Chapter 52: You

Regret? He truly regretted it.

Karl Ludwig Siegel was one of the greatest number theorists of the twentieth century; after the war ended in 1947, he returned from Princeton to the University of Göttingen, his research spanning analytic number theory, Diophantine equations, modular forms, and the theory of quadratic forms.

He was also the leading figure in rebuilding Göttingen’s mathematical center throughout the 1950s, drawing in countless students and visiting scholars through his lectures alone.

It was precisely because of Siegel’s reputation that Horkheimer approached him, hoping he would take on a nominal Chinese student.

Horkheimer even brought this Chinese student, Randolph Lin, to meet Siegel in person; Siegel took an immediate liking to the young Chinese student, and their conversation flowed effortlessly—he could sense the student’s profound mathematical foundation, more than sufficient to earn a Ph.D. from Göttingen.

So, whether out of personal fondness for Lin Ran or respect for Horkheimer’s favor, Siegel agreed—and even helped add Randolph Lin’s name to Göttingen’s mathematics department records.

He was the head of Göttingen’s mathematics department throughout the 1950s; in an era without digital records, adding a single name was trivial.

But the subsequent developments took Siegel completely by surprise.

You solved Fermat’s Last Theorem? Why didn’t you say so earlier? Couldn’t Göttingen University host an academic lecture?

You developed the Randolph Program to unify mathematics? Why didn’t you say so earlier? With my decades of connections across continental Europe, couldn’t I have easily rallied all German mathematicians to make a pilgrimage to Göttingen?

You created the powerful tool of linear forms in logarithms? Why didn’t you say so earlier? I could have arranged for you to be crowned Emperor of Number Theory.

Siegel’s regret was beyond words.

Even within Göttingen University, other professors regarded him with suspicious glances, accusing him of betraying Göttingen—how could he let such a brilliant student slip away to Columbia University?

Max Doering, current head of Göttingen’s mathematics department, held the latest issue of *Advances in Mathematics*.

He was the most restrained among Göttingen’s professors, yet he couldn’t help storming into Siegel’s office to demand: How could you let Randolph go?

“No, I—” Siegel had no excuse, “No, this—” “This matter—”

“In short, this matter is complicated,” Siegel finally settled on an answer. “Yes, in short, this matter is not a simple one.”

He had promised Horkheimer, and he neither wanted nor could reveal the true circumstances.

He didn’t want to because, in front of an old friend, it was already enough to be impressive himself—now his student was even more impressive? It would be too much of a face.

Not long ago, during a research visit to Paris, Grothendieck mentioned Randolph, expressing envy that his own students couldn’t produce results as monumental as Randolph’s; as an aging professor nearing retirement, Siegel felt as refreshed as eating watermelon on a summer day.

Even Berlin newspapers, in their reports, felt compelled to note: Mathematician Siegel’s student, Randolph Lin, proved Fermat’s Conjecture, which had baffled mathematicians for over three centuries.

They also took the opportunity to praise Siegel himself.

Lin Ran was his final disciple; if not for Göttingen University, this would have been unquestionably a good thing for him.

But this was Göttingen—the postwar-rebuilt Göttingen, striving to reclaim its status as the center of mathematics.

Worse still, Göttingen’s postwar recovery strategy began with number theory.

Why? Because number theory conjectures are famous, understandable even to laypeople; solving a few major problems would instantly restore its reputation as a mathematical stronghold.

Then, using that fame to attract gifted young minds, and gradually expanding from number theory into geometry and algebra, it would take decades to fully rebuild the center of mathematics.

You talk about Fermat’s Last Theorem, Goldbach’s Conjecture, the Twin Prime Conjecture—any amateur blogger can explain those in detail. But if you talk about relationships between modular forms, Galois representations, and L-series, who outside the field even knows what you’re saying?

Starting with number theory was the fastest, most effective path.

Siegel thought this way; so did Max Doering, his successor, also a master of number theory.

At least four consecutive heads of Göttingen’s mathematics department had all worked in number theory.

And yet, while everyone in number theory worked to rebuild Göttingen, you handed over a world-class achievement—the proof of Fermat’s Last Theorem—to Columbia University?

You got away with it last time, but now, seeing the latest *Advances in Mathematics*, Doering could no longer hold back.

Hearing Siegel’s evasive answers, Doering finally exploded:

“Professor, in days past, Göttingen University was the holy land of mathematics—names like Gauss, Riemann, Hilbert still shine in mathematical history.

But since the Dark Age, we lost countless masters; Göttingen’s glory has long faded.

Now, we’ve finally found a chance at revival, and you let a figure like Randolph slip through our fingers! Who are you helping?

Every time I visit Bonn or the École Normale Supérieure, the mathematicians there are quietly laughing at us!

As former department head, and I as the current one, isn’t our shared goal to restore Göttingen University as the world’s center of mathematics?

We once were the Mecca of mathematics, drawing the gaze of the entire world. Now, we need every promising soul to rebuild this temple—and yet you handed over a soul who may be the most promising of this century, whose current achievements alone qualify him as one of the most important number theorists of the century, to New York?

You’re throwing Hilbert’s legacy into the water! Had Randolph stayed, his brilliance would have illuminated Göttingen—not have Columbia University reap the reward.”

He had finally lost control.

“If Randolph had gone to Princeton, I could understand—it has so many renowned mathematicians. But he went to Columbia, a place with nothing but the stench of money and no other appeal.

Do we really lack the funds?

If you had told me then that Randolph was just one step from proving Fermat’s Last Theorem, I would have gone to the university, to Göttingen city councilors, to Sartorius to secure sponsorship—whatever salary he demanded.

But Professor, you completely concealed the fact that you had such a prodigious student.”

Siegel was speechless. If he didn’t know the truth himself, he’d almost believe he had committed an unforgivable sin against Göttingen’s resurgence.

But he knew the truth.

“Um...” Siegel truly had no reply.

After venting, Doering calmed down, remembering that Professor Siegel had permanently returned from Princeton in 1947 to help rebuild Göttingen—he couldn’t press further:

“Professor, could you invite Randolph back to teach at Göttingen?”