The opinions of the partners have been consulted, and the paper on the proof of the Beilinson-Bloch conjecture has been published in Future Mathematics as always.

At the same time as the paper entered the review process, the relevant preprints were also hung on Arxiv.

Although the Beilinson-Bloch conjecture is not as well-known as the Riemann conjecture or the Goldbach conjecture, its special significance in linking the higher-order K-groups of elliptic curves E with the algebraic and analytic invariants of the number field F and elliptic curves E has given it an unusual place in the field of algebraic geometry and number theory.

Algebraic geometry, as the most researched and influential branch in the field of pure mathematics in contemporary times, attracted considerable attention as soon as it was published.

And not just because of the Beilinson-Bloch conjecture itself.

It is even more so that the solution to this problem is Professor Lu, who announced the proof of the Riemann conjecture at this year's International Congress of Mathematicians......

Institute for Advanced Study in Princeton.

Cafe on the ground floor.

Sitting by the window, Witten, drinking coffee, was chatting with Professor Deligne, who was holding a printed paper paper in his hand.

"The Lunar Hadron Collider has been completed, and it is said that the first test will begin in December, and it is estimated that I will have to make another long trip by then."

Deligne casually asked, "Oh, it seems that your theory has hopefully been verified?" ”

Hearing this, Witten, who took a sip of coffee, shook his head with a smile.

"It's far away, but it's a boon for the Standard Model. We can reveal more deeply the secrets of the microcosm and the universe in which we live...... Speaking of, what are you looking at? ”

Noticing Witten's curious gaze at the paper in his hand, Deligne pushed down the glasses on the bridge of his nose, and the corners of his mouth, which had not been unwavering at all, suddenly drew a rare smile.

"On the proof of the Beilinson-Bloch conjecture...... It seems that their research has progressed. ”

Witten: "Whose research are you referring to?" ”

"Lu Zhou, and his great unity of algebra and geometry."

Hearing this astonishing proposition, Professor Witten was slightly stunned for a moment, and said after a long while.

"That's too much of an exaggeration...... When did he start working on this subject? ”

As a Fields Medal-winning physicist, he probably knows better than many mathematicians what this project would mean if it was completed.

The old methods will be unified.

Just as analytic geometry was first invented, people combined geometric problems with algebraic problems for the first time through Cartesian coordinates, which directly led to the take-off of a series of sciences and technologies such as astronomy, physics, navigation, and engineering in the 16th century.

Mathematics will also enter a new era.

"After solving the Riemann hypothesis, but maybe he started thinking about it before he studied the Riemann hypothesis......"

Turning the page of the paper in his hand, Professor Deligne continued, "Actually, not only him, but also me and my supervisor, anyone who has made achievements in the field of algebraic geometry will wonder if there is an elegant and aesthetically pleasing way of mathematics that can transform algebraic problems into geometric problems." If this succeeds, if it is just to prove that the path is working, we can all benefit from it. ”

After a long silence, Professor Witten sighed softly and said in a mocking tone.

"It looks like I'm almost out of step with the times."

Deligne: "It's nothing, it's just that you're not paying attention to it. I was also surprised when I first heard that he had begun to work on the subject, especially now that he had already made some phased achievements, and even deceived the old fellow of Faltins out of Germany. I remember that after 2,000 years, he rarely left the Max Planck Society to be a visiting scholar elsewhere. ”

Not very concerned about the old fellow Faltins, Witten watched him seriously ask the question he was most concerned about.

"Do you think he'll make it?"

"Personally, it's only a matter of time," said Deligne, who pushed down his glasses on the bridge of his nose with his thin index finger, and thought for a moment, "Maybe it's empiricism, but I always feel that there is no problem in this world that he can't solve." ”

As if he didn't think this statement was accurate, he added after a while.

"If this problem really belongs to this era, and there is a solution."

"Looks like you think highly of him," Witten said with a smile, "so let's make a bet that you think he'll solve this problem before the first experiment at the Lunar Hadron Collider, or after the first experiment." ”

Hearing this, Deligne was slightly stunned, as if he didn't expect his old friend to ask such a strange question.

His expression seemed to be a little difficult to choose, and he frowned and thought for a moment, but soon his frown relaxed.

“…… If the first experiment had been in December, I think it would have been after that. ”

After all, there are less than two months left until December.

Even if they had made significant progress, it would have been too difficult to solve the problem in two months.

Witten: "Then I'll bet until then." ”

Professor Deligne's eyebrows raised.

"Are you sure?"

Professor Witten smiled and said, "Why not?" I always thought he would surprise us. ”

If the great unified theory of algebra and geometry can be completed, the impact not only on mathematics but also on physics will be enormous.

Whether in condensed matter physics or high-energy physics, the unification of numbers and shapes in the abstract sense will help physicists reveal many things that would otherwise be difficult for them to understand.

It's hard to say whether new physics can be born, but new methods will definitely be born.

And these new methods can be used to solve those "old" problems that they can't solve in the first place.

Deligne asked in a teasing tone with a rare smile on the corner of his mouth.

"So what do you think it's good to gamble on?"

"I remember that the manuscript of Lu Zhou's graduation thesis was with you, the one about Goldbach's conjecture," Professor Witten continued with a smile, "The last time I went to the Flint Library to borrow his manuscript on the 750Gev energy region, I temporarily flipped through his past research results, but I didn't find the one about Goldbach-Lu's theorem, I think it should be you." ”

The expression on his face was a little subtle, and Deligne coughed dryly and said with a blank face.

"It's almost in the coffin, and I'm still thinking about my collection...... So, on the other hand, what are you going to bet on? ”

Witten: "What about the manuscript on Theory M?" ”

Glancing at him, Professor Deligne said unceremoniously, "Are you embarrassed to bet on something that doesn't know when it will be proven wrong?" ”

"But it may also be the ultimate theory that explains the roots of the universe......"

Seeing Professor Deligne's face unchanged, Witten sighed, made a helpless expression on his face, and finally gave up arguing.

"Okay, let's change that...... Some time ago, when I was tidying up my room, I pulled out a lot of notes I made when I used to study topology, and there were probably some things in it that I didn't have time to sort out, but they were very useful, in short, about ten books of quantum physics. ”

Topology is probably what Witten is best at.

One of the reasons why he won the Nobel Prize in 1990 was because of his research on low-dimensional topology, from which he derived quantum invariants.

Sir Attiyah has commented that his attainment of mathematics has surpassed that of many scholars who have actually studied in the field, and his excellent knowledge of physics has provided a rich source of inspiration and intuition for the study of mathematics. There is even a theory that Sir Attiyah's sudden start to study physics in his later years was largely due to Witten.

Regardless of whether or not these manuscripts of topological research are collectible, there is no doubt about their scholarly value.

It was for this reason that Professor Deligne hesitated for a few seconds before holding out his right hand without saying a word.

"Deal!"

-

(I recommend a good urban book "Perfect Good Man", after reading it, the whole person is full of positive energy, my legs don't hurt, my waist doesn't hurt, and my grandmother dares to help me.) ）

Lamp pen