Great Country Academician

After throwing the proof paper of Hodge's conjecture on the arxiv preprint website, Xu Chuan closed his laptop.

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

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

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

On the arxiv preprint website, many scholars who paid attention to tags such as Hodge’s Conjecture, Seven Millennium Problems, Algebraic Varieties, Algebraic Geometry, and Algebraic Topology received recommendations from the website immediately.

France, Paris University of Arts and Sciences.

A PhD student is browsing through a math module on the arxiv preprint website.

If there is any school that can compete with Princeton in mathematics, École des Arts and Sciences is definitely one of them.

Even leaving aside the Princeton Institute for Advanced Study, the Department of Mathematics of the Paris University of Arts and Sciences may be even better than Princeton.

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

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

It has cultivated countless outstanding talents for the Gallic Chicken. In mathematics, top giants such as Lagrange, Cauchy, Galois, Fourier, Laplace, Durkheim, and Romain Rolland, etc. Guys are 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 will be the group of people closest to the Fields Medal", which shows the strength of this school in mathematics.

For mathematicians who have already entered these institutions, keeping their attention on the frontiers 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, it is a source of cutting-edge knowledge.

The former is stable and reliable, while the latter is of varying quality and full of dross, but many mathematicians still like to throw their papers and ideas on it.

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

After all, to be able to enter the doctoral program, basically has entered the stage of knowledge creation.

Not everyone has enough inspiration. In many cases, it is already a very good thing to get some other people's ideas, and then expand or make up by yourself.

Roughly flipping through the papers in the algebraic geometry and algebraic topology in the mathematics module, after selecting the manuscripts he was interested in and reading a few, Theophile Hampley shook his head and rubbed his eyes, got up and prepared to give Make yourself a cup of coffee.

On the arxiv page, today is another day of no gains.

But this is normal. Although arxiv is full of all kinds of weird ideas, and even a lot of folk mathematics, most of the things in it, especially those new ideas that have been uploaded recently, have almost no value.

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

Theophile Hamprie glanced at the prompt label, from his attention, algebraic geometry, algebraic topology.

Although he knew in his heart that this was very likely to be another dross article and not worth wasting time, in the end he couldn't resist moving the mouse and clicking on the reminder sent to him by the website.

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

Seeing the title, Theophile Hampry's eyelids twitched.

Isn't this title the Hodge Standard Conjecture?

Theophile Hampry is full of disdain for finding papers related to the seven millennium problems on the arxiv preprint website.

The seven millennium problems, to be honest, in the hearts of most mathematicians, they may not even have the courage to charge against them.

Only by entering the industry of mathematics can we understand how profound they are.

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

After all, those ideas that are 'messy', 'outrageous' and 'I can't understand', even the most garbage mathematics journals, will not accept them.

Only a preprint website like arxiv, which has no peer review and can express one's own opinions at will, has enough "heart" to accommodate these things.

And at this moment, Theophile Hampry, who was squatting in front of the computer, was holding this kind of thinking.

Previously, he had seen a lot of civil science ideas about various mathematical conjectures on arxiv. The most popular ones were the proofs of the 'Goldbach Conjecture' and the 'Grand Unified Theory of Mathematics'.

The former 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 put on a few strokes.

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

The latter is probably because it is famous enough.

After all, with the thinking of those folk science, they all want to make a big one.

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

But it proves that even if the grave is not dug, you can hold some stones and claim that it is gold, and then the people who eat melons rush up, some say it is fake, some say it is true, and some say it is just in case is it true? Some say that even if it is true, it needs to be authenticated by an authority, while others say that an authority owes people an apology for blind identification.

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

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

Therefore, almost all mathematicians basically dismiss these things produced by Minke, and the same is true for Theophile Hampri.

If it is a mathematical paper related to Goldbach's conjecture or grand unified theory, he will directly fork it out without hesitation.

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

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

Not to mention those folk science people, even many mathematicians may not be able to fully understand this problem.

With the idea of ​​wanting to see what the other party wrote, Theophile Hampri clicked on the link and jumped into the other party's domain.

In addition to the familiar title of the paper, what caught my eye was the name of the contributor.

Xu Chuan

Theophile Hampry: ? ? ? ? ? ?

Seeing the name, he was immediately stunned.

As the hottest fried chicken in the world of mathematics, the shining star of the younger generation, the youngest winner in history who won the Craford Mathematics Award and the Craford Astronomy Award at the end of last year, I am afraid that anyone who is engaged in the mathematics industry Will pay attention to this name.

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

Before that, there was almost no foreshadowing, and almost no mathematical papers were published, and then it was directly proved in a weakened form of the world-class difficult Weyl_Berry conjecture, which caused a sensation in Princeton at the beginning.

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

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

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

Seeing the name of the author of the paper, Theophile Hampry was instantly stunned.

Is it possible that this new star in the mathematics world has solved the Hodge conjecture?

How can this be?

These are the Seven Millennium Problems, not some junk math conjecture.

Countless mathematicians have launched a charge on these seven problems for more than a century, including those mathematicians who are familiar with it, such as Hardy, Hilbert, Sir Atiyah and so on.

But so far only one has been resolved.

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

After muttering, Theophile Hampry clicked on the paper and read it word by word, even the most basic introduction and preliminary knowledge, he did not let go.

Unfortunately, he soon frowned.

The beginning of the thesis was okay. Relying on his own mathematical reserves, he successfully read it in, but he frowned after turning less than three pages of manuscript paper.

Because he couldn't read it anymore.

Staring at the calculations on the computer screen, Humpry sighed.

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

Although not all of them, the first three pages of manuscript paper are mixed with mathematical knowledge in four different fields, such as algebraic geometry, projective varieties, Riemannian geometry, and extended fields.

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

Shaking his head, Theophile Hampri downloaded the thesis from the arxiv webpage, then passed it to the printer, and printed it out completely.

With the remaining warm paper, he hurried to the tutor's office.

""Teacher, I saw a paper about Hodge's conjecture. "

Without knocking on the door, Theophile Hampry broke into the office in a hurry.

In the office, Edbetter Shipley, Hampry's mentor, frowned and looked at the student who rushed in, and said displeasedly: "Hampry, I have a guest here, I'll talk about anything later. "

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

After finishing speaking, he was about to leave the office, but a voice in his ear made him stop.

"please wait for a moment."

It was the old man sitting on the sofa who made the sound, with a trace of curiosity and interest in his eyes: "You just said that you found a paper related to Hodge's conjecture?"

Theophile Hampley stopped in his tracks, turned back and said, "Yes, today when I browsed the arxiv website as usual, I found a new paper that proved Hodge's conjecture."

Hearing this, the eyes of the old man on the sofa and Edbert Shipley both flashed disappointment at the same time.

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

If it's an idea, maybe it might be better.

But forget about the papers that prove Hodge's conjecture.

Who else but an oddball like Perleman would drop a paper on a preprint site that solves the seven millennium puzzles?

This is impossible.

If that paper is worthwhile, it should appear in the hands of editors of journals such as Annals of Mathematics and Advances in Mathematics, not on websites such as arxiv.

Theophile Hampry obviously saw the change in the expressions of the mentor and the old man, thought for a while, and then added: "The author who uploaded this paper is Xu Chuan, who has won the Crawford Award before. "

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

"You mean you proved the Weyl-Berry conjecture?"

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

He didn't go to the Crawford Awards last year, but he heard that it was a very young talent.

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

After thinking about it in his mind, his eyes suddenly brightened, and he said excitedly, "You are Professor Alan Connie?"

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

Alan Connes, a master of contemporary mathematics, a winner of the Fields Medal, a top French mathematician, worked with Professor Wiles who proved Fermat's last theorem and others at the Clay Institute to draw up seven millennium problems .

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

Aside, Edbetter Shipley also added: "Print a copy for me."

Although I am very puzzled about throwing such an important paper on a website like arxiv, I also have a trace of doubt in my heart, wondering whether the papers on it are 'normal' papers.

But he has read the proof papers 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 subtle.

You should read the things published by such a mathematical genius. At least, you should not miss the papers related to this kind of major conjecture.

Maybe this is another geek like Perleman?

After handing the two papers to his mentor and idol respectively, Theophile Hampri waited aside.

Time passed by every minute and every second.

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 this important conjecture would not be clear in a short while, Hampry still couldn't wait to know the result.

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

It's not just the Cray Mathematics Institute's million dollars at stake, but countless other math awards, and most importantly, change math!

Forcibly holding back and waiting for more than half an hour, Theophile Hampri finally couldn't help it, looked at the tutor and idol who were still holding the paper, and asked eagerly: "Teacher, Professor Connie, Huo Odd conjecture, has it been proven?"

Hearing the inquiry, Edbetter 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 Hampry looked surprised. Although his mentor was not as good as Alain Congé and other top leaders who had won the Fields Medal, they were also the top leaders who had won the Gauss Award and other international awards. mathematicians.

Isn't it a little crazy that he now says he doesn't understand the paper?

Swallowing his saliva in surprise, Hampry turned his gaze to Alan Conne, who was reviewing the manuscript paper on the other side, and Edbeth Shipley also cast his gaze over.

Noticing the gazes of the other two, Alan Congé put down the manuscript paper in his hand and sighed: "There are too many fields of mathematics involved in this paper, from algebraic geometry to algebraic topology, to Riemann surfaces and multi-popularity." Even for me, it is not easy to understand this paper, and it may take several months or more."

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

If even Professor Alain Congé can't understand this paper, who can prove whether it is right?