Chapter 52

Regret, truly regret.

Carl Ludwig Siegel was one of the greatest number theorists of the 20th century. After the war ended in 1947, he returned to the University of Göttingen from Princeton, and his research direction covered analytic number theory, Diophantine equations, modular forms, and the theory of quadratic forms.

He was also the representative figure of the reconstruction of the Göttingen mathematical center throughout the 1950s, attracting a large number of students and visiting scholars with his lectures.

It was precisely because of Siegel's fame that Horkheimer begged him, hoping he would accept a nominal Chinese student.

Horkheimer even specially brought this Chinese student named Randolph Lin to the University of Göttingen to meet him. Siegel had a good impression of this young Chinese student, and the two had a pleasant conversation. He could smell the other party's mathematical foundation from the conversation; it was more than enough to get a PhD in mathematics from Göttingen.

So, whether it was because of his good impression of Lin Ran himself or out of face for Horkheimer, Siegel agreed, and even cooperated with the other party to add the existence of Randolph Lin to the files of the Göttingen Department of Mathematics.

He was the head of the Department of Mathematics at Göttingen throughout the 1950s, and in an era when these files were not digitized, adding a person was not difficult at all.

It was just that the subsequent progress of events was a bit beyond Siegel's expectations.

If you had solved Fermat's last conjecture, you should have said so earlier! Could the University of Göttingen not hold an academic report?

If you had the Langlands program capable of unifying mathematics, you should have said so earlier! With the connections I, Siegel, have painstakingly managed in continental Europe for many years, wouldn't it be easy to call on mathematicians from all over Germany to come to Göttingen on a pilgrimage?

If you had made such a useful tool as the theory of linear forms in logarithms, you should have said so earlier! It wouldn't have been impossible for me to find a way to get you the title of Emperor of Number Theory.

Siegel's regret could not be described in words.

Within the University of Göttingen, he was looked at with strange eyes by other professors, who felt that he was a traitor to Göttingen. How could he let such an awesome student run off to Columbia University?

Ma Kesi Deuring, who was holding the latest issue of *Inventiones Mathematicae*, was the current head of the Göttingen Department of Mathematics.

He was the most restrained among the professors in the Göttingen Department of Mathematics, but he couldn't help but run to his office to question him: How could you let Randolph slip away?

"No, I..." Siegel couldn't think of any reason to defend himself, "No, this..." "This matter..."

"In short, this matter is very complicated," Siegel finally found a way to say it, "That's right, in short, this matter is not such a simple matter."

He had promised Horkheimer, and he didn't want to tell the real inside story.

He didn't want to because, in front of an old friend, it was one thing for me to be awesome, but for my student to be this awesome, it was simply too much face.

Not long ago, when he led a team to Paris for an academic visit, Grothendieck talked about Randolph and said he envied his student for being able to produce greater achievements than him. As an old man nearing retirement, Siegel felt as refreshed as eating a watermelon in summer.

Including the Berlin newspapers, when reporting, they all had to mention: Mathematician Siegel's student Randolph Lin proved Fermat's conjecture, which had plagued the mathematical community for over three hundred years.

By the way, they also blew him up a bit.

Lin Ran was his closed-door disciple; if one didn't consider the University of Göttingen, this matter was definitely a good thing for him.

But this was Göttingen, the Göttingen that had recovered after the war, the Göttingen that wanted to return to the status of a mathematical center.

What was even more fatal was that the strategy for the post-war recovery of the Göttingen Department of Mathematics was to start with number theory.

Why? Because the conjectures of number theory are famous, ordinary people can understand them, and if you solve a few big problems, you can become a mathematical highland again in public opinion.

Then use the fame to attract talented young people, and then spread from the field of number theory to geometry and algebra, spending decades to realize the reconstruction of the mathematical center.

You talk about Fermat's Last Theorem, the Goldbach conjecture, the twin prime conjecture—these famous number theory problems—even wild self-media can explain them clearly. You talk about the relationship between modular forms, Galois representations, and L-series—who in the outside world knows what you are talking about?

Starting from number theory to rebuild is the fastest and most effective way.

Siegel thought so, he was a master in the field of number theory, and Ma Kesi Deuring, who succeeded him, also thought so, and was also a master in the field of number theory.

At least four consecutive heads of the Göttingen Department of Mathematics were all doing number theory.

As a result, everyone was doing number theory to rebuild Göttingen, and you actually handed over a world-class achievement like the proof of the Fermat conjecture to Columbia University?

He had endured it last time, but this time, seeing the latest *Inventiones Mathematicae*, Deuring really couldn't hold back.

Hearing Siegel's evasion, Deuring really couldn't hold back and spoke passionately:

"Professor, back in the day, the University of Göttingen was the holy land of mathematics; the names of giants like Gauss, Riemann, and Hilbert still remain in the history of mathematics to this day.

But since the dark ages, we have lost countless masters, and the glory of Göttingen has long since dimmed.

Today, we finally have a chance for revival, yet you let a figure like Randolph slip through our hands! Whose favor are you doing?

No matter if I go to the University of Bonn or the École Normale Supérieure in Paris, the mathematicians there are secretly laughing at us!

As a former department head, and I as the current department head, aren't our goals both to make the University of Göttingen the center of world mathematics again?

We were once the Mecca of mathematics, attracting the eyes of the whole world. But now, we need every potential soul to rebuild this temple, and yet you sent a soul who is possibly the most potential of this century—Randolph, who just with these current achievements can be called one of the most important mathematicians in the field of number theory this century—to New York.

You are throwing Hilbert's legacy into the water! If Randolph could stay, his light would illuminate Göttingen, instead of Columbia University picking up the bargain."

He was ranting crazily; he really couldn't hold it in.

"If Randolph had gone to Princeton, I could still understand; after all, Princeton has many famous mathematicians, but he went to Columbia University, to a Columbia that has no other attraction besides the stench of money.

Is it possible that we can't afford this money?

If you had told me at the time that Randolph was only one step away from the Fermat conjecture, no matter how much annual salary he wanted, I would have found the school, found the councilors of the city of Göttingen, and found Sartorius to provide sponsorship.

But Professor, you completely hid the fact that you had such a gifted student."

Siegel was speechless; he was left speechless. If he didn't know the inside story, he himself would feel that he had committed an unforgivable mistake against the rise of Göttingen.

But he just didn't.

"Um..." Siegel really didn't know what to say.

After Deuring finished complaining, he calmed down. Thinking that Professor Siegel in front of him had returned to Göttingen permanently from Princeton in 1947 to help with the reconstruction of Göttingen, he couldn't bear to say harsh words again:

"Professor, can you invite Randolph back to Göttingen to teach?"