne who was sitting next to him: "Pierre, do you know what subject Professor Pang has been researching recently?"

Deligne shook his head and said, "I don't know. He sent me a message yesterday morning, saying that he had a sudden inspiration. I originally wanted to show him around the Princeton Institute for Advanced Study on the weekend, but he declined it. I guess Yesterday he stayed in the hotel for a day of research."

Peter Sarnak said with a smile: "It is said that Professor Pang suddenly got inspiration while chatting with Schultz at the awards dinner last year, and then solved the ABC conjecture overnight. This time, it took him a day and a night to solve one The puzzle is probably not much weaker than the ABC conjecture."

Deligne nodded, and said with a smile: "The waves of the generation behind push the waves of the past. Since Professor Pang became famous, the world of mathematics has become much more interesting than before."

Pang Xuelin ignored the commotion in the audience.

He turned around and wrote a series of characters directly on the blackboard behind him.

[Define two sets: {odd prime number}={3, 5, 7, 11...}=P. {Odd prime number not greater than √2a+1}={3, 5, 7...pb}=Pb]

[Definition of equations (1-1): (2×4)^2-1≡0 (MODP01) (2×5)^2-1≡0 (MODP02) (2×6)^2-1≡0( MODP03)...(2a)^2-1≡0(MODP0(a-4+1))]

[Proposition 1: For any natural number a greater than 10 (a≥11, a∈N), the system of equations (1-1) always has no positive integer solution. 】

...

Pang Xuelin's writing speed was very fast, and he filled the first blackboard in less than ten minutes.

Fortunately, Princeton University was well prepared this time. After the first blackboard was completed, staff immediately pushed up the second blackboard.

It is said that this is a lesson learned from the insufficient blackboard at the Millennium Awards ceremony a year ago.

No matter which school Pang Xuelin went to or which research institution gave the report, the organizers would prepare a large number of blackboards in advance, in case the boss suddenly did not give a report as planned and chose to enlarge the strategy, resulting in insufficient number of blackboards.

It's just that in the past year, most of the reports that Pang Xuelin participated in have been carried out step by step, so those sponsors are basically self-indulgent.

Deligne did not expect that the blackboard prepared by the organizers in advance for this Princeton report would actually come in handy.

As Pang Xuelin's words filled the first blackboard, at this time, people gradually began to see the clues.

"Professor Pang is trying to prove...the twin prime number conjecture?"

Peter Sarnak was a little surprised.

Deligne nodded with some emotion, "I'm afraid it is!"

The twin prime number conjecture is one of Hilbert's twenty-three questions, which is of great significance in number theory. In a sense, its status is only slightly inferior to Goldbach's conjecture.

If the twin prime number conjecture is solved by Pang Xuelin, count Ponzi's geometry theory, BSD conjecture, ABC conjecture, and the problem of solving nonlinear partial differential equations.

Then this kid is really going to be a god in the mathematics world.

In the next International Congress of Mathematicians, a single Fields Medal may not be enough to recognize Pang Xuelin's contribution to the mathematics community.

"Haha, why do I think this? Let the directors of the International Union of Mathematicians have a headache!"

When Andrew Wiles proved Fermat's Last Theorem, he was exactly forty-five years old, and he had passed the maximum age limit of forty for the Fields Medal stipulated by the International Union of Mathematicians.

Therefore, the International Union of Mathematicians specially made a Silver Fields Medal for Wilster in recognition of his contribution.

Perhaps at the International Congress of Mathematicians two years later, the IMF should consider giving Pang Xuelin the most unique Fields Medal in history.

Deligne smiled secretly.

Qi Xin sat under the stage, looking at Pang Xuelin on the stage with bright eyes.

Although it is not clear what exactly Pang Xuelin wrote, but listening to the sounds of exclamation and praise one after another in his ears, Qi Xin had a faint feeling of pride.

For her, Pang Xuelin at this time is the most handsome.

Sophon on the side looked at Pang Xuelin thoughtfully, and murmured to himself, "I never thought that he would actually find a breakthrough in that paper. Perhaps, following him all the time, there will be unexpected gains in the future."

Qi Xin turned her head, looked at Tomoko with some surprise, and said, "Sister Zhi, what were you talking about just now?"

Sophon smiled and said, "I said that Professor Pang is amazing. I didn't expect to solve a problem that has plagued the mathematics community for many years."

"Of course! If he is not good, who is good!"

Qi Xin was a little proud.

Perhaps only such a man is qualified to make himself one of his many lovers!

Thinking of Pang Xuelin's rich relationship history, Qi Xin's mood suddenly changed, and he couldn't help uttering two words: "Scumbag!"

At this time, Pang Xuelin had no time to pay attention to the commotion in the audience.

His pen tip kept flowing on the blackboard, writing on the blackboard the research results he had spent a day and a night before.

...

[When k is an algebraic number field, the previous Weil theorem can be improved to Theorem 4.2.10: Suppose G is a typical group on k, and G is absolutely almost simply connected, then there are the following three situations. 】

【(1) There is a single-k algebra A with a center, making... (2) There is a single-k algebra A, and the center of A is the quadratic expansion of k, A has a second kind of involution I, making...]

【About the above situation, we can make the following three supplements: We know that for any natural number n and the quadratic expansion of k, there must be a single k algebra A such that ^2】

...

An hour later, the fifth blackboard was filled with writing, and Pang Xuelin's derivation slowed down.

Looking at the words on the blackboard, Pang Xuelin took a deep breath.

This is the end of yesterday's derivation, and the next step is to see my own impromptu performance.

[Assume V is an n-dimensional algebraic variety defined on the algebraic number field k, and let P be a smooth point on V, then there are local coordinates x1x2x3...xn on the open neighborhood U of P in V. In this way, the n-time differential form w on V can be written as...]

Pang Xuelin put away the chalk, stared blankly at the blackboard, lost in thought.

Everyone in the audience obviously also noticed Pang Xuelin's strangeness, and for a while, everyone couldn't help talking about it.

"Professor Pang should have deduced it here. Although I didn't fully follow his train of thought, it shouldn't be a big problem intuitively. As for the latter..."

Someone shook his head.

Peter Sarneck said: "Pierre, do you think Professor Pang can complete the proof?"

Deligne smiled lightly: "I am not surprised by this young man's miracle."

On the other side, Qi Xin asked Sophon worriedly: "Sister Zhi, you are studying mathematics, so he should be fine, right?"

Tomoko smiled and said, "Why, are you worried about your little lover?"

"Miss Zhi..."

Qi Xin couldn't help but draw out the tone.

Sophon laughed and said, "Don't worry, Professor Pang is much more powerful than you imagined!"