Technology invades the modern world

Chapter 14 A Newcomer to the New York Mathematics Community
Zhou Yuanshen is an assistant professor at Columbia University and the only Chinese professor in the Department of Mathematics. When he returned to New York from April 1, he went back to the school first and found that there was no one in the professor's office in the Department of Mathematics.

（上世纪六十年代，阿美莉卡高校的寒假假期一般在12月中旬至次年1月上旬，以斯坦福为例，其1965年的寒假时间为12月18日-1月8日）
"It seems that a young man came and said that he had proved a theorem." said the office staff of the Department of Mathematics.

Zhou Yuanshen was now curious about what theorem was so attractive.

Although school has not officially started today, some professors are already in their offices chatting about interesting things that happened during the winter vacation.

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

The office worker looked apologetic and said, "I don't quite remember, but it seems to be a theorem related to Fermat."

Zhou Yuanshen was shocked. Although he was doing statistics-related research, he had heard of the famous Fermat's Last Theorem. He was extremely curious about which professor had quietly made such a big move.

I have never heard of any professor whose main research area is Fermat's Last Theorem.

Zhou Yuanshen thought about it over and over but couldn't figure out who it was.

Many professors in Columbia University's Department of Mathematics are devoted to differential equations and topology. This is the temperament that Jesse Douglas, the first winner of the Fields Medal, laid for Columbia University's Department of Mathematics.

Columbia University has 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 member shook his head and said, "No, it's not a professor, it's a new Asian guy. He's very young and is said to be a junior brought in by Professor Horkheimer from the philosophy department.

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

In the past few days, more and more professors have returned to school early because of this matter. After returning, they all hide in that room and rarely come out. "

Now he was even more curious. How come he had never heard of this new Asian man with such a level of skill before?

"Please come in."

Zhou Yuanshen was stunned after knocking on the door and walking in, because sitting in the audience were not only professors from the Department of Mathematics at Columbia University, but also professors from the Courant Institute at New York University. All of them were sitting there.

And the rare Chinese people stood in front of the stage:

“No, this is not a conjecture, this is a theorem I have proven, which will be used later.

It connects Galois groups in algebraic number theory with the automorphic forms and representation theory of algebraic groups on local fields and Adairs, and I named it the idea of ​​automorphic representations.

"Isn't this Andre Weil's idea? Transforming from one field to another. Sorry, Randolph, this is too critical. I think we need to call more people." Ralph Fox interrupted.

Then he whispered to Lipman Bales and Paul Cohen beside him:
"I think we are not enough now, we should at least call everyone from Princeton.

Especially André Weil, he must be called up."

Zhou Yuanshen walked in unnoticed. He sat down next to a Japanese scholar, Hironaka Heisuke, a researcher he knew well, and whispered, "What's going on? Has Fermat's Last Theorem been proven?"

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

However, he is better known on the Chinese Internet for the fact that his Korean student Xu Jun'er won the Fields Medal in 2022.

In a curious twist of fate, Huh Jun-il was a literature major in his undergraduate studies. During his senior year, Kwang Jung Pyeong-woo visited Seoul National University and taught him a year-long algebraic geometry course. Huh Jun-il thought this "celebrity" would be a good first topic for a science journalist. However, to his surprise, as the course progressed, over 100 students dropped out due to the difficulty, while Huh Jun-il stayed. Later, Huh Jun-il went directly to graduate school under Kwang Jung Pyeong-woo.

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

Zhou Yuanshen felt relieved. Sure enough, only this theorem could attract so many professors to gather here.

"The entire meeting started on January 1nd. At first, only Professors Ralph Fox, Lipman Bales, and Paul Cohen were present. Later, as Randolph's proof gained recognition, they called Professor Samuel Eilenberg to join.

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

After Samuel Eilenberg spent three days to approve the other party's proposal on the Taniyama-Shimura conjecture, the other party constructed a complete Euler system and used ingenious methods to design the Selmer group calculation and the absolute Galois group structure used to link Fermat's Last Theorem with elliptic curves.

This leads to what he calls a rapidly increasing likelihood of proving Fermat's Last Theorem.

So the professors invited their friends in the New York mathematics community to attend the academic conference, and the number of participants increased, and it became what you see now.

The classroom can seat 200 people, and there are already about people sitting there.

More than half of the New York mathematics community came.

“But it’s still not enough, because the prerequisite theorem in the method framework mentioned by the other party is very likely related to Andrew Weil’s conjecture, so these people now are definitely not enough.

I think at least the Princeton Mathematics Department should be called in, and Andrew Weil himself should be called in."

Andrew Weil is very famous in the current mathematics community, firstly because of his strong ability, and secondly because of his self-confidence.

"Andrew in the top ten?" Zhou Yuanshen said.

There's no way around it, he's too famous, and mathematicians also like gossip.

In the 1950s, the University of Chicago Mathematics Department held a Christmas party. Many prominent mathematicians were in attendance, including André Weil. For entertainment, they attempted to name the ten greatest living mathematicians, but they couldn't include anyone present. However, Weil insisted on including himself.

This also leads to people who know this to like to call Andrew Weil one of the top ten mathematicians when they mention him.

"Yes, maybe your fellow Chinese people have found a 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 may be connected in some 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 Andrew Weil that the Langlands Program evolved from Andrew Weil's conjecture into one of the most influential programs in mathematics.

Lin Ran's proposal is part of the future Langlands Program, claiming to have proven the transformation between number theory and automorphic functions. If this path is successful, Andrew's conjecture is no longer a conjecture but has the potential to become reality.

Obviously, this is not just a matter for Columbia University, but a major event for the entire mathematics community.

As the head of the mathematics department, Ralph Fox immediately realized that the current academic conferences were not of high quality and not enough people came, and many big names had not yet arrived.

How could one finish explaining Fermat's Last Theorem so hastily, especially when it involves the more important unification of mathematics?

Fermat's Last Theorem is certainly more famous, but for the entire mathematical community, tools that can connect multiple fields such as number theory, algebraic geometry, and groups are much more important.

Why is Alexander Grothendieck known as the Pope of algebraic geometry? Isn’t it because he invented tools and later mathematicians have to use his tools to do their work?

“Fox, I think what we need to think about now is not to call someone, but to give Randolph a contract as soon as possible. Didn’t you notice that Louis Nirenberg is gone?
I think if we don’t offer him a professorship, the Courant Institute would be happy to offer him one.” Paul Cohen reminded him.

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

Louis Nirenberg, with his beard and high hairline, was very conspicuous in the crowd. He disappeared at this critical moment, apparently to contact the chairman of the Department of Mathematics at New York University.

"Yes, you are right. I will prepare it right away."

By the time he reached Randolph, he had already heard other professors at New York University asking about his specific situation and whether he had any thoughts of changing jobs.

"Come on, Randolph, let's talk alone." Fox took Lin Ran's hand and was about to walk out. He turned his head and said to the professor from New York University, "Don't even think about poaching people from Columbia University."

Of course, he would not reveal 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 still hadn't reacted. Randolph Lin, Chinese? How come he had never heard of such a person?

"This is the proof of the Taniyama-Shimura conjecture. You can take a look at it. 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 he proposed it."

Lin Ran’s reply to Fox was that he would think about it again and talk to his “elder” Professor Horkheimer.

Fox could no longer sit still and watch Columbia University's opportunity to surpass Princeton, or even become a mecca of mathematics, slip away.

The strengths of Columbia University's Department of Mathematics lie in topology, probability theory, and logic, but it is almost blank in number theory, algebra, etc.

The emergence of Lin Ran not only fills the gaps in the fields of number theory and algebra, but also brings in an entire framework of work.

If Lin Ran joins Columbia University, the value of perfecting Andrew Weil's conjecture here alone cannot be measured in money.

"How is it? I heard that Randolph's performance was amazing." Seeing Fox come to him on his own initiative, Horkheimer obviously guessed the general situation.

Fox nodded and said, “Yes, Randolph’s work is of great significance to the Department of Mathematics at Columbia University.

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

Although no one knows why a Chinese person has a Jewish elder, from Fox's perspective, Lin Ran's guide is Horkheimer.

"Did he really prove Fermat's conjecture?" Horkheim was also shocked.

Although he is not a mathematician, he also knows how valuable a conjecture with a history of more than 300 years is.

"So far, there's great hope. And more importantly, if his proof is valid, he will have created a framework tool that connects algebra and number theory, which is more valuable than the proof itself.

In short, from every perspective, he is fully qualified to teach at Columbia University." Fox explained.

Horkheimer asked, "But what if, I mean what if, it turns out that his proof is flawed?"

Fox said: "That doesn't matter, at least his proof of the Taniyama-Shimura conjecture has been unanimously recognized by mathematicians at Columbia University and New York University.

For this job alone, teaching at Columbia University would not be a big problem.

Later, we plan to invite more mathematicians from American universities to New York for a meeting to discuss Fermat's conjecture.

If it turns out that Princeton or Harvard offered him an olive branch, we might not be able to keep him at Columbia."

Fox knew the connection between Horkheimer and Columbia University, so he told him everything in detail.

Horkheimer paused for a moment and then said, "Okay, I understand. I will persuade him to teach at Columbia University, but the academic conference will be postponed to at least two weeks later."

"Okay." Although he had some doubts in his heart, Fox agreed. "But first, let him write a paper on the proof of the Taniyama-Shimura conjecture. We can publish it in the Proceedings of the National Academy of Sciences."

After Horkheimer finished talking with Fox, he returned home that night and found Lin Ran.

That’s right, Lin Ran is temporarily living in Horkheimer’s home.

"Randolph, I didn't expect you to have such an outstanding talent in mathematics.

Then I think we need to have a frank chat.

There is a problem with your identity. First of all, even if you have a badge, and I am sure that this badge is real, you still cannot prove your identity. You do not have an American identity, and there is no way to prove the relationship between yourself and Larry Mayer except for the badge.

You can mention it in front of me, but I really can't tell whether it is true or not.

But if you bring this up in front of Theodor Adorno, his questions are much sharper than mine. You can't even deal with atonal ensembles, let alone Adorno's other questions.

So it’s best not to mention your Fabian identity again.

I will help you with all the identity-related concealment. I will fly to Göttingen in the next two days to help you arrange a Ph.D. in mathematics from the University of Göttingen. Secondly, I will arrange a refugee status for you and apply for a national interest waiver through Section 1952(d)(212) of the Immigration Act of 5.

In addition, we will arrange for the Rockefeller Foundation to help endorse your identity."

(End of this chapter)