November 25th.
Rain was pouring down in North Rhine-Westphalia, almost making people worry about the Rhine river overflowing.
Situated near the Rhine riverbank was a plain-looking research institute.
After being attacked by the wind and rain, the gray-black stone bricks had deteriorated over the years. It was almost like an old man, struggling to stay alive in his later years.
Of course, the bad weather was nothing compared to what they were really worried about.
Once the center of the Bourbaki and Göttingen schools of thought, it had been doing research for the past 200 years, and likely for the next 200 years as well.
However, this was the first time…
The first time a problem had bothered them so much…
The door opened, and an old man walked into the research institute. He was drenched.
He shook off the water droplets on his raincoat and handed it to his assistant. Professor Faltings came here from his home. He rubbed his hands together and walked into a meeting room.
It had been almost a month since he returned from China.
Many things happened in the mathematical world over the past month.
The paper on the Beilinson-Bloch-Kato conjecture was published in the Future Mathematics journal, popularizing the research on the motive theory and cohomology theory.
A large number of research papers had emerged in this field, and more and more people began to believe that Grothendieck’s algebraic geometry predictions were true.
Most people wanted to witness the day algebra and geometry was unified!
“Long time no see, Professor Faltings,” an old man said as he looked at Faltings walking into the conference room. He smiled and reached out his hand.
“The last time I saw you was at the Blue Hall in Stockholm; it’s been six years.”
“Nice to see you again, Sarnak.” Faltings shook his hands and glanced at his fat belly. He couldn’t help but say, “Looks like you’re doing well.”
“I’m okay.” Sarnak smiled and said, “I missed your humor.”
Professor Sarnak, the former editor-in-chief of Annual Mathematics, winner of the 2014 Wolf Prize. Scholars who won a lifetime achievement award were considered world-renowned.
As for why the former editor-in-chief of Annual Mathematics was here…
He was here for the same reason Deligne was also here.
This great mathematics meeting gathered almost all of the top scholars of the Bourbaki Group.
This included Sarnak, Grothendieck’s proudest student Deligne, Faltings, who was named the pope of mathematics, as well as Schultz, the scholar Faltings appointed as the one most likely to surpass him…
This meeting had been going on for three whole days.
“Now that everyone is here, let’s get into the business.” Faltings sat down at the conference table and looked at the rain pouring outside the window. “Winter is coming; it’s going to get cold here.”
“That’s true,” Deligne said as he pushed his glasses up the bridge of his nose. He added, “That’s my least favorite part about Europe. It rains every day this time of year, and my jacket is never dry.”
The meeting on the Grand Unified Theory kicked off.
The first presenter was Schultz, who reported his research on the smooth projective morphism Hom(hX, hY) on k clusters, confirming it to be a non-Abelian category.
This attracted the attention of all of the participants.
Everyone knew that the Abelian category was the basic framework of homology algebra. If the morphism of the smooth projective cluster k was a non-Abelian category, this disproved the method of solving the Grand Unified Theory using homology groups and algebraic topology methods.
Even though this result was frustrating, proving something was not feasible was still productive.
At the very least, now they didn’t have to assume various possibilities of Hom(hX, hY).
The meeting lasted for two hours.
Everyone disclosed their research over the past month. Finally, the meeting came to an end.
Faltings looked at the lines of notes in his notebook and nodded with satisfaction.
At least compared to yesterday, they had made some progress.
In addition to proving that using cohomology groups and algebraic topology to study the morphisms of smooth projective clusters on k was a waste of time, by using algebraic chain theory, they successfully deduced that the category of smooth projective clusters on k was V(k), proving one of Grothendieck’s standard conjectures.
Normally, this result was enough for a celebration.
This wasn’t just an in-progress result of the Grand Unified Theory.
It was also an in-progress of proving Grothendieck’s standard conjectures.
However, no one was in the mood to celebrate. No one was even remotely happy. Instead, they began to feel a sense of urgency.
Algebraic chain theory wasn’t a particularly complicated theory. Faltings knew that if they were able to figure it out, Lu Zhou must have figured it out either.
Lu Zhou hadn’t published a paper in over a month.
This either meant he was in a bottleneck or there was something amazing in the works.
Faltings believed the latter was more likely.
After more than a month of hard work, he had no hope that he or Schultz could solve this proposition alone.
His only hope now was to gather the power of the entire Bourbaki Group to solve this problem, to continue the glory of the institute, and to be a lighthouse in the dark.
And if Lu Zhou really solved Grand Unified Theory…
Unlike Riemann’s hypothesis, which would make thousands of propositions become theorems, the Grand Unified Theory would connect thousands of theorems in a straight line.
This achievement alone would be worth more than the sum of all the mathematical achievements of the 20th century.
And this undoubtedly would be remembered in history as the peak of mathematics…
The meeting was over.
More than a dozen participants got up and left.
Professor Faltings put away his notebook and was about to leave. However, he suddenly noticed a notification on his phone for a new email.
He tapped on the screen and picked up his phone from the desk.
When he opened the email, he froze.
The email was very short.
There was only one word.
[Finished.]