Chapter 1109 The Old Method Will Be Unified

I have asked my partners for their opinions, and Lu Zhou published the paper on the proof of the Beilinson-Bloch conjecture in "Future Mathematics" as usual.

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

Although the Beilinson-Bloch conjecture is not as famous as the Riemann conjecture or the Goldbach conjecture, it can connect the high-order K-group of the elliptic curve E with the number field F and the algebraic and analytical invariants of the elliptic curve E. meaning, but endowed it with an extraordinary position in the fields of algebraic geometry and number theory.

Algebraic geometry, as the branch with the largest number of researchers and the most influential in the field of contemporary pure mathematics, immediately attracted considerable attention after this preprint was posted.

Not just because of the Beilinson-Bloch conjecture itself.

It is because it is Professor Lu who announced the proof of Riemann's conjecture at this year's International Conference of Mathematicians...

Princeton Institute for Advanced Study.

Cafe on the first floor.

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

"The Lunar Hadron Collider has been completed. It is said that the first test will start in December. I guess I will have to take a long-lost trip by then."

Deligne asked casually without much concern: "Oh, it seems that your theory has hope to be verified?"

Hearing this sentence, Wei Teng, who took a sip of coffee, smiled and shook his head.

"It's too far away, but for the standard model, this is a boon. We can reveal the secrets of the microcosm and the universe we live in more deeply... Speaking of which, what are you looking at?"

Noticing the curious gaze that Witten cast on the thesis in his hand, Deligne pushed down the glasses on the bridge of his nose, and the corners of his mouth, which usually did not have any ups and downs, suddenly evoked a rare smile.

"About the proof of the Beilinson-Bloch conjecture... It seems that their research has made progress."

Witten: "Whose research are you referring to?"

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

Hearing this astonishing proposition, Professor Witten was slightly taken aback, and spoke after a while.

"This is too exaggerated... Since when did he start studying this subject?"

As a physicist who has won the Fields Medal, he probably knows better than many mathematicians what this subject will mean if it is completed.

The old methods will be unified.

Just like when analytic geometry was just invented, people first combined geometrical problems with algebraic problems through Cartesian coordinates, which directly led to the take-off of a series of science and technology such as astronomy, physics, navigation, engineering, etc. in the 16th century.

Mathematics will thus enter a new era.

"After solving the Riemann Hypothesis, but maybe he started thinking about it before studying the Riemann Hypothesis..."

Turning the page of the paper in his hand, Professor Deligne continued, "In fact, not only him, but also my supervisor and me, anyone who has made achievements in the field of algebraic geometry will think about this question, whether there is an elegant and An aesthetically pleasing mathematical way of translating algebraic and geometrical problems into each other. If this works, even if it just proves that this path works, we can all benefit from it."

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

"It seems that I can hardly keep up with this era."

Deligne: "It's nothing, it's just that you didn't pay attention to this direction. I was also surprised when I first heard that he started to study this topic, especially now that he has made some phased results, even Deceived that old fellow Faltings from Germany. In my impression, after two thousand years, he rarely leaves the Max Planck Society to be a visiting scholar in other places.”

Not very concerned about that old guy Faltins, Witten watched him seriously ask the question he cared about most.

"Do you think he can succeed?"

"Personal opinion, it's just a matter of time," Deligne said as he pushed the glasses on the bridge of his nose with his skinny index finger, "Maybe it's a fault of empiricism, but I always feel that there is no one in this world who can't solve it." The problem."

It seemed that this statement was not accurate enough, and after a while, he added another sentence.

"If this problem really belongs to this era and has a solution."

"It seems that you have a high opinion of him," Witten said with a smile, "Why don't we make a bet, you think he will solve this problem before the first experiment of the Lunar Hadron Collider , after the first experiment."

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

The expression seemed to be difficult to choose. He frowned and thought for a while, but soon his frowning brows relaxed.

"...if the first experiment was in December, I think it should be later."

After all, no matter what, there are only less than two months left before December.

Even if they have made significant progress, it is too difficult to solve this problem within two months.

Witten: "Then I'll bet before that."

Professor Deligne raised his eyebrows.

"you sure?"

Professor Witten said with a smile, "Why not? I always think he will bring us a surprise."

If the grand unified theory of algebra and geometry can be completed, it will have a huge impact not only on mathematics, but also on physics.

Whether it is condensed matter physics or high-energy physics, the unification of number and shape in the abstract sense will help physicists reveal many things that were originally difficult for them to understand.

It is hard to say whether new physics will be born, but new methods will definitely be born.

And these new methods can be used to solve the "old" problems that they could not solve.

Deligne gave a rare smile and asked in a teasing tone.

"Then what do you think is a good bet?"

"I remember that the manuscript of Lu Zhou's graduation thesis is 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 study of the 750Gev energy zone , On the spur of the moment, I looked through his past research results, but I couldn't find the one about the Goldbach-Lu theorem, so I think it should be with you."

The expression on his face was a bit subtle, Deligne coughed dryly, and said expressionlessly.

"I'm almost in the coffin, but I still can't forget my collection... Then, what are you going to use as a bet?"

Witten: "How about the manuscript on M-theory?"

After squinting at him, Professor Deligne said unceremoniously: "Are you willing to bet on something that will be proven wrong someday?"

"But it also has the potential to be the ultimate theory of the origin of the universe..."

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

"Okay, let's change it... When I was tidying up the house some time ago, I dug out a lot of notes I made when I was studying topology. There may be some useful things that I didn't have time to sort out. In short, probably It's as thick as ten volumes of quantum physics."

Topology is probably Witten's best field.

One of the big reasons why he was able to win the Fields Medal in 1990 was because of his research on low-dimensional topological structures, from which he derived quantum invariants.

Sir Attia once commented that his attainment in mathematics has surpassed many scholars who have actually engaged in research in this 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 saying that the reason why Sir Attia suddenly started to study physics in his later years was largely because of Witten.

Regardless of whether these topological research manuscripts have the significance of collection, there is no doubt about their academic value.

It was precisely because of this that Professor Deligne only hesitated for a few seconds before extending his right hand without saying a word.

"make a deal!"

-

(I recommend a good urban book "The Perfect Good Man". After reading it, my whole body is full of positive energy. My legs don't hurt anymore, my waist doesn't hurt anymore, and my grandmother dares to help her.)