Great Country Academician

Noticing Deligne's gaze, Witten shook his head, handed him the manuscript, and said, "I can't make too many comments on this method in a short time."

"Although this method is very familiar with algebraic geometry, topology, and manifolds, it contains a lot of mathematical methods and concepts such as group theory and metric spaces. These fields are not within the scope of my research."

"It is no exaggeration to say that I may not be able to understand this paper in a short period of time. After all, in terms of mathematics, the knowledge I have mastered is basically related to physics. Many mathematics in the method of this paper are not in my within the scope of the study."

Hearing this, Deligne showed a look of surprise. As the first physicist to win the Fields Medal, Witten's mathematical ability is beyond doubt.

Mathematical physics has always been a frontier and hot field in mathematics, because it provides a large number of new ideas and new problems for pure mathematics. In the foreseeable future, there will be many contributions from mathematical physics in the mathematical community.

And Weiteng has been working in the frontier fields of theoretical physics and mathematical physics for nearly fifty years. In the field of mathematical physics, he is not only the first person, but also the top three.

Now he actually said that he could not understand the method of this paper in a short time, how can this not be surprising.

With surprise and a hint of doubt, Deligne took the manuscript paper from Witten, and Witten took the manuscript left by Professor Mirzakhani and read it.

In the dormitory illuminated by the setting sun, it became quiet again, but this time it didn't take long. Within half an hour, Deligne and Witten put down the manuscripts in their hands.

"It's really subtle. It introduces concepts such as multifractals, dimensions, group theory, metric spaces, Riemann surfaces, and projective clusters. It's quite complicated. Even if I want to understand these things, it's not so easy."

Putting down the manuscript in his hand, Professor Deligne praised.

Now he understood why Wei Teng said that he could not understand the method of this paper in a short time.

Let alone Wei Teng, even him, it will take a certain amount of time to understand the method of this paper.

Half an hour is just enough for him to go through the manuscript paper in his hand roughly, and there is almost no time to think about the core things.

The time is too short, even he can't really understand the method of this paper.

But some kind of scientific research intuition told him that with this tool, there might be hope to solve Hodge's conjecture.

Thinking about it, Deligne glanced at Xu Chuan, who was sitting on the other side busy with something, feeling a little emotional.

As a disciple of his, his current mathematical ability has not only surpassed him, but it is definitely not far behind him.

More importantly, he is still young and talented. He is less than twenty years old, and he can enter the golden age of a scholar or scientific researcher.

If you give him some more time, how far can he grow?

Comparable to a mentor, or higher?

Suddenly, some figures appeared in Deligne's mind.

He didn't know why such thoughts appeared in his mind.

But he knows that every time such a person appears in history, he can promote the development of science and even the entire society by himself.

Such as Archimedes, Gauss, Newton.

Deligne and Witten left, and Xu Chuan was left alone in the dormitory, sorting out the documents in his hand.

Suddenly, he patted his head in frustration.

He remembered that he was just taking care of his own business, and forgot to ask Wei Teng what he had done before calling him.

He picked up the mobile phone from the table and called Wei Teng. After two rings, the call was quickly connected.

"Hello, Xu Chuan, what's the matter?" Wei Teng's questioning voice came from the other end.

"Teacher, did you call me for something before? I forgot to mention it just now." Xu Chuan asked.

"Actually, it's nothing. The second half of the collision experiment at CERN has already started. I have a group of experiments here. I'm asking if you are interested in participating. But now you have more important things on your hands, so forget it. You should deal with the papers in hand first."

Hearing this, Xu Chuan's eyes lit up, and he quickly asked, "The experiment at CERN? What is it about?"

For him in his previous life, it was 18 years after he formally started contacting high-energy physics, so the experiments at CERN in 2016 and 2017 were blank for him.

If there is a chance to contact, he will naturally not give up.

Of course, he does not want to participate in all collision experiments. After all, the LHC conducts a large number of collision experiments every year, and many experiments are not to discover something new, but to make up for some previous data or models. .

Xu Chuan is not very interested in such experiments, even if he has never experienced them. What he is interested in is the exploration of the unknown, the discovery of new particles, and the transcendence of the Standard Model.

"The work of CERN in the second half of this year is mainly about the search for subatomic particles, in order to complete the standard model, and conduct a basic symmetry study between hydrogen atoms and antihydrogen atoms."

On the other end of the phone, Witten explained the work arrangement of CERN.

"In search of subatomic particles and fundamental symmetries?"

Xu Chuan stroked his chin for a while, then asked, "Teacher, when will the basic symmetry between hydrogen and antihydrogen be studied?"

He is not very interested in the collision experiment of CERN to search for subatomic particles. From his perspective, he basically knows all kinds of subatomic particles discovered by CERN over the years, who discovered them, and is very clear about these subatomic particles. properties of the original particle.

He has no great interest in cutting off other people's discoveries and opportunities in advance, and doing things that are destined to happen in history.

Instead, he is interested in the study of the basic symmetry between atoms and antihydrogen atoms.

At least, in his memory, he has never heard of any major discovery or breakthrough in the field of basic symmetry research in 2017.

So he may be able to take a look at this experimental research, but he doesn't know if it will be too late in terms of time.

After all, compared with a collision experiment, the most important thing at present is to replenish the tools in hand and try to break through the Hodge conjecture.

That's the most important thing right now.

As for the collision experiment at the European Atomic Energy Research Center, there is still a lot of time to do it in the future.

If there are enough discoveries, it is not impossible for CERN to repeat a particle collision experiment with exactly the same parameters and energy levels.

"The study of fundamental symmetries between hydrogen and antihydrogen atoms?"

"This experiment will be later. The current plan is to be carried out by the ALPHA laboratory in December. Why, are you interested in this?"

Wei Teng's curious voice came from the phone, Xu Chuan nodded with a smile, and said, "Well, I'm very interested in basic symmetry research, and I won't go to the subatomic particle discovery experiment. I hope my side You can finish what you have in hand before December."

Wei Teng smiled and said, "There's no rush, you still have plenty of time."

After a pause, he continued, "If there are any new discoveries in Hodge's conjecture, please let me know."

Xu Chuan nodded and said, "Of course."

After hanging up the phone, Xu Chuan re-immersed himself in the perfection of his opponent's mathematical method.

Although the core idea already exists, it is not so easy to complete it.

Sometimes, some minor details, seemingly insignificant things, may become the most fatal flaw in the method of the whole paper.

It's like Wiles proved Fermat's last theorem in the first place.

At first it was just mathematician Katz who found a flaw in the paper's mathematical logic framework.

Initially, both Wiles and Katz believed that this was just a 'little' defect, and a simple fix would suffice.

But when Wiles set out to fix the flaws, fragments of the logical framework proving Fermat's conjecture began to fall off.

At this time, Wiles realized that this seemingly "small" defect was not a simple mistake, and it might even exceed the scope of a repairable defect.

If it were a crack, an irreparable flaw, it would collapse the entire proof of the Theorem.

As time went by, more than eight months passed, and Wiles still failed to fix this loophole. At this time, he became more panicked and even began to doubt himself.

But fortunately, he finally found a useful method in the ashes of the failed technology, which completely made up for the defect, thus proving Fermat's last theorem.

So in mathematics, in science, never underestimate those seemingly insignificant problems.

These seemingly inconspicuous little problems are very likely to ruin all your previous achievements.

Days passed by like this day by day.

With the core method already finalized, Xu Chuan did not lock himself in the dormitory anymore.

He resumed his studies after a break of more than a month. He would go to Deligne to study every day, and sometimes he would listen to some basic courses with other doctoral students.

But more time is spent in the Flint Library of Prince University.

To launch a charge against Hodge's conjecture, there are too many preparations that need to be made.

Hodge's conjecture is very simple, so simple that it can be described in one sentence, but it is so complicated that only a very small number of professional mathematicians can really understand this problem.

"Every (of a certain type) harmonic and differential form on a nonsingular projective algebraic variety is a rational combination of the cohomology class of an algebraically closed chain."

When this sentence appeared in front of you, did you find that you didn't understand every technical term in this sentence.

There is not even a simple analogy for the Hodge conjecture.

Of all the Millennium Dilemmas, it is without a doubt the hardest of all Millennium Dilemmas.

It shows most clearly that the nature of modern mathematics makes much of it almost impossible for the common man to grasp. Even, you can't even find the threshold.

If you want to describe it in the simplest words, maybe you can describe it like this.

That is: "No matter how good or complex a palace is, it can be built from a pile of building blocks." In the words of literati: any geometric figure, no matter how complicated it is (as long as you can think of it), can be assembled with a bunch of simple geometric figures. "

For ordinary people, this should be the easiest to understand.

It's just that in actual work, we can't draw a complex multi-dimensional figure on a two-dimensional plane paper.

And Hodge's conjecture is to split complex topological graphs into individual components, and we can understand the designer's thinking as long as we install them according to the rules.

This is probably the easiest way to understand it.

If solving the Hodge conjecture is likened to the first climb of Mount Everest by human beings, it can be said that the mathematics world does not even have a base camp on Mount Everest.

Only when the tool in his hand was fully completed, climber Hodge guessed that the Everest base camp was first established, ready for climbers to advance to the summit.

As for how long it will take to establish this base camp, Xu Chuan doesn't know.

However, the progress of the matter seemed to be much smoother than he had imagined.

Before that, he promised Deligne and Witten a month, but now, less than twenty days have passed, and he has already started to finish this tool.

And his biggest breakthrough came from his ancestor, Mr. Grothendieck.

The Flint Library in Princeton is indeed a place with treasures. Here, Xu Chuan found some ideas left by his ancestors.

Something about Motive theory, that is about the construction of the standard conjecture by the grandfather.

is something about the representation of a series of Galois groups and Hodge structures in complex geometry, which completely determine the L-function, and in this case, field theory has solved the case of commutative Galois groups, let Xu Chuan turned his thinking to the original Weyl group.

With the help of this line of thinking, he successfully completed the final supplementary work.

Staring at the manuscript paper on the table, Xu Chuan took a deep breath, and then let out a long breath.

After two months of conceiving and sorting out, he finally completed the final work in September and built a tool that could launch a charge against Hodge's conjecture.

After checking the method in his hand completely, and after confirming that there was no problem, Xu Chuan picked up the mobile phone on the table, opened the address book, found the number of his mentor Deligne and dialed it.

"Hey~ Teacher, I need to take some time off. I may not be sure about the time."

After the phone was connected, Xu Chuan said to the other end. After hearing his voice, the other end was silent for a while before asking: "Have you completed the perfection of the method of that thesis?"

Maybe the phone sound is distorted? The tutor's voice on the other end of the phone trembled slightly, but the sense of satisfaction and accomplishment in his heart made him ignore these.

Nodding his head, Xu Chuan responded, "Well, I just finished it today, and I might use it to try Hodge's conjecture next, so I'm going to ask you for a leave of absence. As for how long it will take, I'm not sure. "

There was another silence on the other end of the phone, and Deligne's voice sounded after half a ring.

"Good luck~"