After dropping the proof paper of Hodge's conjecture onto the ARXIV preprint website, Xu Chuan closed his laptop.

His work has been completed, and the rest is left to the rest of his peers and time.

As for him, it's the most serious thing to do now to wash up and get a good night's sleep.

......

When Xu Chuan fell asleep, an undercurrent began to surge in the mathematical world.

On this ARXIV preprint site, a lot of attention is paid to the Hodge conjecture, the Seven Millennium Problems, algebraic clusters, algebraic geometry, algebraic topology, ..... Scholars who waited for the label received the recommendation from the website for the first time.

France, Paris University of Arts and Sciences Sciences.

A PhD student browses through a mathematics module from Arxiv's preprint website.

If there is any school that can compete with Princeton University in mathematics, it is the Paris University of Arts and Sciences.

Even aside from the Institute for Advanced Study in Princeton, the mathematics department at the Institut des Arts et Lettres de Paris is probably even better than Princeton.

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

The École Normale Supérieure de Paris, abbreviated as the "École Normale Supérieure de Paris", has a history of more than 200 years, almost the same age as the country of France.

It produced countless outstanding talents for the Gallic chicken, and in mathematics, the top giants we know as Lagrange, Cauchy, Garois, Fourier, Laplace, Durkheim, Romain Rolland, etc., all came from this academy.

There is a saying about this school: "If you are admitted to the mathematics department of the École Supérieure de Paris, you are the closest group of people to the Fields Medal", which shows the strength of mathematics in this school.

And for mathematicians who have already entered this institution, keeping an eye on the frontiers of mathematics is one of the most important things.

Whether it's a mathematical paper in a mathematics journal or a preprint website like ARXIV, it's a source of cutting-edge knowledge.

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

For a PhD student, the many creative ideas on Arxiv's preprint site are very inspiring.

After all, to be able to enter the doctoral program, you have basically entered the stage of creating knowledge.

Not everyone has enough inspiration, and a lot of times, it's good to get some ideas from other people and then expand them yourself, or patch them up.

After cursively flipping through the papers in Algebraic Geometry and Algebraic Topology in the math module, and selecting the manuscripts he was interested in and reading a few, Theophile Hampley shook his head and rubbed his eyes, and got up to make himself a cup of coffee.

】

On the arxiv webpage, today is another day with little to gain.

But that's normal, and while Arxiv is full of weird ideas, and even a lot of folk math, most of it, especially the new ideas that have come out recently, are of little value.

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

Theophile Hampley glanced at the prompt labels, from his concern, algebraic geometry, algebraic topology.

Although he knew in his heart that there was a great possibility that this was another piece of dross and not worth wasting his time, in the end, he still couldn't resist moving his mouse and clicking on the prompt sent to him by the website.

[On a nonsingular complex projective algebraic cluster, any Hodge class is a rational linear combination of algebraic closed-chain classes.] 】

Seeing the title, Théophile Hampley's eyelids jumped.

Isn't this title the Hodge standard conjecture?

Théophile Hampley was dismissive of finding papers on Arxiv's preprint site related to the Seven Millennium Puzzles.

To be honest, in the minds of most mathematicians, the seven millennial problems do not even have the courage to charge against them.

Only by entering the profession of mathematics can you understand how broad and profound they really are.

Perhaps only those 'civil sciences' will throw the proof of the seven millennial problems on arxiv.

After all, those ideas that are 'messy', 'outrageous' and 'can't even be understood by themselves' will not be accepted even by the most rubbish mathematics journals.

Only a preprint site like arxiv, which has no peer review and is free to express its own opinions, has the 'heart' to accommodate these things.

And Théophile Hampley, who is squatting in front of the computer at the moment, has such an idea.

Previously, he had seen a lot of civil ideas about various mathematical conjectures on arxiv, and the most important ones were the proofs of the 'Goldbach conjecture' and the 'grand unified theory of mathematics'.

The former is because it's simple enough.

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

This question is so simple that anyone can understand it, and even if they have not studied mathematics, they can pretend to be two sentences.

For example, 4=2+2, 6=3+3, 8=3+5, 10=3+7...

And the latter, probably because they are famous enough.

After all, with those civil science thinking, they all want to make a big one.

Proving a big mathematical conjecture is like digging up an ancient emperor's tomb, and the falsification is that there is no hair in it after digging it up, and the crowd of onlookers disperses with a bang.

But it proves that even if you don't dig a grave, you can take some stones and claim that it's gold, and then the people who eat melons rush up, some say it's fake, some say it's true, and some say what if it's true? Some say that even if it is true, it must be authenticated by authority, and some say that the authority owes an apology to the person for blind identification......

In the end, Minke left happily, leaving a bunch of people arguing there.

But in fact, these people may not even be able to figure out what the grand unification theory is, the difference between Goldbach's conjecture and 1+1=2.

So almost all mathematicians are basically dismissive of these things made by civil science, and Théophile Hampley is no different.

If it was a mathematical paper related to Goldbach's conjecture or grand unified theory, he would not hesitate to fork it out.

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

After all, this is the most difficult of the seven millennial problems to understand.

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

With the idea of seeing what the other party had written, Theophile Hampley clicked on the link and jumped into the other party's domain.

In addition to the familiar title of the paper, the name of the contributor also catches your eye.

xu·

Theophile Hampley: ??????

When he saw this name, he was directly stunned.

As the reddest fried chicken in mathematics today, the shining star of the younger generation, and the youngest winner in history to win the Cafford Prize in Mathematics and the Cafford Prize in Astronomy at the end of last year, I am afraid that anyone who works 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 foreshadowing, and almost no mathematical papers were published, and then it was directly proved in the weakened form of world-class problems weyl_berry conjectures, which caused a sensation at Princeton.

Subsequently, in just a few months, the weakened form of the weyl_berry conjecture proof was pushed directly to the full weyl_berry conjecture.

Not only that, but after completing the proof of this mathematical conjecture, he used the xu-weyl-berry theorem to create a calculation tool in the astronomical community that can be called the 'grandfather'.

Since then, he has successfully solved the mystery of the proton radius, a problem that has plagued the physics community for several years, using mathematical methods.

Seeing the name of the author of the paper, Théophile Hampley was instantly stunned.

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

How is this possible?

These are the seven millennial puzzles, not some kind of rubbish math conjecture.

For more than a century, countless mathematicians have charged these seven questions, including those who have known well, such as Hardy, Hilbert, Sir Atia, and so on.

But so far, there is still only one that has been resolved.

"Is there any real hope of solving the Hodge conjecture? It's unimaginable. ”

With a mouthful of words, Théophile Hampley clicked on the paper and read it word by word, even the most basic introduction and preparatory knowledge, he did not let go.

Regrettably, however, he soon frowned.

The beginning of the paper was fine, and with his own mathematical reserves, he successfully gnawed into it, but after only turning less than three pages of manuscript paper, he frowned.

Because he began to lose comprehension.

......

Staring at the equation on the computer screen, Hampley 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 process of calculus of the paper.

Although it is not all, the first three pages of manuscript paper are mixed with four different fields of mathematical knowledge, such as algebraic geometry, projective clusters, Riemannian geometry, and field expansion.

Among them, Riemannian geometry and expansion are areas that he has not studied in depth.

Shaking his head, Théophile Hampley downloaded the paper from the arxiv web page, passed it to the printer, and printed it out in its entirety.

With the remnants of warm paper, he hurried to his mentor's office.

“

Teacher, I saw a paper on the Hodge conjecture. ”

Without knocking on the door, Théophile Hampley hurried into the office.

In the office, Hampley's mentor, Edbert Shipley, frowned at the student who had broken in in a hurry, and said unhappily: "Hampley, I have a guest here, and I will talk about it later." ”

Hearing this, Théophile Hampley noticed another old man sitting on the sofa in the room, and hurriedly said, "I'm sorry, teacher, I'm too excited. ”

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

"Please wait a minute."

The voice was made by an 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?" ”

Théophile Hampley paused, turned and replied, "Yes, today I was browsing the ARXIV website as usual, and I found a new paper that proves Hodge's conjecture. ”

Hearing this, the old man on the sofa and Edbet Shipley both had a look of loss in their eyes at the same time.

Although arxiv is the most popular website for mathematicians, most of the papers and ideas related to mathematics are worthless dross.

If it's an idea, maybe it's a little better.

But the paper that proves Hodge's conjecture is better to forget it.

Who but a weirdo like Pell Lehman would throw a paper on a preprint site that solves the Seven Millennium Puzzles?

It's something that can't happen.

If the paper is valuable, it should be in the hands of the editors of journals like Annals of Mathematics and New Advances in Mathematics, not on websites like ARXIV.

Théophile Hampley clearly saw the change in the demeanor of the mentor and the old man, and after thinking about it, he added: "The author who uploaded this paper is Xu Chuan, who has previously won the Cafford Prize. ”

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

"You mean to prove Weyl-Berry's conjecture?"

The old man on the couch asked with a surprised face.

He didn't go to last year's Cafford Prize, but he had heard that it was a very young talent.

Théophile Hampley nodded, he always felt that the old man with a sparse head was a little familiar, as if he had seen it somewhere.

After thinking about it in his mind, his eyes suddenly brightened, and he said excitedly: "You are Professor Alain Conne? ”

The figure in his mind gradually coincided with the old man in a gray cardigan in front of him, which made Hampley very excited, this was his idol, and he didn't expect to see it here.

Alain Conne, a contemporary mathematician, Fields Medal winner, and a top mathematician in France, worked with Professor Wiles, who proved Fermat's theorem, and others to formulate the seven millennial problems at the Clay Institute.

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

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

Although I was puzzled by the fact that such an important paper was thrown on a website like arxiv, there was also a slight doubt in my mind that the paper on it was a 'normal' paper.

But he has seen the proof of the Weyl-Berry conjecture, and he has also seen some mathematical methods derived from the Xu-Weyl-Berry theorem, whether the former or the latter, can be said to be very subtle.

The things published by such a mathematical genius should still be seen, at least, the papers related to this major conjecture should not be missed.

Perhaps, this is another geek like Perleman?

.........

After handing the two papers to his mentor and idol, Théophile Hampley waited on the sidelines.

Minutes and seconds passed.

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

Although knowing the proof of such an important conjecture would not be figured out in a moment, Hampley was eager to know the outcome.

After all, this is Hodge's conjecture, one of the seven millennial problems.

It's not just the Kray Institute of Mathematics that has a million meters of gold at stake, but countless other math awards, and most importantly, changing math!

After forcibly waiting for more than half an hour, Theophile Hampley finally couldn't help it, looked at the tutor and idol who were still holding the paper, and asked eagerly: "Mentor, Professor Conne, has Hodge's conjecture been proven?" ”

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

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

Theophile Hampley was surprised, although his mentor was not as good as Alain Conne, who had won the Fields Medal, but he was also a top mathematician who had won international awards such as the Gauss Prize.

Now he even says that he can't understand the paper, isn't that a little too crazy?

Swallowing a spit of surprise, Hampley turned his gaze to the other side, who was still reviewing the manuscript paper in his hand, and Edbet Shipley also cast his gaze.

Noticing the gazes of the other two, Alain Kunne put down the manuscript paper in his hand and sighed: "There are so many fields of mathematics involved in this paper, from algebraic geometry to algebraic topology to Riemannian surfaces and multiple pops...... Even for me, it was not easy to figure out the paper, and it could take months or more. ”

Hearing this, Theophile Hampley couldn't help but swallow the air again.

If even Professor Alain Kune can't read this paper, who else can prove that it is correct?

........