Noticing Deligne's gaze, Witten shook his head, handed him the manuscript paper in his hand, and said, "I can't make much evaluation of this method in a short time. ”

Although this method is very familiar with algebraic geometry and topology and manifolds, it is mixed with a lot of group theories and metric spaces..... and other mathematical methods and concepts, and these areas are outside the scope of my research. ”

"It's no exaggeration to say that I may not be able to understand this paper in a short period of time, after all, in mathematics, my knowledge is basically related to physics, and many of the mathematics in the methodology of this paper are not within my scope of study."

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

Mathematical physics is inherently a frontier and hot field in the field of 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.

Witten has been working in the frontier fields of theoretical physics and mathematical physics for nearly 50 years, and in the field of mathematical physics, he is now in the top three, not to mention the first position.

How can it not be surprising that he has now said that he will not be able to understand the methodology of this paper in a short period of time.

With a hint of surprise and doubt, Deligne took the manuscript paper from Witten's hand, and Witten, who took the manuscript left behind by Professor Mirzahani and read it.

The dormitory in the sunset was quiet again, but this time it didn't take long, and in half an hour, Deligne and Witten put down the manuscript in their hands one after another.

"It's really subtle, and it introduces multifractals, dimensionality, group theory, metric spaces, Riemann surfaces, projective clusters, ...... These concepts are quite complex, and even if I had to understand them, it was not so easy. ”

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

Now he understands why Witten would say that he couldn't read the paper in a short period of time.

Not to mention Witten, it's him, it will take a certain amount of time to understand the method of this paper.

Half an hour was only enough time for him to roughly go through the manuscript paper in his hand, and almost nothing about the core things had time to think.

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

But a scientific intuition told him that with this tool, there might be real hope for solving the Hodge conjecture.

Thinking about it, Deligne glanced at Xu Chuan, who was sitting on the other side and was busy with something, and sighed with some emotion.

As a disciple of his, not to mention that his mathematical ability has surpassed him, it is definitely not far from him.

What's more, he is still young and talented, less than 20 years old, and can enter the golden age of a scholar or scientific researcher.

Give him some more time, how far can he grow?

Comparable to a mentor, or higher?

Suddenly, some figures came to Drenne's mind.

He didn't know why such thoughts were in his head.

But he knows that every time such a person appears in history, he can single-handedly promote the development of science and even the whole society.

For example, Archimedes, Gauss, Newton......

......

Deligne and Witten left, leaving Xu Chuan alone in the dormitory to sort out the manuscripts in his hands.

Suddenly, he patted his head in frustration.

He remembered that he had just been patronizing his own business, and had forgotten to ask Witten what was the matter with the previous call to him.

I picked up my phone from the table and dialed Witten, and after two rings, the phone was quickly connected.

"Hey, Xu Chuan, what's the matter?" On the other end, Witten's inquiring voice came.

"Teacher, did you call me for anything earlier? I just forgot to say it. Xu Chuan asked.

"Actually, it's nothing, it's just that the collision experiment in the second half of the year has already begun, and I have a group of experiments here, ask if you are interested in participating in it. But now that you have more important things in your hands, forget it, you can deal with the paper in your hand first. ”

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

For him in his previous life, he officially started to get in touch with high-energy physics after 18 years, so the experiments of 16 and 17 years were blank for him.

If there is an opportunity to get in touch, he will naturally not give up.

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

】

Xu Chuan is not very interested in this kind of experiment, even if he has never experienced it, he is interested in the exploration of the unknown, the discovery of new particles, and the transcendence of the Standard Model.

"The work in the second half of this year is mainly to find subatomic particles, in order to complete the Standard Model, and to conduct a study of the fundamental symmetry between hydrogen atoms and antihydrogen atoms."

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

"Looking for subprimordial particles and fundamental symmetry?"

Xu Chuan touched his chin and thought for a moment, and then asked, "Teacher, when did the basic symmetry between hydrogen atoms and antihydrogen atoms be studied?" ”

He was not very interested in the collision experiments to find sub-protoparticles, and in his perspective, the various sub-protoparticles discovered over the years were basically known, and it was clear who discovered them, and he was also very clear about the characteristics of these sub-proto-particles.

He doesn't have much interest in cutting off other people's discoveries and chances in advance, and doing what is destined to happen in history.

On the other hand, he was interested in the study of the basic symmetry between atoms and anti-hydrogen atoms.

At least, as far as he can remember, he had never heard of any major discoveries or breakthroughs in the study of basic symmetry in the past year or seven.

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

After all, the most important thing to do now is to make up for the tools at hand and try to break through the Hodge conjecture compared to a collision experiment.

That's the most important thing right now.

As for the Euratom collision experiment, there is still a lot of time to do in the future.

If enough discoveries are made, it is not impossible to repeat a particle collision experiment with the exact same parameters and energy levels.

"Is the fundamental symmetry between hydrogen atoms and antihydrogen atoms studied?"

"This experiment will be a little later, the current plan is for December, by Alpha Labs, what, are you interested in this?"

Witten's curious voice came from the phone, Xu Chuan nodded with a smile, and said, "Well, I'm quite interested in the study of basic symmetry, and I won't go to the subatomic particle discovery experiment." Hopefully, I'll be able to get my hands done by December. ”

Witten smiled and said, "Don't worry, you still have time." ”

After a pause, he continued, "If there's anything new to Hodge's conjecture, let me know." ”

Xu Chuan nodded and said, "Of course." ”

.......

Hanging up the phone, Xu Chuan reimmersed himself in perfecting the mathematical method in his hand.

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

Sometimes, small details, things that seem less important, can become the most fatal flaw in the entire essay methodology.

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

At first, it was just the mathematician Katz who found a flaw in the mathematical logical framework of the paper.

Initially, both Wiles and Katz thought it was a 'minor' flaw that could be fixed simply.

But as Wyles set out to fix the flaws, the pieces of the logical framework that proved Fermat's conjecture began to fall off.

It was only then that Wiles realized that this seemingly 'small' flaw was not a simple mistake, and that it could even go beyond a repairable flaw.

If it were a crack, a flaw that could not be repaired, it would have made the whole proof of the Great Theorem collapse.

As time passed, more than eight months later, and Wiles still failed to fix the vulnerability, at which point he became more and more panicked and even began to doubt himself.

But fortunately, he finally found a useful way to completely remedy the shortcomings in the remnants of the once failed technology, thus proving Fermat's theorem.

So in mathematics, in science, never underestimate seemingly inconspicuous problems.

These seemingly inconspicuous small problems are very likely to bury all your previous achievements.

......

The days passed like this, day by day.

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

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

But more time was spent in the flintstone library at Prince University.

There is too much preparation to charge Hodge's conjecture.

The Hodge conjecture is simple, simple enough to describe in a single sentence, but it is so complex that only a handful of professional mathematicians can really understand the problem.

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

When this sentence appears in front of you, do you find that you don't understand every technical term in this sentence?

I didn't even think of a simple analogy to the Hodge conjecture.

Of all the millennial puzzles, it is undoubtedly the most difficult to understand of all.

It illustrates most clearly that the nature of modern mathematics makes much of it almost impossible for the average person to grasp. You can't even find the threshold.

If I had to describe it in the simplest words, it would probably be like this.

That is: "No matter how good and complex a palace is, it can be made of a pile of bricks." In literati parlance: any shape of geometry, no matter how complex it may be (as long as you can imagine it), can be put together from a bunch of simple geometric figures. ”

For the average person, this should be the easiest to understand.

It's just that in practice, we can't draw a complex multi-dimensional figure on a two-dimensional flat piece of paper.

The Hodge conjecture is to break down the complex topological graphics into components, and we can understand the designer's mind as long as we install them according to the rules.

This is probably the simplest way to understand.

If the solution of the Hodge conjecture is likened to the first human ascent of Mount Everest, it can be said that the mathematical community does not even have a base camp on Mount Everest.

It was only when the tool in his hands was completely completed that the base camp for climbing Hodge's conjecture on Mount Everest 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, things seemed to be going much smoother than he expected.

The time he had promised Déligne and Witten was a month, but now, less than twenty days later, he had already begun to put the finishing touches on the tool.

And its biggest breakthrough point actually came from his ancestor 'Mr. Grothendieck'.

Princeton's Flintstone Library is a place of treasure, and here, Xu Chuan found some of the ideas left by his grandfather.

Something about Motive's theory, it's about the construction of the standard conjecture of the grandfather.

It's about the representation of a series of Galova groups and something about the Hodge structure in complex geometry that completely determines the l function, and in this case, the class domain theory has solved the case of commutative Galova groups, allowing Xu Chuan to turn his mind around the original Weyl group.

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

.......

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

After two months of conceiving and organizing, he finally completed the final work in September, building a tool that could charge Hodge's conjecture.

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

"Hey~, teacher, I need to take a leave of absence for a while, and the time may not be very certain."

After the phone was connected, Xu Chuan said to the other end, and after hearing his voice, the other end was rarely silent for a while before asking, "Have you completed the improvement of the paper method?" ”

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

Nodding, Xu Chuan responded: "Well, I just finished it today, and next, I may use it to try the Hodge conjecture, so I'm going to ask you for a leave, as for how long it will take, I can't be sure." ”

There was silence on the other end of the line for a while, and it was only after half a ring that Deligne's voice rang.

"Good luck~"

..........