Chapter 15

Zhou Yuanshen was an assistant professor at Columbia University and the only Chinese professor in the mathematics department; when he returned to New York on January 8 from his four-week trip, he first went back to campus and found no one in the mathematics faculty offices.

(In the 1960s, American universities typically observed winter break from mid-December to early January; for example, Stanford’s winter break in 1965 ran from December 18 to January 8.)

“It seems a young man came claiming he proved some theorem,” said the department staff.

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

Although classes had not officially resumed, some professors usually gathered in their offices to chat about winter break anecdotes.

“What specific theorem?” Zhou Yuanshen asked.

The staff looked apologetic: “I can’t quite remember—it had something to do with Fermat’s theorem.”

Zhou Yuanshen was stunned. Though his research was in statistics, he had heard of the legendary fame of Fermat’s Last Theorem; he was intensely curious which professor had quietly pulled off such a major breakthrough.

He had never heard of any professor whose main focus was Fermat’s Last Theorem.

Zhou Yuanshen racked his brain but could not think of anyone.

Columbia’s mathematics department was dominated by professors working on differential equations and topology—a tradition established by Jesse Douglas, the first Fields Medalist.

Algebra and number theory related to Fermat’s Last Theorem had never been Columbia’s strength.

Zhou Yuanshen gave up guessing: “I simply can’t imagine who it could be.”

The staff shook his head: “No, not a professor—a new Asian visitor. He’s very young; reportedly brought by Professor Horkheimer from the philosophy department.”

“They should still be in the classroom on the southwest side of the second floor—if you’re interested, go listen.”

“Over the past few days, more and more professors have returned early because of this. After arriving, they’ve all locked themselves in that room and barely come out.”

Now he was even more curious: a new Asian with such ability? How had he never heard of this person before?

“Come in.”

When Zhou Yuanshen knocked and entered, he was stunned: the audience wasn’t just Columbia’s mathematics faculty—it included professors from the Courant Institute at New York University, all seated below.

And standing at the front was a rare Chinese face:

“No, this isn’t a conjecture—it’s a theorem I’ve already proven, one I’ll need later.”

“It connects the Galois groups in algebraic number theory with automorphic forms and representation theory on local fields and adeles. I call it the Automorphic Representation Idea.”

“Isn’t that André Weil’s idea? Translating between fields? Sorry, Randolph, this is too crucial—we need to call more people,” Ralph Fox interrupted.

He then whispered to Lipman Bers and Paul Cohen beside him:

“I think even we’re not enough—we need to bring in everyone from Princeton.”

“Especially André Weil—he must be summoned.”

At this point, Zhou Yuanshen entered unnoticed; he sat beside his acquaintance, the Japanese scholar Hironaka Heisuke, and whispered: “What’s going on? Has Fermat’s Last Theorem been proven?”

Hironaka Heisuke was a Japanese mathematician and the 1970 Fields Medalist.

Yet in China’s internet circles, he was better known for his Korean student Xu Juner, who won the Fields Medal in 2022.

The irony of fate lay in this: Xu Juner had majored in literature as an undergraduate; in his senior year, Hironaka visited Seoul National University and taught a year-long course in algebraic geometry. Xu Juner thought this “celebrity” would make a perfect first subject for a science journalist. But he never expected that as the course progressed, over a hundred students dropped out due to its difficulty—yet Xu Juner stayed. Eventually, Xu Juner followed Hironaka directly into graduate studies.

“Yes, Randolph Lin claims he proved Fermat’s Last Theorem.”

Zhou Yuanshen’s tense heart eased—only this theorem could draw so many professors together.

“The session began on January 2 with only three professors: Ralph Fox, Lipman Bers, and Paul Cohen. As Randolph’s proof gained acceptance, they invited Professor Samuel Eilenberg.”

“Because they couldn’t determine whether the first proven Taniyama-Shimura conjecture was true.”

After three days, Samuel Eilenberg accepted his argument on the Taniyama-Shimura conjecture; Randolph then constructed a complete Euler system, designing an elegant method to compute Selmer groups and the absolute Galois group structure linking Fermat’s Last Theorem to elliptic curves.

This caused the likelihood of his proof of Fermat’s Last Theorem to rise rapidly.

So professors began calling their colleagues in the New York mathematical community; more and more arrived, until it became what you see now.”

The classroom seats two hundred; it already held about seventy.

Half of New York’s mathematical community had shown up.

“But it’s still not enough. The foundational theorems in his framework likely relate to Andrew Weil’s conjecture—so these people aren’t nearly enough.”

“We need to bring in Princeton’s entire math department—and Andrew Weil himself.”

Andrew Weil was famous in the current mathematical world—for his formidable ability and his extreme confidence.

“The top ten Andrew?” Zhou Yuanshen said.

There was no help for it—his fame was too great; even mathematicians loved gossip.

In the 1950s, the University of Chicago’s math department held a Christmas party. Many famous mathematicians attended, including André Weil. To entertain themselves, they tried to list the ten greatest living mathematicians—but excluded anyone present. Weil insisted on being included in the candidate pool.

As a result, those who knew this story often referred to Andrew Weil as “the top ten mathematician.”

“Correct. Perhaps your Chinese compatriot has found a bridge between number theory and complex analysis.”

“If such a bridge exists between number theory and complex analysis, then number theory, geometry, and the finite fields in between might all be connected by a single framework.”

This was the future famed Langlands Program, called the Grand Unified Theory of mathematics.

But the Langlands Program wouldn’t be proposed until 1967—only when Langlands sent Andrew Weil a seventeen-page handwritten letter did his conjecture transform into one of mathematics’ most influential programs.

Lin Ran was proposing precisely a part of the future Langlands Program, claiming to have proven a transformation between number theory and automorphic functions.

If this path proved viable, Andrew Weil’s conjecture would cease to be mere speculation and become reality.

Clearly, this was no longer just Columbia’s affair—it was an event for the entire mathematical world.

Ralph Fox, as department chair, instantly realized the academic meeting’s stature was insufficient and too few top scholars had arrived.

How could they rush through Fermat’s Last Theorem? Especially when it involved the grand unification of mathematics?

Fermat’s Last Theorem was more famous, but for the entire mathematical community, a tool linking number theory, algebraic geometry, and group theory was far more valuable.

Why was Alexander Grothendieck called the Pope of Algebraic Geometry? Because he invented tools that every subsequent mathematician had to use.

“Fox, we shouldn’t be thinking about calling people—we need to offer Randolph a contract immediately. Haven’t you noticed Louis Nirenberg is gone?”

“If we don’t give him a professorship soon, the Courant Institute will gladly offer him one,” Paul Cohen reminded him.

Fox snapped to attention, looked around, and realized Louis Nirenberg of the Courant Institute had indeed vanished.

The man with the bushy beard and receding hairline stood out in the crowd; his disappearance at this critical moment clearly meant he was contacting the chair of NYU’s math department.

“You’re right—I’ll handle it immediately.”

By the time he reached Randolph’s side, he heard other NYU professors asking him directly about his situation and whether he was considering a move.

“Come, Randolph, let’s talk alone,” Fox grabbed Lin Ran’s hand and pulled him toward the door, then turned to the NYU professors: “Don’t even think about poaching from Columbia.”

He would never reveal that Lin Ran hadn’t yet signed any contract with Columbia.

By the time the two left the classroom, Zhou Yuanshen still hadn’t processed it: Randolph Lin? Chinese? He’d never heard of this person before.

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

Lin Ran’s reply to Fox was that he needed more time to consider—he wanted to speak with his “elder,” Professor Horkheimer.

Fox couldn’t sit still—he couldn’t let Columbia miss the chance to surpass Princeton, or even become a mathematical holy land.

Columbia’s mathematics department excelled in topology, probability, and logic—but was nearly barren in number theory and algebra.

Lin Ran’s arrival would not only fill that void but bring an entire framework of work with him.

If Lin Ran joined Columbia, merely perfecting Andrew Weil’s conjecture here would be priceless.

“How’s it going? I heard Randolph’s performance was extraordinary,” Horkheimer said, seeing Fox arrive—clearly guessing the situation.

Fox nodded: “Yes. Randolph’s work holds profound significance for Columbia’s mathematics department.”

“I hope you’ll help persuade him to stay and teach here.”

Though he didn’t understand why a Chinese man had a Jewish mentor, from Fox’s perspective, Lin Ran’s guide was unquestionably Horkheimer.

“He really proved Fermat’s conjecture?” Horkheimer was deeply shocked.

Though not a mathematician, he knew the immense weight of a conjecture three centuries old.

“For now, the likelihood is high. More importantly, if his proof holds, he will have created a framework linking algebra and number theory—more valuable than the proof itself.”

“In any case, he fully qualifies for a professorship at Columbia,” Fox explained.

Horkheimer asked: “But what if—just hypothetically—the proof turns out to be flawed?”

Fox replied: “Then it doesn’t matter. At least his proof of the Taniyama-Shimura conjecture has already been unanimously accepted by mathematicians at Columbia and NYU.”

“Even just that one achievement makes his appointment at Columbia viable.”

“We plan to invite more American university mathematicians to New York for a conference on Fermat’s conjecture.”

“If it’s ultimately proven and Princeton or Harvard offers him a position, we may not be able to keep him at Columbia.”

Fox knew Horkheimer’s ties to Columbia—that’s why he laid everything out plainly.

After listening, Horkheimer paused and said: “Alright, I understand. I’ll persuade him to teach at Columbia—but delay the academic conference. Push it back at least two weeks.”

“Agreed,” Fox said, though puzzled, he accepted: “But first, have him write a paper on the Taniyama-Shimura proof—we can publish it in the Proceedings of the National Academy of Sciences.”

After speaking with Fox, Horkheimer returned home that night and summoned Lin Ran.

Yes, Lin Ran was temporarily staying at Horkheimer’s home.

“Randolph, I didn’t realize you possessed such extraordinary talent in mathematics.”

“So we need to speak frankly.”

“Your identity is problematic. Even if your badge is genuine—which I confirm it is—you still cannot prove your identity. You have no American status, and no documentation linking you to Larry Meyer.”

“You can mention it to me—I can’t judge its truth or falsehood.”

“But if you mention it to Theodor Adorno, his questions will be far sharper. You can’t even handle atonal sets—how will you answer Adorno’s other questions?”

“So you must stop mentioning your Fabian Society affiliation.”

“I’ll arrange all necessary cover for your identity. In the next two days, I’ll fly to Göttingen to secure you a Ph.D. from Göttingen University. Then I’ll arrange a refugee status under Section 212(d)(5) of the 1952 Immigration Act for a national interest waiver.”

“Also, I’ll arrange for the Rockefeller Foundation to endorse your identity.”