Chapter 187 The Undercurrent in the Mathematical World

After posting the proof of the Hodge conjecture on the arxiv preprint website, Xu Chuan closed his laptop.

His work has been completed, and the rest is up to other colleagues and time.

As for him, the most serious thing now is to wash up and have a good sleep.

When Xu Chuan fell asleep, undercurrents began to surge in the mathematics world.

On the arxiv preprint website, many scholars who paid attention to the Hodge conjecture, the seven millennium problems, algebraic clusters, algebraic geometry, algebraic topology, etc. received the website's recommendation for the first time.

France, Paris Science and Arts Research University.

A doctoral student is browsing the mathematics module on the arxiv preprint website.

If there is any school that can compete with Princeton University in mathematics, Paris Science and Arts Research University is definitely one of them.

Even leaving aside the Princeton Institute for Advanced Study, the mathematics department of Paris Science and Arts Research University may be better than Princeton.

And all this comes from another university under its name, the École Normale Supérieure de Paris.

The Ecole Normale Supérieure de Paris, referred to as "Ecole Normale Supérieure de Paris", has a history of more than 200 years, almost the same age as France.

It has cultivated countless outstanding talents for the Gallic chickens. In mathematics, the well-known top giants such as Lagrange, Cauchy, Galois, Fourier, Laplace, Romain Rolland, etc. all come from this college.

For this school, there is a saying: "If you are admitted to the Department of Mathematics of the Ecole Normale Supérieure de Paris, you are the closest group of people to the Fields Medal", which shows how strong the mathematics of this school is.

For mathematicians who have entered this school, keeping an eye on the forefront of mathematics is one of the most important things.

Whether it is a mathematical paper in a mathematical journal or a preprint website such as arxiv, they are all sources of cutting-edge knowledge.

The former is stable and reliable, and although the latter has uneven quality and is full of dross, many mathematicians still like to post their papers and ideas on it.

For a doctoral student, many very creative ideas on the arxiv preprint website are very inspiring to them.

After all, those who can enter the doctoral program have basically entered the stage of creating knowledge.

Not everyone has enough inspiration. Often, getting some ideas from others and then expanding or patching them up is already a good thing.

After roughly flipping through the papers in algebraic geometry and algebraic topology in the mathematics module and selecting a few papers that he was interested in, Theophile Hampry shook his head and rubbed his eyes, then got up and prepared to make himself a cup of coffee.

On the arxiv website, today was another day without any gains.

But this is normal. Although arxiv is full of all kinds of strange ideas, and even a lot of folk science mathematics, most of the things in it, especially those new ideas that have been uploaded recently, are almost worthless.

However, at this moment, his personal page suddenly received a prompt from the arxiv website.

Theophile Hampry glanced at the prompt label, which came from his attention, algebraic geometry and algebraic topology.

Although he knew in his heart that this was very likely to be another dregs that was not worth wasting time, he finally couldn't help moving the mouse and clicking on the prompt sent to him by the website.

[On a non-singular complex projective algebraic variety, any Hodge class is a rational linear combination of algebraic closed chain classes. ]

When he saw the title, Theophile Hampry's eyelids twitched.

Isn't this title the Hodge standard conjecture?

For the papers related to the seven millennium problems found on the arxiv preprint website, Theophile Hampry was full of disdain.

To be honest, most mathematicians don't even have the courage to charge at the seven millennium problems.

Only by entering the field of mathematics can you understand how profound they are.

Perhaps only those "folk scientists" will throw the proof ideas of the seven millennium problems on arxiv.

After all, those "messy", "extremely outrageous" and "incomprehensible" ideas will not be accepted even by the most garbage mathematics journals.

Only arxiv, a preprint website without peer review where you can freely publish your own opinions, has enough "heart" to accommodate these things.

Theophile Hempry, who was squatting in front of the computer at the moment, had such an idea.

Previously, he had seen many amateur scientists' ideas about various mathematical conjectures on arxiv, and the most were the proofs of the 'Goldbach Conjecture' and the 'Grand Unified Theory of Mathematics'.

The former is because it is simple enough.

[That is, any even number greater than 2 can be written as the sum of two prime numbers. ]

This problem is so simple that anyone can understand it, and even if they have not studied mathematics, they can pretend to write a few sentences.

For example, 4=2+2, 6=3+3, 8=3+5, 10=3+7. Therefore, this simple question also makes many people mistakenly think that its proof will not be too difficult.

And the latter is probably because it is famous enough.

After all, with the thinking of those amateur scientists, they all want to make a big deal.

Proving a big mathematical conjecture is like digging up an ancient emperor's tomb. Falsification means that there is nothing inside after digging it up, and the crowd of onlookers will disperse with a bang.

But to prove it, even if you don't dig up the tomb, you can still hold some stones and claim that they are gold, and then the onlookers will rush in. Some say it is fake, some say it is real, and some say what if it is real? Some say that even if it is true, it must be authenticated by the authority, and some say that the authority owes people an apology for blindly authenticating.

In the end, the amateur scientist left happily, leaving a bunch of people arguing.

But in fact, these people probably don't even know what the grand unified theory is, and what is the difference between the Goldbach conjecture and 1+1=2.

So almost all mathematicians are basically dismissive of these things produced by amateur scientists, and Theophile Hampry is the same.

If it is a mathematical paper related to the Goldbach conjecture or the grand unified theory, he will cross it out without hesitation.

However, the paper related to the Hodge conjecture aroused his curiosity.

After all, this is the most difficult problem to understand among the seven millennium problems.

Not to mention those amateur scientists, even many mathematicians may not be able to fully understand this problem.

With the idea of ​​seeing what the other party wrote, Theophile Hempry clicked on the link and jumped into the other party's field.

In addition to the familiar title of the paper, what came into view was the name of the contributor.

Xu Chuan

Theophile Hempry: ? ? ? ? ? ?

When he saw this name, he was stunned.

As the most popular and shining star in the mathematics world today, the youngest winner of the Crafford Mathematics Award and the Crafford Astronomy Award at the end of last year, I am afraid that anyone working in the mathematics industry will pay attention to this name.

In the eyes of ordinary mathematicians, this is a "strange" genius.

There was almost no preparation before, and almost no mathematical papers were published, and then he directly proved the weakened form of the world-class problem Weyl_Berry conjecture, which caused a sensation in Princeton at the time.

Then, in just a few months, he pushed the proof of the weakened form of the Weyl_Berry conjecture directly to the complete Weyl_Berry conjecture.

Not only that, after completing the proof of this mathematical conjecture, he used the Xu-Weyl-Berry theorem to create a calculation tool that can be called the "ancestor" level in the astronomical community.

After that, he successfully solved the mystery of the proton radius, a problem that has troubled the physics community for several years, using mathematical methods at CERN.

Seeing the name of the author of the paper, Theophile Hempry was stunned for a moment.

Could it be that this rising star in the mathematical world has solved the Hodge conjecture again?

How is this possible?

These are the seven millennium problems, not some garbage mathematical conjectures.

For more than a century, countless mathematicians have launched attacks on these seven problems, including those who are familiar with them, such as Hardy, Hilbert, Sir Atiyah, etc.

But so far, only one has been solved.

"Is there really a hope of solving the Hodge conjecture? This is too unimaginable."

Muttering in his mouth, Theophile Hampry opened the paper and read it word by word, even the most basic introduction and preparatory knowledge, he did not miss it.

However, it is regrettable that he frowned soon.

The beginning of the paper was fine, relying on his own mathematical reserves, he successfully got into it, but he frowned after just turning over less than three pages of manuscript paper.

Because he began to not understand it.

Staring at the formula on the computer screen, Hampry sighed.

I thought I could get some inspiration or knowledge from this paper, but I didn't expect to encounter the biggest problem at the beginning. He couldn't understand the calculation process of the paper.

Although not all, the first three pages of manuscript paper are mixed with mathematical knowledge from four different fields, such as algebraic geometry, projective clusters, Riemann geometry, and extension fields.

Among them, Riemann geometry and extension fields are fields he has not studied in depth.

Shaking his head, Theophile Hampry downloaded the paper from the arxiv website, then passed it to the printer and printed it out completely.

With the remaining warm paper, he quickly rushed to his tutor's office.

"Teacher, I saw a paper about the Hodge conjecture."

Without knocking on the door, Theophile Hampry rushed into the office.

In the office, Hampry's tutor, Edbet Shipley, frowned at the student who rushed in, and said unhappily: "Hampry, I have a guest here, and I'll talk about it later."

Hearing this, Theophile Hampry noticed the other old man sitting on the sofa in the room, and hurriedly said: "Sorry, teacher, I'm too excited."

After that, he was about to leave the office, but a voice in his ear stopped him.

"Please wait a moment."

The voice came from the old man sitting on the sofa, with a hint of curiosity and interest in his eyes: "You just said that you found a paper related to the Hodge conjecture? ”

Theophile Hampry stopped and turned around to reply: “Yes, today when I was browsing the arxiv website as usual, I found a new paper that proves the Hodge conjecture. ”

Hearing this, the old man on the sofa and Edbet Shipley both had disappointment in their eyes.

Although arxiv is the most commonly used website for mathematicians, most of the papers and ideas related to mathematics on it are worthless dregs.

If it is an idea, it may be better.

But forget about the paper proving the Hodge conjecture.

Apart from a weirdo like Perelman, who else would post a paper solving the seven millennium problems on a preprint website?

This is impossible.

If the paper is valuable, it should appear in the hands of editors of journals such as "Annals of Mathematics" and "New Advances in Mathematics", not on a website like arxiv.

Theophile Hampry clearly saw the changes in the demeanor of his mentor and the old man. After thinking about it, he added: "The author who uploaded this paper is Xu Chuan, who has won the Crafford Award before."

Hearing this, the old man on the sofa and Edbet Shipley were stunned, with strange expressions on their faces.

"Are you talking about proving the Weyl-Berry conjecture?"

The old man on the sofa asked with surprise.

He did not attend the presentation of the Crafoord Prize last year, but he had heard that it was a very young genius.

Theophile Hampry nodded. He always felt that the old man with sparse hair looked familiar, as if he had seen him somewhere.

After thinking about it in his mind, his eyes suddenly brightened and he excitedly asked, "Are you Professor Alain Connes?"

The figure in his mind gradually overlapped with the old man in the gray woolen sweater in front of him, which made Hampry very excited. This was his idol, and he did not expect to see him here.

Alain Connes, a contemporary mathematics master, a winner of the Fields Medal, and a top mathematician in France, once formulated seven millennium problems at the Clay Institute with Professor Wiles, who proved Fermat's Last Theorem.

Hearing his name, the old man sitting on the sofa nodded with a smile and said, "Can you help print out the paper?"

On the side, Edbet Shipley also added, "Print a copy for me too."

Although he was puzzled about posting such an important paper on a website like arxiv, he also had a little doubt in his heart, wondering whether the paper on it was a "normal" paper.

But he had read the proof paper of the Weyl-Berry conjecture and some mathematical methods derived from the Xu-Weyl-Berry theorem. Both the former and the latter can be said to be very exquisite.

It is still worth reading what such a mathematical genius published. At least, papers related to such major conjectures should not be missed.

Maybe, this is another geek like Perelman?

After handing the two papers to his mentor and idol respectively, Theophile Hampry waited on the side.

Time passed by minute by minute.

After waiting for a long time, he did not wait for the two professors to express their opinions.

Although he knew that the proof of such an important conjecture would not be figured out in a short time, Hampley still couldn't wait to know the result.

After all, this is the Hodge conjecture, one of the seven millennium problems.

It is not only related to the one million gold medals of the Clay Mathematics Institute, but also countless other mathematics awards, and the most important thing, changing mathematics!

After forcing himself to wait for more than half an hour, Theophile Hampley finally couldn't help it. He looked at his mentor and idol who was still holding the paper, and asked eagerly: "Mentor, Professor Connes, has the Hodge conjecture been proved?"

Hearing the question, Edbet Shipley raised his head and said: "I don't know~"

"Strictly speaking, I don't even understand some of the mathematical methods in this paper."

Theophile Hampley was surprised. Although his mentor was not as good as Alan Connes who had won the Fields Medal, he was also a top mathematician who had won international awards such as the Gauss Prize.

Now he even said that he couldn't understand this paper. Isn't this a bit too crazy?

Swallowing his saliva in surprise, Hampry turned his eyes to Alainconne, who was still reviewing the manuscript in his hand, and Edbet Shipley also looked over.

Noticing the gazes of the other two, Alainconne put down the manuscript in his hand and sighed: "There are too many mathematical fields involved in this paper, from algebraic geometry to algebraic topology, to Riemann surfaces and multiple manifolds. Even for me, it is not an easy task to understand this paper. It may take several months or more."

Hearing this, Theophile Hampry couldn't help swallowing the air again.

If even Professor Alainconne couldn't understand this paper, who else could prove whether it was correct?