Chapter 17: Unexpected Guest

Professor Grothendieck, word has come from New York that a young Chinese-American professor named Randolph Lin at Columbia University has proven Fermat’s Conjecture.

He employed a radically new method that transforms number theory problems into complex function theory; the full proof reportedly contains vast amounts of similar content, bridging disparate fields of mathematics.

New York is now asking whether you would like to attend Professor Lin’s academic lecture on Fermat’s Last Theorem.

If you are interested, they will postpone the lecture until after your arrival in New York.

At this time, Grothendieck was teaching in Paris; English has no distinction between “you” and “you (formal),” but French does.

Initially, Columbia University had only intended to invite American mathematicians for discussion, but both Fermat’s Conjecture and the Langlands Program proved too shocking.

Upon hearing the news, mathematicians spread it rapidly—by transatlantic phone calls and faxes—and the news quickly reached Europe.

Columbia University thought: since it’s already out there, why not invite Grothendieck, the greatest mathematician of the time (perhaps the greatest ever), to attend Randolph’s lecture?

After Lin Ran submitted his 150-page paper on Fermat’s Conjecture to Princeton University, Princeton’s mathematics department held three straight days and nights of meetings, concluding that the proof was fundamentally sound, though some points required further clarification from Lin Ran.

In mathematics, if your paper is not written clearly, what you call “obvious” or “easily derived” may seem anything but to others—this is why detailed academic lectures are necessary.

With Princeton’s mathematics department endorsing it, Professor Fox now had full confidence to invite Grothendieck; at least no major blunders would occur.

With all the great minds gathered, this was an opportunity to shine before the global mathematical community—Fox clearly did not intend to miss it.

“Randolph Lin? I’ve never heard that name before,” Grothendieck asked his assistant.

The assistant said: “I don’t know the details myself. Here’s the latest New York Times article on Lin, and here’s the fax from Columbia University with his proof of Fermat’s Conjecture.”

The assistant handed both documents to Grothendieck, who first picked up the New York Times—the front-page headline read:

“333-Year-Old Mathematical Mystery Solved: Columbia Professor Announces End of Fermat’s Conjecture.”

“It is reported that Columbia University’s Chinese-American professor, Randolph Lin, has allegedly proven Fermat’s Conjecture, a problem spanning 333 years. Fermat’s Conjecture was proposed in 1637 by French mathematician Pierre de Fermat as his final theorem: there are no three positive integers such that, for n greater than 2, the sum of two numbers raised to the nth power equals the third number raised to the nth power...”

Grothendieck skimmed it briefly, then picked up the paper on Fermat’s Conjecture.

The office fell silent. When he reached the section on the relationship between elliptic curves and modular forms, he suddenly said: “Heit, book me the earliest flight to New York.”

Similar conversations echoed among countless European mathematicians.

After reading the part of the paper concerning the Langlands Program, all realized mathematics was about to be shaken.

Whether or not Lin’s proof of Fermat’s Conjecture was correct, the bridge linking number theory, arithmetic geometry, and complex function theory was real; the mathematical ideas embedded within were real; his proposed theory of automorphic representations had applications across too many domains to ignore.

Anyone who could understand this paper could not resist booking a flight to New York.

The most intense reaction came from André Weil, who was already in New York; had Lin Ran not been staying at Horkheimer’s home, Weil would have wanted to talk with him all night.

Because the mathematical ideas and methods Lin used were nearly the very best application of what Weil himself had envisioned.

“I was right all along—there is a deep connection between number theory, algebraic geometry, and group representation theory! Randolph, you are a genius! Perhaps you will become an even greater mathematician than I am!”

Yet Weil expressed displeasure at Lin Ran studying philosophy under Horkheimer: “Randolph, you shouldn’t study philosophy with him—it’s wasting your talent.

You’re young; you should devote more energy to mathematics, not rush into philosophy so early.

Besides, Horkheimer is a coward—following him leads to no good end!”

Under Lin Ran’s persistent questioning, he learned that André Weil’s sister, Simone Weil, was also a philosopher. Horkheimer had fled to America long before the war, escaping Europe’s battlefield, while Simone Weil remained on the front lines in Europe resisting the Nazis, eventually dying from overwork and poor health.

In Weil’s view, anyone who fled to America was a coward.

I forgot to mention—they were both Jewish.

“How can Weil dare say that about me? He himself fled to America during WWII—back then, I was the one who introduced him to the University of Chicago. How can he call me a coward?” Horkheimer said, stunned, after hearing this from Lin Ran.

When Lin Ran repeated this to Weil during the day, Weil was furious: “My situation is different. I was arrested in Finland for anti-Nazi activities before coming to America.

If it weren’t for Rolf Nevanlinna’s intervention, I would have been shot in a Finnish prison. Horkheimer ran without even resisting. How can that be the same?”

Once Grothendieck’s travel date was set, Lin Ran’s academic lecture on Fermat’s Conjecture at Columbia University was also scheduled—for the last day of January.

While mathematicians flooded in, one unexpected visitor came to Lin Ran’s door.

“Professor Lin, I am Zhou Shukai, the Consul General of ** in New York. In addition to consular duties, I oversee overseas Chinese affairs. After hearing of your extraordinary achievements in mathematics, I’ve come to offer my congratulations. This is a small token—please accept it.”

Zhou Shukai, former secretary to Gu Weijun, a seasoned diplomat.

Lin Ran guessed the man had come specifically to court him after seeing the New York Times article.

But his sensitivity was astonishing.

Lin Ran took the envelope from him; just by touch, he guessed it contained ten $100 bills. “A generous gift,” he thought.

If China’s aerospace sector surges forward in the future, cultivating good relations with the 4V would be a way to mitigate risk, Lin Ran thought.