After throwing 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 other colleagues and time.

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

...

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

On the arxiv preprint website, many scholars who followed labels such as Hodge's conjecture, seven millennium problems, algebraic varieties, algebraic geometry, algebraic topology, etc. immediately received recommendations from the website.

France, Paris University of Arts and Sciences.

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 University is definitely one of them.

Even putting aside the Institute for Advanced Study in Princeton, the mathematics department of the Paris University of Arts and Sciences may be even better than Princeton.

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

École Normale Supérieure in Paris, referred to as "Paris Normal School", has a history almost as old as France, with a history of more than 200 years.

It has cultivated countless outstanding talents for Gallic chickens. In mathematics, we are familiar with top giants such as Lagrange, Cauchy, Galois, Fourier, Laplace, Durkheim, Romain Rolland and so on.

Lao Jun came from this college.

Regarding this school, there is a saying: "If you are admitted to the Mathematics Department of the Ecole Normale Supérieure, you will be among the people closest to the Fields Medal." This shows how strong this school's mathematics is.

For mathematicians who have entered these institutions, maintaining attention to the frontiers of mathematics is one of the most important things.

Whether it is mathematics papers in mathematics journals or preprint websites like arxiv, they are all sources of cutting-edge knowledge.

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

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

After all, if you can enter a doctoral program, you have basically entered the stage of creating knowledge.

Not everyone has enough inspiration. In many cases, it is good to get some other people's ideas and then expand or tinker with them yourself.

After roughly flipping through the papers in the algebraic geometry and algebraic topology in the mathematics module, and selecting the manuscripts that interested him and reading a few, Theophele Hempry shook his head, rubbed his eyes, and got up to prepare for

Make yourself a cup of coffee.

】

On the arxiv page, today is another unproductive day.

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, are almost of no value.

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

Theophile Hamprey glanced at the prompt label, which came from his focus on algebraic geometry and algebraic topology.

Although he knew in his heart that this was likely to be another piece of crap and not worth wasting his time, in the end he couldn't help but move his mouse and click on the prompt sent to him by the website.

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

When he saw the title, Theophile Hamprey's eyelids jumped.

Isn't this title just Hodge's standard conjecture?

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

To be honest, most mathematicians may not even have the courage to attack the Seven Millennium Problems.

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

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

After all, even the most rubbish mathematics journals will not accept those ideas that are ‘messy’, ‘outrageous’ and ‘you can’t even understand’.

Only a preprint website like arxiv, which has no peer review and allows you to express your own opinions at will, is broad enough to accommodate these things.

At this moment, Theophile Hamprey, who was squatting in front of the computer, had this idea.

Previously, he had seen a lot of popular 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 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 never 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 is not too difficult.

The latter is probably because he is famous enough.

After all, with those people's thinking, they all want to make it big.

Proving a big mathematical conjecture is like digging up an ancient emperor's tomb. To falsify it is to dig it out and there will be no hair inside, and the crowd of onlookers will disperse with a bang.

But it proves that even if you don't dig a grave, you can still hold some stones and claim that they are gold, and then the crowd will rush to the scene. Some say it is a 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 authoritative certification, while others say that authoritative organizations owe people an apology for making blind identifications...

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

But in fact, these people probably don’t even understand what a grand unified theory is, or the difference between Goldbach’s conjecture and 1 1 = 2.

Therefore, almost all mathematicians are basically dismissive of these things produced by civilian science, and the same is true for Theophile Hamprey.

If it was a mathematical paper related to Goldbach's conjecture or grand unified theory, he would fork it without hesitation.

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

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

Not to mention those in the civil science field, even many mathematicians may not be able to fully understand this problem.

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

What catches the eye, in addition to the familiar title of the paper, is the name of the contributor.

xu·

Theophile Hamprey:??????

When he saw this name, he was immediately stunned.

As the most popular person in mathematics today, a shining star of the younger generation, and the youngest winner in history to win the Crafford Prize in Mathematics and the Crafford Prize in Astronomy at the end of last year, I am afraid that anyone who is engaged in the mathematics industry

Everyone 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 it was directly proved in a weakened form of the world-class problem Weyl_berry conjecture, which caused a sensation in Princeton.

Subsequently, in just a few months, the proof of the weakened form of weyl_berry conjecture was directly extended 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 at the level of the 'grandfather' in the astronomy community.

Since then, mathematical methods have been used to successfully solve the mystery of the proton radius, a problem that has troubled the physics community for several years.

When he saw the name of the author of the paper, Theophele Hempry was instantly confused.

Is it possible that this rising star in mathematics has solved the Hodge conjecture again?

How can this be?

These are the seven millennium problems, not some rubbish mathematical conjecture.

Countless mathematicians have attacked these seven problems for more than a century, including those familiar with them, such as Hardy, Hilbert, Sir Atiyah, etc.

But so far, only one has been solved.

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

With the words in his mouth, Theophile Hempry opened the paper and read it word by word. He did not miss even the most basic introduction and preparatory knowledge.

Unfortunately, he soon frowned.

The beginning of the paper was okay. He relied on his own mathematical reserves to get into it smoothly, but after turning less than three pages of the manuscript, he frowned.

Because he couldn't understand it anymore.

...

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

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

Although not all, the first three pages of the manuscript contain mathematical knowledge from four different fields, including algebraic geometry, projective varieties, Riemannian geometry, and field expansion.

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

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

Taking the remaining warm paper with him, he quickly rushed to his instructor's office.

"

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