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 paid attention to tags such as Hodge’s conjecture, seven millennium problems, algebraic varieties, algebraic geometry, algebraic topology, etc. received recommendations from the website immediately.
Université de Paris, France.
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 of Arts and Sciences 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 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, and Romain Rolland. Lao Jun came from this college.
There is a saying about this school: "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 the strength of this school's mathematics.
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, and although the latter has uneven quality and is full of dross, many mathematicians still 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 degree, 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 on 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.
Theofele 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 to 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 in the civil science field will post the proof ideas for the seven millennium problems on arxiv.
After all, even the most rubbish mathematics journals will not accept those ideas that are 'messy, outrageous, and even you can't 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, Theofele Hempry, who was squatting in front of the computer, had this idea.
Previously, he had seen a lot of folk 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 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 the thinking of those in civilian science, 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 find that there is no hair inside after digging, and the crowd of onlookers disperses 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 forward. 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 authoritative certification, while others say that the authoritative organization owes an apology to the blind identification...
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 Hodge's conjecture aroused his curiosity.
After all, this is the most difficult question to understand among 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 Hamprey 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 the name, he was stunned.
As the most popular person in the field of mathematics, 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 proved to be a weakened form of the world-class problem Weyl_berry conjecture, which caused a sensation in Princeton.
Then, in just a few months, the proof of the weakened form of 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 at the level of the 'grandmaster' 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, Theofele Hamprey was instantly confused.
Could it be that this rising star in mathematics has solved the Hodge conjecture again?
How can this be?
These are 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? It's too unimaginable."
With the words in his mouth, Theophele 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. Relying on his own mathematical reserves, he successfully read into it, but after turning less than three pages of the manuscript, he frowned.
Because he started not to understand.
...
Staring at the calculations on the computer screen, Hanpri 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, Theofele 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 mentor's office.
"
Teacher, I saw a paper about Hodge's conjecture. "
Without knocking on the door, Theofele Hamprey hurried into the office.
In the office, Hanpuri's tutor, Adelbert Shipley, frowned and looked at the student who hurried in, and said displeasedly: "Hampry, I have guests here, I'll talk about anything later. "
Hearing this, Theofele Hanprey noticed another old man sitting on the sofa in the room, and said quickly: "I'm sorry, teacher, I'm too excited."
After that, he was about to exit the office, but a voice in his ear stopped him in his tracks.
"please wait for a moment."
The one who made the sound was the old man sitting on the sofa, with a trace of curiosity and interest in his eyes: "Did you just say that you found a paper related to the Hodge Conjecture?"
Theophile Hamprey stopped, turned around and replied: "Yes, today when I was browsing the arxiv website as usual, I found a new paper that proves Hodge's conjecture."
Hearing this, the old man on the sofa and Adelbert Shipley both looked disappointed at the same time.
Although arxiv is the most commonly used website by mathematicians, most of the mathematics-related papers and ideas on it are worthless dross.
If it were an idea, maybe it would be better.
But forget about the paper that proves Hodge’s conjecture.
Who else but a weirdo like Perreman would dump a paper solving the Seven Millennium Puzzles on a preprint site?
This is impossible to happen.
If that paper is valuable, it should appear in the hands of editors of journals such as "Annals of Mathematics" and "New Advances in Mathematics" rather than on websites like arxiv.
Theophile Hamprey clearly saw the change 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 previously won the Crafford Prize. "
Hearing this, the old man on the sofa and Adelbert Shipley were both stunned, with strange expressions on their faces.
"You mean that proved Weyl-berry's conjecture?"
The old man on the sofa asked with surprise on his face.
He didn't go to the Craford Award last year, but he heard that it was a very young talent.
Theophile Hamprey nodded. He always felt that the old man with the sparse head looked a bit familiar, as if he had seen it somewhere before.
After thinking about it in his mind, his eyes suddenly brightened, and he said excitedly: "Are you Professor Alan Connet?"
The figure in his mind gradually overlapped with the old man wearing a gray woolen sweater in front of him, which made Hanprey very excited. This was his idol, and he didn't expect to see it here.
Alain Connet, a contemporary mathematics master, winner of the Fields Medal, France's top mathematician, and Professor Wiles who proved Fermat's Last Theorem worked out seven millennium problems at the Clay Institute .
Hearing his name, the old man sitting on the sofa smiled and nodded, and said, "Can you please help me print out that paper?"
On the side, Adelbert Shipley also added: "Print a copy for me too."
Although I feel very puzzled that such an important paper is posted on a website like arxiv, I also have a doubt in my heart as to whether the paper on it is a 'normal' paper.
But he has read papers proving the Weyl-Berry conjecture, and he has also seen some mathematical methods derived from the Xu-Weyl-Berry theorem. Both the former and the latter can be said to be very sophisticated.
You should still read what such a mathematical genius published. At least, papers related to such major conjectures should not be missed.
Maybe, this is another weirdo like Perreman?
.........
After handing the two papers to his mentor and idol respectively, Theofele Hamprey waited aside.
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 this important conjecture would not be clear in a short time, Hanprey still couldn't wait to know the result.
After all, this is the Hodge Conjecture, one of the seven millennium problems.
At stake is not just the $1 million from the Clay Mathematics Institute, but countless other mathematics prizes, and most importantly, changing mathematics!
After forcing himself to wait for more than half an hour, Theophile Hamprey finally couldn't bear it any longer. He looked at his mentor and idol who were still holding the paper, and asked eagerly: "Tutor, Professor Kongye, Huo Strange conjecture, has it been proven?"
Hearing the inquiry, Adelbert Shipley raised her head and said, "I don't know~"
"Technically speaking, I don't even understand some of the math in the paper."
Theophile Hamprey looked surprised. Although his mentor was not as good as Alaincongne and other top mentors who had won the Fields Medal, he was also a top mentor who had won international awards such as the Gauss Medal. Mathematician's.
Now he's saying he doesn't understand the paper. Isn't it a little crazy?
Swallowing his mouth in surprise, Hanprey turned his gaze to the idol Alaincone on the other side who was still reviewing the manuscript paper in his hand, and Adelbert Shipley also cast his gaze over.
Noticing the gazes of the other two people, Alaincongne put down the manuscript paper in his hand and sighed: "This paper involves too many mathematical fields, from algebraic geometry to algebraic topology, to Riemann surfaces and multiple popular ... Even for me, it is not easy to understand this paper, and it may take several months or more."
Hearing this, Theofele Hamprey couldn't help but swallowed the air again.
If even Professor Alaincongne cannot understand this paper, who else can prove whether it is correct?
........
