Maybe there is some selfishness in it, but it is definitely not for myself.
A large number of research results have emerged in this field, making people more and more convinced that Grothendieck's predictions about algebraic geometry are close at hand, and there is a high probability that they are correct.
This achievement will even exceed the sum of all mathematical achievements in the 20th century.
November 25th.
The theory of algebraic chains is not a particularly complex method, and Faltings believes that if they can figure it out, that person must also be able to figure it out.
As a witness to the past glory of the Göttingen School and an inheritor of the Bourbaki School, it has been thinking about the world for nearly two hundred years, and will continue to think about it.
However, now, not only did no one mention the champagne, no one even felt optimistic about it. Instead, the sense of urgency in their hearts became stronger and stronger.
Although this result is somewhat frustrating, it can prove that an idea is not feasible, and it still saves everyone a lot of precious time.
So far, this meeting has lasted for three full days.
Unlike the Riemann Hypothesis, which makes thousands of propositions rise to theorems, a grand unified theory will allow thousands of theorems to be connected in a straight line.
It is well known that the Abelian category is the basic framework of homology algebra. If the morphism of the smooth projective variety on k is a non-Abelian category, it will undoubtedly deny the most likely way to solve the grand unified theory that they once guessed - that is, through cohomology Methods in group and algebraic topology theory.
The door opened, and an old man walked in from outside the institute, stepping on the water-soaked steps.
He tapped the screen with his index finger. He picked up the phone and was about to take a look at who sent the email.
He has not published a single paper for more than a month.
The gray-black stone bricks are covered with mottled marks of time, and they emit a low lamentation under the baptism of wind and rain, just like an old man leaning on the grape vine, panting gently for the running out of time.
Faltings' proposal was unanimously approved by more than a dozen participants.
End of the meeting.
Basically, everyone put their research results of the past month on the conference table for discussion without reservation until the conference came to an end.
Including him, Sarnak, Grothendieck's favorite disciple Deligne, Faltings, the first person known as the Pope of Mathematics, and Faltings recognized as the most promising person to surpass him. Young scholar Schulz…
If that person really completes the Grand Unified Theory...
As short as six letters—
More than a month has passed since I returned to Europe from China.
After putting away his notebook, Professor Faltings was about to get up when he suddenly noticed the smartphone on the table. The screen flickered and a reminder of an unread email popped up.
He now only hopes to gather the strength of the entire Bourbaki school to overcome this difficulty, so that the glory of this school can continue, rather than being eclipsed by the light of a brighter lighthouse.
Normally, this exciting result alone would be enough for them to open at least one bottle of champagne.
At least now they don't have to discuss an uncertain proposition with uncertain probability while assuming various possibilities of Hom (hX, hY).
The meeting lasted a full two hours.
As for why the former editor-in-chief of "Annals of Mathematics" appears here...
Shaking off the water drops on his raincoat, he handed it to the assistant who came here with him. Professor Faltings, who had just arrived from home, rubbed his hands in the white mist and walked towards the dusty road. Walk in the direction of the conference room.
This turbulent meeting in the field of mathematics gathered almost the top scholars of the entire Bourbaki school.
[Finish.]
But when his eyes touched the mail, he was stunned.
"It's okay," Sanak laughed heartily, "Your humor is still so unpleasant."
Located in a corner of the right bank of the Rhine River, an unattractive research institute is suffering from such troubles at this moment.
"Be well, Sanak, you're finally here," holding his hand and shaking it gently, Faltins glanced at his belly like a rubber ball tightened by a rope, and couldn't help but twitch the corners of his mouth. After a while, "It seems that your life has been good in recent years."
However, this is probably the first time.
"Long time no see, Professor Faltings." Looking at Faltings walking in from the conference room, an old man who looked a little fatter had a smile on his face and warmly extended his right hand to greet him.
"I agree with your point of view." After finally reading the minutes of the meeting in his hand, Professor Deligne pushed up the reading glasses on the bridge of his nose and said in a steady voice, "I can't stand the thing about Europe. It rains constantly at this time every year. , my coat hasn’t been dry a day.”
Because a certain problem bothers it so much...
This seminar with the theme of grand unified theory quickly kicked off.
Of course, the bad weather pales in comparison to the things that really bother it.
In addition to proving that using cohomology groups and algebraic topology theory to study morphisms of smooth projective varieties on k is a waste of time, through algebraic chain theory, they successfully derived the category of smooth projective varieties on k as V(k) , which verified one of Grothendieck's guesses about the standard conjecture.
The attendees stood up and left.
Starting from the paper on the proof of the Beilinson-Bloch conjecture published in "Future Mathematics", the research on motive and cohomology theory in algebraic geometry was directly pushed from the shoals near the coast to the deep water area.
Compared with yesterday, today can barely be regarded as making some progress.
Faltings is more inclined to believe that the latter is more likely.
After more than a month of difficulty, he no longer expects to solve this problem with his own or Schultz's strength.
If there are not too many accidents, most people may hope to see that day in their lifetime.
"Speaking of which, it has been six years since I last met you at the Blue Hall in Stockholm."
Looking at the lines of scrawled notes recorded in the notebook, Faltings nodded slightly with satisfaction.
And after completing this great undertaking, his achievements will undoubtedly reach the pinnacle of history...
The first person to speak was Schultz, who reported on his research on the morphism Hom (hX, hY) of smooth projective clusters on k over the past month, and determined that it is a non-Abelian category.
The day when algebra and geometry were unified in a sense!
Once this point of view was published, it immediately attracted great attention from all participants.
It is not just a staged achievement of the grand unified theory.
The reason is naturally the same as Deligne, who was sitting at the conference table and flipping through the meeting minutes without saying a word. They are both sitting here for the same reason and for the same goal.
Professor Sarnak is the former editor-in-chief of the Annals of Mathematics and the winner of the Wolf Prize in Mathematics in 2014. Scholars who can win this award that includes lifetime achievement may not be the top academically, but they must be The kind that is famous around the world.
"Now that everyone is here, let's go straight to today's topic," Faltings walked to the conference table and sat down shakily. He looked at the heavy rain pouring outside the window and said slowly, "Winter will begin in a few days, and it will be too uncomfortable to sit together in a meeting like this."
This is also a phased achievement in verifying the standard conjecture.
This either means that he has hit a bottleneck, or that he is brewing something even more amazing.
In more than a month, a lot has happened in the mathematical world.
The text is very short.
It's raining heavily in North Rhine-Westphalia, making people worried whether the Rhine River will overflow its banks.