After Lu Zhou talked with his teammates, he decided to publish the proof of the Beilinson-Bloch-Kato conjecture in the “Future Mathematics” journal.
While the paper was in the review process, its preprint was uploaded to arXiv.
Even though the Beilinson-Bloch-Kato conjecture wasn’t as famous as Riemann’s hypothesis or Goldbach’s conjecture, being able to connect high-dimensional K-groups with analytical invariants of the elliptic curve E gave it a special meaning in the field of algebraic geometry and number theory.
Algebraic geometry was the branch of mathematics that had the most influential researchers, so this preprint immediately attracted a considerable amount of attention.
Not just because of the Beilinson-Bloch-Kato conjecture itself.
But also because the person who solved this conjecture was Professor Lu, the one who proved Riemann’s hypothesis at the International Congress of Mathematicians…
Princeton Institute for Advanced Study.
The cafe on the first floor.
Professor Witten was sitting by a window drinking coffee. He spoke to Professor Deligne, who was reading a paper in his hand.
“The Lunar Hadron Collider has already been completed. Apparently, the first experiment begins in December. I guess I’ll have to make a long-distance trip when the time comes.”
Deligne asked casually, “Oh, looks like there’s a chance to verify your theory?”
With a coffee in his hand, Witten smiled and shook his head.
“Not yet, but this is good news for the standard model. We’ll be able to reveal the secrets of the universe… Speaking of which, what are you reading?”
Deligne noticed Witten’s look of curiosity. He pushed the glasses up the bridge of his nose and smirked, which was a rare sight for a serious man like him.
“It’s a proof of the Beilinson-Bloch-Kato conjecture… It seems like their research is progressing.”
Witten: “What research?”
“Lu Zhou and his quest to unify algebra and geometry.”
When Witten heard this, he was shocked. He spoke after a moment of silence.
“That is ridiculous… When did he start this research project?”
As a Fields Medal-winning physicist, he knew more about mathematics than most scientists.
Unifying old methods.
When analytical geometry was first discovered, people combined algebraic problems using Cartesian coordinates. This led to the rapid development of science and technology, particularly in physics, astronomy, and engineering.
And this also began a new era of mathematics.
“He started working on this after he solved Riemann’s hypothesis, but he’s probably had the idea in his mind for a long time…”
Professor Deligne flipped through the page in his hand and said, “He’s not the only one that has thought about this. My supervisor and I, as well as anyone proficient in algebra and geometry, have thought about this problem. Is there an elegant connection between algebra and geometry? That is the question. If their research is successful, then it would benefit the entire mathematics community…”
After a long silence, Professor Witten spoke.
“Looks like I can’t catch up with the times.”
Deligne: “That’s not a big deal, you’re just not in this field of research. I was also surprised when I first heard about this research project. Especially now that he has made significant in-progress results and even recruited Faltings. From what I understand, Faltings rarely leaves the Max Planck Society.”
Witten didn’t really care about Faltings.
He asked in a serious manner, “Do you think they will succeed?”
“In my opinion, it’s only a matter of time.” Deligne’s wrinkly finger adjusted his glasses and said, “Maybe I’m biased, but I feel like there’s no problem in this world he can’t solve.”
After a while, he spoke again.
“As long as the problem has a real solution.”
“Looks like you think highly of him.” Witten smiled and said, “Let’s make a bet then. Do you think he’ll be able to solve this problem before the first Lunar Hadron Collider experiment or after the first experiment?”
Deligne paused for a second. He didn’t expect his friend to ask such a weird question.
He hesitated for a bit as he contemplated. He finally spoke.
“If the first experiment is happening in December, then I would bet on it after the experiment.”
After all, there was only two months left until December.
Even though they had made good progress, it was unrealistic to think they would solve the problem in two months.
Witten: “Then I’ll bet on them solving it before the experiment.”
Professor Deligne frowned.
“You sure?”
Professor Witten smiled and said, “Why not? I feel like they will surprise us.”
If they could unify algebra and geometry, it would impact not only mathematics, but also the physics field.
Whether it was condensed matter physics or high-energy physics, the abstract meaning of numbers and shapes could help physicists understand many complicated concepts.
Perhaps it wouldn’t revolutionize the physics world, but it would definitely create new theories and methods.
People could then use these new theories to solve “old” problems.
Deligne smirked and asked, “Then what should we bet on?”
“I think you have Lu Zhou’s graduation paper on Goldbach’s conjecture.” Witten smiled and said, “Last time I went to the Firestone Library to borrow his manuscript on the 750 GeV research, I happened to search through some of his other manuscripts and wasn’t able to find the one on Goldbach’s conjecture. Thus, you’re the only person who could have it.”
Deligne coughed and said, “Sure, I’ll wager it, I don’t care about sentimental things… Then, what do you plan on betting with?”
Witten: “How about the manuscript on M Theory?”
Professor Deligne looked at him and said, “Are you really going to wager something that might not even be correct?”
“But it might be the ultimate theory at explaining the origins of the universe…”
Witten sighed and gave up.
“Okay, what else… A while ago, I was cleaning up my house and found a bunch of my notes from when I was studying topology. There is probably something useful in there, I just haven’t organized it. It’s almost ten-textbook thick.”
Witten was an expert in Topology.
The reason he was able to win the 1990 Fields Medal was because of his research on low-dimensional topology structures and his deduction of quantum invariants.
Atiyah once commented that his achievements in mathematics had surpassed many mathematicians, while his knowledge of physics had provided him a source of inspiration and intuition for mathematics research. There was even a rumor that Atiyah had begun studying physics because of Witten.
Regardless of whether these topology notes had sentimental value, it undoubtedly had academic value.
Therefore, Professor Deligne spoke immediately.
“Deal!”
