Chapter 15: A newcomer came to the New York mathematics circle

Zhou Yuanshen was an assistant professor at Columbia University and the only Chinese professor in the Department of Mathematics. When he returned to New York from 4v on January 8, 1960, he went back to school first and found that there was no one in the professors' office in the Department of Mathematics.

(In the 1960s, the winter vacation of American universities generally lasted from mid-December to early January of the following year. Taking Stanford as an example, its winter vacation in 1965 was from December 18 to January 8.)

"It seems that a young man came and said he proved some theorem," the staff of the Department of Mathematics said.

Zhou Yuanshen was curious now. What kind of theorem has such great attraction?

Although school hasn't officially started today, there will always be some professors chatting in the office about interesting things during the winter vacation.

"What specific theorem is it?" Zhou Yuanshen asked.

The staff looked apologetic: "I don't remember very well, it seems to be a theorem related to Fermat."

Zhou Yuanshen was shocked. Although he was doing research related to statistics, he had heard of the famous Fermat's Last Theorem. He was incomparably curious about which professor had released a big move without a sound.

He hadn't heard of any professor whose main direction was Fermat's Last Theorem before.

Zhou Yuanshen thought and thought but couldn't think of who it was.

A large number of professors in the Department of Mathematics at Columbia University were all doing differential equations and topology. This was the temperament laid down for the Department of Mathematics at Columbia University by Jesse Douglas, the winner of the first Fields Medal.

Columbia University had never been good at algebra and number theory 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 his head: "No, it's not a professor. It's a new Asian who is very young. It is said that he is a junior brought by Professor Horkheimer of the Department of Philosophy.

They should still be in the classroom on the southwest side of the 2nd floor now. If you are interested, you can go and listen.

More and more professors have returned to school early because of this matter these days. After returning, they all drilled into that room and almost never came out."

This made him even more curious. A new Asian, how could an Asian with this level be someone he had never heard of before.

"Please come in."

After Zhou Yuanshen knocked on the door and walked in, he was stunned, because not only were the professors of the Department of Mathematics at Columbia University sitting below, but also the professors of the Courant Institute at New York University were all sitting below.

And the rare Chinese stood in front of the stage:

"No, this is not a conjecture. This is a theorem I have already demonstrated, and it will be needed in the follow-up.

It will connect the Galois group in algebraic number theory with the automorphic forms and representation theory of algebraic groups on local fields and adeles. I named it the automorphic representation idea."

"Isn't this André Wei Yi's idea? Transforming from one field to another, sorry, Randolph, this is too critical, I think we have to call more people," Ralph Fox interrupted.

Subsequently, he whispered to Lipman Bers and Paul Cohen beside him:

"I think these people are not enough now. At least we have to call people from Princeton.

Especially André Wei Yi, we have to call him."

At this time, Zhou Yuanshen walked in and no one noticed: "What's wrong? Is Fermat's Last Theorem proven?"

Heisuke Hironaka is a Japanese mathematician and a Fields Medal winner in 1970.

However, he is more familiar on the Huaguo Internet because his Korean student Heo Jun-yi won the Fields Medal in 2022.

The interesting thing about fate is that Heo Jun-yi majored in literature as an undergraduate, and when he was a senior, Heisuke Hironaka visited Seoul National University and offered a one-year course on algebraic geometry. Heo Jun-yi thought that this "celebrity" could be used as the first topic for a science reporter. However, unexpectedly, as the course deepened, more than 100 students gradually dropped the course because of the difficulty, but Heo Jun-yi stayed. Later, Heo Jun-yi followed Heisuke Hironaka to read for a postgraduate degree.

"Yes, Randolph Lin said he proved Fermat's Last Theorem."

Zhou Yuanshen's hanging heart was put down. Sure enough, only this theorem could attract so many professors to gather here.

"The whole meeting started on January 2. At the beginning, only three professors, Ralph Fox, Lipman Bers, and Paul Cohen, were there. Later, as Randolph's proof idea was recognized, they called Professor Samuel Eilenberg over.

Because they couldn't judge whether the first proven Taniyama-Shimura conjecture was true.

It took three days for Samuel Eilenberg to recognize the other party's Taniyama-Shimura conjecture. Later, the other party constructed a perfect Euler system, used ingenious methods to design Selmer group calculations, and the absolute Galois group structure used to connect Fermat's Last Theorem and elliptic curves.

This led to the possibility that he proved Fermat's Last Theorem was rising rapidly.

So the professors called their friends in the New York mathematics circle to attend the academic conference. More and more people participated, and it became what you see now."

The classroom could seat 200 people, and now more than 70 were sitting.

More than half of the New York mathematics circle came.

"But that is not enough, because the prerequisite theorems in the framework of the method mentioned by the other party are very likely related to André Wei Yi's conjecture, so these people now are definitely not enough."

I think at least we have to call the Princeton Department of Mathematics and call André Wei Yi himself over."

André Wei Yi was very famous in the current mathematics circle, partly because of his strong strength, and partly because of his confidence.

"The top ten André?" Zhou Yuanshen said.

No way, the fame is too big, and mathematicians also like gossip.

In the 1950s, the Department of Mathematics at the University of Chicago held a Christmas party. Many famous mathematicians attended, including André Wei Yi. For entertainment, everyone tried to list the ten greatest living mathematicians, but they could not include the people present. However, Wei Yi insisted on being included in the candidate list.

This also led to people who knew about this matter referring to André Wei Yi as a top-ten mathematician.

"That's right, maybe your Chinese compatriot found a bridge between number theory and complex function theory.

If there is a bridge between number theory and complex function theory, then number theory, geometry, and the finite fields in between may be connected in one way."

This is also the famous Langlands program in the future, known as the grand unified theory of mathematics.

However, the Langlands program was not proposed until 1967. It was not until Langlands sent a 17-page handwritten letter to André Wei Yi that the Langlands program changed from André Wei Yi's conjecture to one of the most influential programs in the mathematics circle.

And what Lin Ran proposed was exactly a part of the Langlands program in the future, claiming that he proved the conversion form between number theory and automorphic functions.

If this road can be walked through, it means that André's conjecture is no longer a conjecture, but may become a reality.

Obviously, this is not a matter for Columbia University alone, but a grand event for the entire mathematics circle.

As the chairman of the Department of Mathematics, Ralph Fox instantly realized that the grade of the current academic conference was not high enough, and the people who came were not enough. A lot of big shots hadn't come yet.

How could Fermat's Last Theorem be finished so hastily? What's more, it also involves more important mathematical grand unification.

Fermat's Last Theorem is certainly more famous, but for the entire mathematics circle, the tools that can connect number theory, algebraic geometry, groups, and other fields are much more important.

Why is Alexander Grothendieck hailed as the Pope of Algebraic Geometry? Isn't it because he invented tools, and later mathematicians have to use his tools to do work.

"Fox, I think what we need to think about now is not calling people, but giving Randolph a contract as soon as possible. Haven't you noticed that Louis Nirenberg has disappeared?

I think if we don't give him a professor position, the Courant Institute is very willing to provide him with a professor position," Paul Cohen reminded.

Fox reacted, and he looked around and found that Louis Nirenberg, a professor at the Courant Institute of New York University, had indeed disappeared.

Louis Nirenberg, who had sideburns and pushed his hairline very high, was very conspicuous in the crowd. Disappearing at such a critical moment was obviously to contact the chairman of the

"Yes, you are right, I will go and prepare now."

By the time he walked to Randolph's side, he could already hear other professors from New York University asking him about his specific situation and whether he had any thoughts of changing jobs.

"Come, Randolph, let's talk in private." Fuchs grabbed Lin Ran's hand and started to walk out, while turning his head to say to the professor from New York University: "Don't even think about poaching people from Columbia University."

Of course, he would not expose the fact that the other party had not yet signed a contract with Columbia University.

By the time the two left the classroom, Zhou Yuanshen had not yet reacted. Randolph Lin, of Chinese descent? How had he never heard of such a person?

"This is the proof of the Taniyama-Shimura conjecture; you can take a look, it's a very interesting line of thought." Hironaka Heisuke handed a stack of papers to Zhou Yuanshen. "Taniyama probably didn't expect that his conjecture would be proven just five years after it was proposed."

Lin Ran's reply to Fuchs was that he needed to consider it further and talk to his "elder," Professor Horkheimer.

Fuchs could not sit still; he could not watch the opportunity for Columbia University to surpass Princeton slip away in vain, or even the chance to become a holy land of mathematics.

The strengths of the Columbia University mathematics department were in topology, probability theory, and logic, while it was almost a blank slate in number theory and algebra.

And Lin Ran's appearance could not only fill the void in the fields of number theory and algebra but also bring in an entire framework of work.

If Lin Ran joined Columbia University, the value of just perfecting André Wei Yi's conjecture here would be immeasurable in monetary terms.

"How is it? I heard that Randolph's performance was particularly astonishing." Seeing Fuchs take the initiative to come to him, Horkheimer clearly guessed the general situation.

Fuchs nodded and said: "That's right, Randolph's work has significant meaning for the Columbia University mathematics department.

I hope you can help persuade him to stay at Columbia University to teach."

Although he did not know why a person of Chinese descent would have a Jewish elder, from Fuchs's perspective, Lin Ran's guide was Horkheimer.

"Did he really prove the Fermat conjecture?" Horkheimer was also shocked inside.

Although he was not a mathematician, he knew how valuable a conjecture with a history of more than three hundred years was.

"Currently, there is great hope. And more importantly, if his proof holds, he will create a framework tool connecting algebra and number theory, which is even more valuable than the proof itself.

In short, no matter from which angle you look at it, he is fully qualified to teach at Columbia University," Fuchs explained.

Horkheimer asked: "But if, and I mean if, it turns out that his proof has problems?"

Fuchs said: "That is not important either; at least his proof regarding the Taniyama-Shimura conjecture has already received unanimous recognition from mathematicians at Columbia University and New York University.

Just this one piece of work is enough to make teaching at Columbia University not a problem.

We plan to invite more mathematicians from American universities to New York to hold a meeting to discuss the Fermat conjecture.

If it is finally proven, and Princeton or Harvard offers him an olive branch, we might not be able to keep him at Columbia."

Fuchs knew the connection between Horkheimer and Columbia University, which is why he broke the matter down to tell the other party.

After listening, Horkheimer pondered for a moment and said: "Good, I know. I will persuade him to teach at Columbia University, but the time for the academic conference must be pushed back, at least to half a month later."

"Good." Although he had doubts inside, Fuchs still agreed: "But let him write a paper on the proof of the Taniyama-Shimura conjecture first; we can publish it in the Proceedings of the National Academy of Sciences first."

After Horkheimer and Fuchs finished talking, he returned to his home that evening and called for Lin Ran.

That's right, Lin Ran was staying temporarily at Horkheimer's home.

"Randolph, I didn't expect that you truly have outstanding talent in the field of mathematics.

Then I think we need to have a frank and open talk.

Your identity has problems. First, even if you have the badge, and I am certain this badge is real, you still cannot prove your identity. You do not have American status, and besides the badge, you have no way to prove your relationship with Larry Mayer.

It is fine if you mention it in front of me; I truly cannot judge whether it is true or false.

But if you mention it in front of Theodor Adorno, his questions will be much sharper than mine. You cannot even handle the set of atonal music, let alone Adorno's other questions.

So it is best not to mention your Fabian Society identity again.

I will help you handle all identity-related cover-ups. I will fly to Göttingen in the next two days to arrange a mathematics doctorate from the University of Göttingen for you there. Secondly, I will arrange a refugee status for you and apply for a National Interest Waiver through Section 212(d)(5) of the Immigration and Nationality Act of 1952.

In addition, I will arrange for the Rockefeller Foundation to help you with identity endorsement."