Chapter 14: A Newcomer Arrives in the New York Mathematics Community

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Zhou Yuanshen was 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 to the university and found that there was no one in the mathematics professors’ offices.

(In the 1960s, American universities typically held winter breaks from mid-December to early January. For example, Stanford’s winter break in 1965 was from December 18 to January 8.)

“It seems a young man came in claiming to have proven some theorem,” said one of the administrative staff in the math department.

Zhou Yuanshen grew curious—what theorem could possibly attract such attention?

Although the semester had not officially begun, some professors usually lingered in their offices, chatting about their winter break adventures.

“What specific theorem?” Zhou inquired.

The staff member apologized, “I don’t quite remember. I think it was related to Fermat.”

Zhou was stunned. Though his research focused on statistics, he had at least heard of the famed Fermat’s Last Theorem. He was intensely curious about which professor had quietly made such a breakthrough.

He had never heard of any professor specializing primarily in Fermat’s Last Theorem.

After pondering, Zhou could not guess who it might be.

Most of Columbia’s math faculty were focused on differential equations and topology—a tradition established by Jesse Douglas, the first Fields Medalist affiliated with Columbia.

Columbia had never excelled in algebra or number theory related to Fermat’s Last Theorem.

Zhou gave up guessing. “I really can’t think of who it is.”

The staff shook his head. “No, it’s not a professor. It’s a new young Asian man, said to be a junior brought by Professor Horkheimer from the philosophy department. They’re probably still in a classroom on the southwest side of the second floor. If you’re interested, you could listen in. More and more professors have come back early because of this. Once they arrive, they all dive into that room and barely leave.”

Now even more curious, Zhou wondered how such a young Asian newcomer could be so accomplished—he had never heard of this person before.

“Please come in.”

When Zhou knocked and entered, he was stunned. Not only were Columbia’s math professors seated in the audience, but also professors from New York University’s Courant Institute. All sat below.

And at the front stood a rare Chinese figure:

“No, this is not a conjecture. It’s a theorem I have proven, and it will be used later. It connects the Galois groups in algebraic number theory with local fields and the automorphic forms and representation theory on adelic algebraic groups. I call it the automorphic representation concept.”

“Isn’t this exactly what André Weil envisioned? Transforming from one field to another. Sorry, Randolph, this is crucial. I think we need to call more people,” Ralph Fox interrupted.

He then whispered with Lipman Bers and Paul Cohen beside him.

“I don’t think just the three of us are enough now. We should at least call the Princeton people. Especially André Weil himself. We have to get him over here.”

At that moment, no one noticed Zhou Yuanshen entering. He sat beside his acquaintance, the Japanese-American scholar Hirakata Heisuke, and quietly asked, “What’s going on? Has Fermat’s Last Theorem been proven?”

Hirakata Heisuke was a Fields Medalist from 1970, well known on Chinese-language internet due to his Korean student Xu Jun’er winning the Fields Medal in 2022.

Fate was curious: Xu Jun’er’s undergraduate major was literature, but when Hirakata was a visiting scholar at Seoul National University in his senior year, he taught a year-long algebraic geometry course. Xu initially considered profiling Hirakata as a science journalist’s first subject. Unexpectedly, over a hundred students dropped out as the course grew difficult, but Xu stayed and eventually followed Hirakata into graduate school.

“Yes, Randolph Lin claims to have proven Fermat’s Last Theorem.”

Zhou felt relieved. Indeed, only this theorem could draw so many professors together.

“The meetings started on January 2. Initially, only Ralph Fox, Lipman Bers, and Paul Cohen were present. Later, as Randolph’s proof gained acceptance, they invited Professor Samuel Allenberg because they couldn’t verify if the first proven Taniyama-Shimura conjecture was valid.”

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After three days, Samuel Allenberg accepted the Taniyama-Shimura conjecture proof and the construction of a complete Euler system. Using ingenious methods, they designed Selmer group calculations and related the absolute Galois group structure connecting Fermat’s Last Theorem with elliptic curves.

This dramatically increased confidence in the proof’s validity.

Thus, the professors called more friends from New York’s mathematical community to the seminar, swelling attendance to the current size.

The classroom held 200 seats; already about seventy were occupied.

More than half of New York’s mathematicians had arrived.

“But it’s still not enough. The preliminary theorems in the proposed framework may be related to André Weil’s conjecture, so these people aren’t sufficient. We definitely need to call Princeton’s math department and get André Weil himself here.”

André Weil was highly renowned in contemporary mathematics, not only for his formidable skills but also his confidence.

“The André ranked in the top ten?” Zhou asked.

With such fame, mathematicians loved gossip.

In the 1950s, the University of Chicago’s math department held a Christmas party attended by many famous mathematicians, including André Weil. For amusement, they tried to list the ten greatest living mathematicians, excluding those present. Weil insisted on including himself among the candidates.

This led people to affectionately call him a top-ten mathematician when mentioning André Weil.

“Yes. Perhaps your Chinese compatriot has found a bridge between number theory and complex analysis. If such a bridge exists, number theory, geometry, and the finite fields in between might be linked in some way.”

This was the future celebrated Langlands program, hailed as the grand unified theory of mathematics.

However, the Langlands program would not be formally proposed until 1967, when Langlands sent André Weil a 17-page handwritten letter. The program then evolved from Weil’s conjecture into one of the most influential frameworks in mathematics.

Lin Ran’s work proposed a portion of this future Langlands program, claiming to have proven the transformation between number theory and automorphic functions.

This path being viable meant that Weil’s conjecture might cease to be conjecture and become reality.

Clearly, this was no longer just a Columbia matter but a monumental event for the global mathematics community.

Ralph Fox, as department chair, instantly realized the seminar’s current scale and tone were insufficient. Many top experts hadn’t arrived yet.

How could they so casually conclude the Fermat’s Last Theorem discussion, especially when it involved a far more significant mathematical unification?

Though Fermat’s Last Theorem was famous, a tool linking number theory, algebraic geometry, and groups was far more crucial to mathematics.

Why was Alexander Grothendieck hailed as the pope of algebraic geometry? Because he invented the tools later mathematicians relied upon.

“Fox, I think what we need to consider now isn’t who to call but to quickly offer Randolph a contract. Didn’t you notice Louis Nirenberg has disappeared?”

Paul Cohen reminded him.

Fox then looked around and realized Louis Nirenberg from NYU’s Courant Institute was indeed gone.

Nirenberg, with his thick beard and high receding hairline, was very conspicuous in the crowd. Disappearing at such a critical time likely meant he was contacting NYU’s math department head.

“Yes, you’re right. I’ll prepare it immediately.”

As Fox approached Randolph, he heard other NYU professors asking about Randolph’s situation and whether he was considering changing jobs.

“Come, Randolph, let’s talk privately,” Fox said, taking Lin’s hand and starting to leave. He glanced back at the NYU professors and added, “Don’t think about poaching people from Columbia.”

Of course, he wouldn’t reveal the fact that Randolph hadn’t signed with Columbia yet.

After they left, Zhou still hadn’t fully processed it. Randolph Lin, Chinese? How had he never heard of such a figure?

“This is the proof of the Taniyama-Shimura conjecture. Take a look—it’s a very interesting approach,” Hirakata handed Zhou a thick stack of papers. “Taniyama probably never imagined his conjecture would be proven just five years after he proposed it.”

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Lin Ran’s reply to Fox was that he needed to consider it further and discuss with his “elder,” Professor Horkheimer.

Fox grew restless. He could not watch the chance for Columbia to surpass Princeton—or even become a mathematical mecca—slip away.

Columbia’s math department excelled in topology, probability theory, and logic but was nearly empty in number theory and algebra.

Lin Ran’s arrival could fill that gap and bring a whole framework of work.

If Lin joined Columbia and refined André Weil’s conjecture here, the value would be priceless.

“So? I heard Randolph’s performance is extraordinary,” Horkheimer said, evidently guessing the general situation when Fox took the initiative to approach him.

Fox nodded. “Indeed. Randolph’s work is of great significance to Columbia’s math department. I hope you can persuade him to stay and teach here.”

Though it was unclear why a Chinese scholar had a Jewish elder, from Fox’s perspective, Lin’s mentor was Horkheimer.

“Has he really proven Fermat’s Last Theorem?” Horkheimer was shocked inwardly.

Though not a mathematician himself, he knew how valuable a conjecture that had stood for over three centuries was.

“At this point, there’s great hope. More importantly, if his proof holds, he will create a framework connecting algebra and number theory—a tool more valuable than the proof itself. In any case, he fully qualifies to teach at Columbia.”

Horkheimer asked, “But what if—just if—it turns out his proof has flaws?”

Fox said, “That’s not so important. At least his proof of the Taniyama-Shimura conjecture has unanimous support from Columbia and NYU mathematicians. That alone suffices for a teaching position here. We plan to invite more American university mathematicians to New York to discuss Fermat’s conjecture. If it’s ultimately proven, and Princeton or Harvard offers him a position, we might lose him.”

Fox understood Horkheimer’s ties to Columbia and carefully explained the situation.

After a moment’s thought, Horkheimer said, “Alright, I understand. I will persuade him to teach at Columbia but ask to postpone the academic conference by at least two weeks.”

“Okay.” Though puzzled, Fox agreed. “But first, have him write a paper on his proof of the Taniyama-Shimura conjecture. We can publish it in the Proceedings of the National Academy of Sciences.”

After their conversation, that evening Horkheimer returned home and summoned Lin Ran.

Indeed, Lin was temporarily staying at Horkheimer’s house.

“Randolph, I didn’t expect you truly have exceptional talent in mathematics. We need to have an honest talk. Your identity is problematic. Even if you have a badge—and I am certain it’s genuine—you still can’t prove your identity. You don’t have American citizenship, and aside from the badge, you have no way to prove your relationship with Larry Meyer.

“You can assert it in front of me—I honestly can’t judge its truth. But if you say so before Theodor Adorno, his questions are far sharper. You barely handle the collection of non-modular forms, let alone his other queries.

“So it’s best not to mention your affiliation with the Fabian Society anymore.

“I will help you cover all identity issues. In the next few days, I’ll fly to Göttingen to arrange for you to obtain a mathematics PhD from the University of Göttingen. Also, I will arrange refugee status for you under the 1952 Immigration Act’s Section 212(d)(5) for a national interest waiver.

“Additionally, the Rockefeller Foundation will endorse your identity.”