Great Country Academician

On the side, Wei Teng raised his head and said: "I think the Weyl group mapping of algebraic varieties is more essential. It directly reverses the application of the maximum torus, which makes me feel quite amazing."

After a pause, Wei Teng then added: "This is a brand new way of thinking, maybe it can continue to expand on it."

Hearing this, Professor Deligne thought for a while, his eyes suddenly lit up, and he said quickly: "The topology of algebraic varieties and algebraic manifolds!"

Wei Teng smiled and said: "Yes, I should be more sensitive to this aspect than you. You know, I am better at quantum field theory, string theory and related topology and geometry."

"If we start from this aspect and continue to extend, it may become a new tool for solving the problems of differential form types generated by non-singular projective complex algebraic varieties"

Before Witten finished speaking, Deligne added: "For example, Hodge's conjecture."

On the side, Xu Chuan looked at the two mentors with a smile, and sighed in his heart.

As expected of the two top experts in the mathematics world, after just reading it, they noticed the two most critical and core points in this paper on the association method of algebraic varieties in field theory.

One is used to solve the irreducible decomposition problem of differential algebraic varieties, and the other is extended to solve Hodge's conjecture.

Even though the two instructors in front of me are already in their sixties or seventies, their sensitivity to mathematics is still terrifyingly high.

No detail, even a small one, could escape their eyes.

Hearing Deligne's words, Witten put down the manuscript in his hand and said, "Indeed, it may have such a potential, but it's unknown whether this path will work."

After a pause, he looked at Xu Chuan, and continued, "I wonder if you have thought about this?"

Xu Chuan grinned and said, "Of course I have. In fact, I've almost finished this job."

Hearing this, Deligne and Witten were stunned at the same time.

Almost done, what do you mean?

"Have you solved Hodge's conjecture?" Wei Teng couldn't hold back and asked tentatively. If that's what he meant, it would be too scary.

Xu Chuan shook his head and said, "That's not true. I just expanded and extended the idea of ​​generation, and used it to make a mathematical tool."

"I have been dealing with this these days. I haven't finished it all. I just made a core and I haven't had time to sort it out. Otherwise, I would bring it here today."

Hearing that Hodge's conjecture had not been resolved, Witten and Deligne were relieved at the same time.

If it is said that their student killed Hodge's conjecture in more than a month, that would be really appalling.

This is Hodge's conjecture, one of the seven millennium puzzles.

The millennium is a thousand years on the calendar. As the name suggests, it means a thousand years. The first millennium is 1000 years, and the second millennium is 2000 years.

Of course, the seven millennium problems are not problems that need human beings to solve in a thousand years.

It is the seven mathematical conjectures announced on May 24, 2000. Because of the special year, they are called the seven millennium problems.

Although it does not mean that it will take a thousand years to solve, when the Clay Institute of Mathematics and Wiles, Connie and other top professors drafted these seven mathematical problems, it is ready for the mathematics community to solve in a whole century prepared.

A century, a hundred years, to solve seven mathematical problems, we can see the difficulty of these seven mathematical conjectures.

Facts have also proved the difficulty of these seven questions. As of now, more than ten years have passed, and only the Poincaré conjecture has been solved.

This was accomplished through the efforts of countless mathematicians after the 1930s.

From the Whitehead manifold and Dean's lemma in the 1930s, to the high-dimensional Poincaré conjecture in the 1960s, which was proved one after another, to the Ritchie curvature flow in the 1970s and 1980s.

Countless people have made great contributions to the Poincaré conjecture, and it was finally Perleman who put the roof on the problem of the century.

As for the other millennium problems except the Poincaré conjecture, if there is some progress in the other several problems, it may be the BSD conjecture.

In 2014, Manuel Bhargava, a professor at Princeton University who won the Fields Medal, said that there are currently "probably one more of the seven millennium problems solved than I expected."

Professor Bhargava has recently reported a number of results related to the Beh and Swinton-Dell conjectures.

In one of the results, he said that he and his colleagues "demonstrated that more than 66% of elliptic curves satisfy the Bech and Swinton-Dale conjectures".

This means that the Beh and Swinnerton-Dell conjecture, that is, the BSD conjecture, has been overcome halfway.

Of course, no one knows how long it will take to conquer the remaining half.

Maybe three years, maybe five years, maybe thirty or fifty years may not be able to complete.

Even if one is able to look up at the peak, but before reaching the peak, no one can know how tortuous the road ahead is, and whether there is an abyss that cannot be crossed.

Apart from this, there is not much progress on the other millennium problems.

And like the Riemann conjecture, a super problem that was proposed in the 19th century and spanned three centuries, there is almost no movement.

Finding the answer to the Millennium Prize Puzzle is akin to trying to climb Mount Everest for the first time.

Along the way, there are many steps, which symbolize the progress made.

But the real question is: "Can you make it to base camp? Even if you can, you know you're still far from the summit."

As for problems such as the Bayh, Swinton-Dell conjecture, and the Riemann conjecture, the current mathematical community is obviously still in Nepal, which is one of the starting countries for climbing Mount Everest.

Even if they can successfully reach the base camp of Mount Everest, mathematicians may still need additional "equipment" to reach the summit.

Just like the "p-adic perfect space theory" established by Peter Schultz, using this tool, mathematicians can make a series of major breakthroughs in the Langlands program.

The same is true for solving the seven millennium problems. Perhaps for each problem, mathematicians need to build one or more new tools to remove it from the palace of mathematics.

"You mean, you made a mathematical method following the idea of ​​the Weyl group mapping of algebraic varieties and the reversal of the maximum torus?"

After soothing his violently beating heart, Wei Teng asked impatiently.

Although I really believe in the mathematical ability of the student in front of me, no matter how I look at it, in more than a month, while solving the problem of irreducible decomposition of differential algebraic varieties, I also made a mathematical analysis that may be used in Hodge's conjecture. The method is incredible too.

Perhaps the problem of irreducible decomposition of differential algebraic varieties has the help of another Fields Medalist, but mathematical methods for solving Hodge's conjecture or problems of the type of differential form that arise from nonsingular projective complex algebraic varieties, this is his own achievements.

Have the young people of today become so perverted?

Previously, Dr. Schultz made a "appearing complete geometric theory method", and later, his student also made new mathematics during his doctoral period.

More importantly, the latter is younger than the former.

Hearing this, Deligne on the side also cast a concerned look. Xu Chuan nodded and said, "Some ideas and cores have been compiled, but they haven't been sorted out and perfected yet."

After the words fell, Wei Teng quickly asked: "Then how long will it take you to sort it out?"

Compared with Deligne, he is more concerned about whether Hodge's conjecture can be solved.

Because the Hodge conjecture is related to a series of physical problems such as general relativity, M theory, and three-dimensional physics.

Hodge's conjecture is one of the basic carriers of general relativity and M-theory structural geometry topology, and its importance to physics is beyond doubt.

As a physicist, he has solved the positive energy theorem in general relativity, and is also the main core figure of M theory and string theory. No one pays more attention to the research and attention of these two aspects than him.

Xu Chuan thought for a while and said, "Maybe it will take about a month?"

After a pause, he then added: "Now I just made a core, it has not been verified, and it is not an easy thing to continue to improve."

Wei Teng took two deep breaths, suppressed his beating heart and wild thoughts, and said, "Can I read your manuscript?"

It is actually a very presumptuous thing to ask others to read unfinished and unpublished manuscripts, even in front of your own students,

But at the moment Wei Teng can't care so much, he just wants to see hope at the first time.

He proposed and perfected M theory, but he also struggled on this road for most of his life. Now that he sees a glimmer of hope, he can't wait.

Xu Chuan nodded and said, "Of course."

Witten made a request, and Deligne followed along.

A group of three people came to Xu Chuan's dormitory and opened the door. The bad environment even made the two old people who entered the dormitory nowhere to go.

In the dormitory, waste paper was all over the floor, some were crumpled up, some were scattered in the corner, and in the corner, there was still a bag of household garbage that had not been cleared out.

Seeing this scene, Xu Chuan smiled awkwardly and said, "I've been sorting out my thoughts these days, and I haven't had time to tidy up the dormitory yet."

But neither Deligne nor Witten showed any dislike.

This is where science is born. No matter how dirty or messy the surface is, it cannot conceal the knowledge contained within.

Walking into the dormitory, Deligne leaned over and picked up a crumpled waste manuscript from the ground.

When it was disassembled, the black writing inside occupied about half of the manuscript paper.

Looking from top to bottom, we can see the fluctuation of the writer's thoughts, from the smooth writing at the beginning without any alterations, to the intermittent writing at the end, the smearing of revisions, and the last one was written by the author before it was finished. The formula with the horizontal line completely crossed out shows the author's tossing on this road.

Deligne didn't care that it was a waste manuscript. After smoothing the manuscript paper with his palm, he began to read it with relish.

As for Wei Teng, he is not very interested in these messy manuscript papers on the ground, or he is more interested in the complete method, so from the moment he entered the door, his eyes fell on the stack on the desk. on thick printing paper.

That records methods for solving differential form-type problems arising from nonsingular projective complex algebraic varieties.

The two top bosses were sitting in the dormitory, and Xu Chuan couldn't stay indifferent any longer. He started tidying up the dormitory while Deligne and Wei Teng were browsing the manuscript paper.

The manuscript paper on the ground, whether it was useful or useless, even if it was crumpled, was picked up by him temporarily and put aside.

These things, even if they are completely discarded and useless, have extremely high collection value. At least for himself that is the case.

After all, these things have witnessed the complete process of the birth of a new mathematics.

If this mathematical method can be used to solve the Hodge conjecture, their value will be increased to unparalleled. After all, no matter when, knowledge is the most precious wealth.

"Xu Chuan, where is the manuscript that Professor Mirzakhani left for you?"

After reading the waste manuscript in his hand, Professor Deligne put it on the desk and asked Xu Chuan.

Although he is also interested in Xu Chuan's research results, Wei Teng has already occupied the manuscript paper and is flipping through it. Instead of leaning over to read it together, it is better to look at Professor Mirzakhani's manuscript first.

The only female Fields Medal winner in history, what left behind before her death is fascinating to any mathematician.

"Wait a mininute."

Xu Chuan responded, and after sorting out the manuscript paper in his hand in order, he found the manuscript from the bookcase and handed it to the math tutor.

Looking at the manuscript that was completely preserved in the storage bag, Deligne showed a glimmer of approval in his eyes.

Maintaining respect for the achievements of others is a necessary scientific spirit.

In dormitory No. 306, Deligne and Witten were immersed in the manuscripts in their hands.

Time passed bit by bit, until the sun set on the mountain and the golden afterglow shone in through the glass window, the two big men woke up one after the other.

"As expected of Professor Mirzakhani, the ideas left behind are amazing."

Looking at the golden afterglow falling on him through the glass window, Professor Deligne pushed the glasses on the bridge of his nose with one hand, and pinched the deep part of his nose.

From this manuscript, he saw the initial starting point of the problem of "incompressible decomposition of differential algebraic varieties", and also saw the insights of this female Fields Medal winner in Riemannian geometry, differential geometry, Weyl group, and algebraic group .

Deligne believes that this is not all of Professor Mirzakhani, and it may not even be one percent.

But it is a pity that the life of such an excellent mathematician stopped this year.

Sighing slightly in his heart, Deligne looked up at Witten, wanting to see his evaluation of the mathematical method in his hand.