Chapter 14: A Newcomer In The New York Mathematics Community
Zhou Yuanshen is an assistant professor at Columbia University and the only Chinese professor in the Mathematics Department. When he returned to New York from 4v on January 8th, he first went back to the school and found that there was no one in the professors’ offices of the Mathematics Department.
(In the 1960s, the winter break for America universities was generally from mid-December to early January of the following year. For example, Stanford’s winter break in 1965 was from December 18 to January 8.)
“It seems a young man came and said he proved some theorem.” The office staff said.
Zhou Yuanshen was now curious; exactly what theorem had such great appeal.
Although classes hadn’t officially started today, there would still be some professors chatting idly in their offices about interesting things from the winter break.
“What specific theorem?” Zhou Yuanshen asked.
The office staff looked apologetic: “I don’t quite remember, but it seems to be a theorem related to Fermat.”
Zhou Yuanshen was shocked. Although he worked in statistics-related research, he had still heard of the great fame of Fermat’s Last Theorem. He was extremely curious which professor had quietly dropped such a bombshell.
He hadn’t heard before of any professor whose main direction was Fermat’s Last Theorem.
Zhou Yuanshen thought and thought but couldn’t figure out who it was.
Columbia University’s Mathematics Department had a bunch of professors all diving headfirst into differential equations and topology; this was the temperament established for the Columbia University Mathematics Department by Jesse Douglas, the first Fields Medalist.
Columbia had never been good at the algebra and number theory directions related to Fermat’s Last Theorem.
Zhou Yuanshen didn’t want to guess anymore: “I really can’t think of which professor it is.”
The staff shook their head: “No, it’s not a professor; it’s a new Asian who arrived. He is very young, and it’s said he was brought by Professor Horkheimer from the Philosophy Department.
They should still be in the classroom on the southwest side of the second floor right now. If you’re interested, you can go listen.
In the past few days, more and more professors have returned to the school early because of this matter, and after coming back, they all holed up in that room and hardly came out.”
Now he was even more curious. A new Asian who had this level—how had he never heard of such an Asian before.
“Please come in.”
After Zhou Yuanshen knocked and walked in, he was stunned because sitting in the audience were not only professors from Columbia University’s Mathematics Department, but also professors from the Courant Institute of Mathematical Sciences at New York University, all sitting below.
And the rare Chinese descent person was standing at the front:
“No, this is not a conjecture; this is a theorem I have already demonstrated, which will be used in the subsequent steps.
It connects the Galois group in algebraic number theory with automorphic forms and representation theory on algebraic groups over local fields and adeles. I name it automorphic representation thought.”
“Isn’t this exactly Andrei Weil’s idea? Transforming from one field to another field. Sorry, Randolph, this is too crucial; I think we need to call more people.” Ralph Fox interrupted.
Then he whispered with Lipman Bers and Paul Cohen beside him:
“I think just us people now aren’t enough; at least we need to call people from Princeton.
Especially Andrei Weil; we need to call him.”
At this time, Zhou Yuanshen walked in and no one noticed him at all. He sat next to his familiar researcher, the Japanese scholar Heisuke Hironaka, and asked in a low voice: “What’s going on? Has Fermat’s Last Theorem been proved?”
Heisuke Hironaka is a Japanese mathematician and the 1970 Fields Medalist.
However, he is more well-known on China internet for the fact that his later Korean student Hur Joon-ho won the Fields Medal in 2022.
The interesting part of fate is that Hur Joon-ho majored in literature as an undergraduate, and when he entered his senior year, Heisuke Hironaka visited Seoul National University and taught a year-long algebraic geometry course. Hur Joon-ho thought this “celebrity” could be the first topic for a science reporter. However, unexpectedly, as the course progressed, over 100 students gradually dropped due to the difficulty, but Hur Joon-ho stayed on. Later, Hur Joon-ho directly followed Heisuke Hironaka to do graduate studies.
“Yes, Randolph Lin says he proved Fermat’s Last Theorem.”
Zhou Yuanshen’s suspended heart settled; sure enough, only this theorem could attract so many professors to gather here.
“The whole meeting started from January 2nd. At first, there were only three professors: Ralph Fox, Lipman Bers, and Paul Cohen. Later, as Randolph’s proof ideas gained recognition, they called Professor Samuel Eilenberg.
Because they couldn’t judge if the first proved Yoshiyuki Goro-Shimura conjecture was real.
After three days, Samuel Eilenberg acknowledged the other’s proof of the Yoshiyuki Goro-Shimura conjecture, and the other constructed a complete Euler system, using ingenious methods to design Selmer group calculations and the absolute Galois group structure used to connect Fermat’s Last Theorem and elliptic curves.
This caused the possibility of his claimed proof of Fermat’s Last Theorem to be rapidly rising.
So the professors called friends from the New York mathematics community to join the academic conference, and more and more people participated, becoming what you see now.”
The classroom can seat 200 people, and now there are already about seventy.
Half of the New York mathematics community has come.
“But it’s still not enough, because the prerequisite theorem in the method framework he mentioned might be related to Andrew Weil’s conjecture, so these people now are definitely not enough.
I think at least we need to call the Princeton Mathematics Department and get Andrew Weil himself here.”
Andrew Weil is very famous in the current mathematics community, first because of his formidable strength, and second because of his confidence level.
“The top ten Andrew?” Zhou Yuanshen said.
No way around it; his fame was too great, and mathematicians also liked gossip.
In the 1950s, the University of Chicago Mathematics Department held a Christmas party. Many famous mathematicians attended, including Andrei Weil. For entertainment, everyone tried to list the ten greatest living mathematicians, but excluding those present. However, Weil insisted on including himself in the candidates.
This also led to people who knew about it liking to call him the top ten mathematician when mentioning Andrew Weil.
“That’s right; maybe your Chinese compatriot found the bridge between number theory and complex functions.
If there is a bridge between number theory and complex functions, then number theory, geometry, and the finite fields in between might be connected in some way.”
This is also the future famous Langlands Program, called the grand unified theory of the mathematics community.
However, the Langlands Program wouldn’t be proposed until 1967, and only after Langlands sent Andrew Weil a 17-page handwritten letter did the Langlands Program transform from Andrew Weil’s conjecture into one of the most influential programs in the mathematics community.
And what Lin Ran proposed is exactly part of the future Langlands Program, claiming to have proved the transfer form between number theory and automorphic functions.
If this path works, it means Andrew’s conjecture is no longer a conjecture and could become reality.
Obviously, this is no longer just Columbia University’s matter, but a grand event for the entire mathematics community.
Ralph Fox, as the head of the Mathematics Department, instantly realized that the current academic conference wasn’t high-level enough and not enough people had come; many big shots hadn’t arrived yet.
How could they so casually finish lecturing on Fermat’s Last Theorem? Moreover, it involved the even more important mathematical unification.
Fermat’s Last Theorem was certainly more famous, but for the entire mathematics community, the tool that connects number theory, algebraic geometry, groups, and multiple fields was far more important.
Why is Alexander Grothendieck hailed as the pope of algebraic geometry? It’s because he invented tools that later mathematicians all had to use for their work.
“Fox, I think what we need to think about now isn’t calling people, but quickly giving Randolph a contract. Haven’t you noticed that Louis Nirenberg is already gone?
I think if we don’t give him a professor position soon, the Courant Institute is very willing to provide him one.” Paul Cohen reminded.
Fox then reacted, looked around, and found that Louis Nirenberg, the professor from the Courant Institute of Mathematical Sciences at New York University, had indeed disappeared.
Louis Nirenberg, with his bushy beard and hairline pushed way back, was very conspicuous in the crowd. For him to disappear at such a critical time obviously meant he went to contact the head of the New York University Mathematics Department.
“Yes, you’re right; I’ll go prepare right now.”
When he walked to Randolph’s side, he already heard other professors from New York University asking about his specific situation and if he had ideas about switching jobs.
“Come on, Randolph, let’s chat alone.” Fox took Lin Ran’s hand to go out, and turned his head to say to the professors from New York University: “Don’t think about poaching from Columbia University.”
Of course, he wouldn’t expose the fact that the other hadn’t signed with Columbia University yet.
By the time the two left the classroom, Zhou Yuanshen still hadn’t reacted. Randolph Lin, Chinese descent? How had he never heard of such a person.
“This is the proof about the Yoshiyuki Goro-Shimura conjecture; you can take a look. It’s a very interesting idea.” Heisuke Hironaka handed a stack of papers to Zhou Yuanshen. “Yoshiyuki Goro probably didn’t expect his conjecture, proposed only five years ago, to be proved by someone.”
Lin Ran’s reply to Fox was that he needed to think about it and chat with his “elder” Professor Horkheimer.
Fox couldn’t sit still; he couldn’t let the opportunity for Columbia University to surpass Princeton slip away, or even the opportunity to become the mathematical holy land.
Columbia University Mathematics Department’s strengths were in topology, probability theory, and logic; it was almost a blank slate in number theory and algebra.
And Lin Ran’s appearance not only filled the blanks in number theory and algebra, but also brought an entire framework work with him.
If Lin Ran joined Columbia University, just perfecting Andrew Weil’s conjecture here would have value that couldn’t be measured by money.
“How about it? I heard Randolph’s performance was particularly shocking.” Horkheimer saw Fox coming to him proactively and obviously guessed the general situation.
Fox nodded: “Yes, Randolph’s work has important significance for Columbia University Mathematics Department.
I hope you can help persuade him to stay at Columbia University to teach.”
Although he didn’t know why a Chinese descent person had a Jewish elder, from Fox’s perspective, Lin Ran’s guide was Horkheimer.
“Did he really prove Fermat’s Conjecture?” Horkheimer was also shocked inside.
Although he wasn’t a mathematician, he also knew how much value a conjecture with over three hundred years of history had.
“From the current perspective, there is great hope. And more importantly, if his proof holds, then he will create a framework tool connecting algebra and number theory, which has even more value than the proof itself.
In short, from any angle, he fully qualifies to teach at Columbia University.” Fox explained.
Horkheimer asked: “But if, I mean if, it turns out his proof has problems?”
Fox said: “That doesn’t matter either; at least his proof of the Yoshiyuki Goro-Shimura conjecture has already been unanimously recognized by mathematicians from Columbia University and New York University.
Just this one work alone makes teaching at Columbia University not a big issue.
Subsequently, we plan to invite more mathematicians from America universities to New York for a meeting to discuss Fermat’s Conjecture.
If it’s ultimately proved, Princeton or Harvard throwing him an olive branch—we might not be able to keep him at Columbia.”
Fox was clear about Horkheimer’s connections with Columbia University, so he explained the matter in detail.
After hearing this, Horkheimer pondered for a moment and said: “Okay, I understand. I will persuade him to teach at Columbia University, but push back the academic conference time, at least half a month later.”
“Good.” Although he had some doubts inside, Fox still agreed: “But first have him write a paper on the Yoshiyuki Goro-Shimura conjecture proof; we can publish it first in the Proceedings of the National Academy of Sciences.”
After Horkheimer finished chatting with Fox, that evening he returned home and called Lin Ran.
Yes, Lin Ran was temporarily staying at Horkheimer’s home.
“Randolph, I didn’t expect you to indeed have outstanding talent in the mathematics field.
So I think we need to have an open and honest chat.
There’s a problem with your identity. First, even if you have the badge and I confirm it’s real, you still can’t prove your identity; you have no America identity, and besides the badge, there’s no way to prove your relationship with Larry Meyer.
You mentioning it in front of me, I indeed can’t judge the truth.
But if you mention it in front of Theodor Adorno, his questions will be much sharper than mine; you can’t even handle unmodulated collectives, let alone Adorno’s other questions.
So it’s best not to mention your Fabian Society identity anymore.
I will handle all identity-related cover-ups for you. In the next couple of days, I will specially fly to Göttingen city to arrange a PhD in Mathematics from the University of Göttingen for you. Secondly, I will arrange a refugee identity for you, applying for a national interest waiver under Section 212(d)(5) of the Immigration and Nationality Act of 1952.
Additionally, I will arrange for the Rockefeller Foundation to provide endorsement for your identity.”
