Chapter 55: Why the hell do I regret this more the more I talk?

"Nixon himself? Of course not,"
John Morgan shook his head repeatedly.
"If it were a fundraiser hosted by himself, you wouldn't see any of those fascinating highlights. Besides, if I were to take you to a dinner hosted by him personally, we'd have to prepare at least 200,000 dollars in donations. It's both expensive and boring. Tonight's campaign dinner is hosted by Robert Finch, Nixon's aide and his presidential campaign manager. He's a veteran member of the Elephant Party, though his two previous consecutive bids for the House of Representatives were unsuccessful. Fundraising dinners hosted by him are impossible to attend for newcomers without a personal introduction, no matter how much money you're willing to donate. Tonight, I'll take you there to broaden your horizons."
A flicker of anticipation involuntarily arose within Lin Ran's mind. An *impart*, huh.
......
Inside room 313 on the south side of the third floor of the Columbia University administration building.
Siegel and Horkheimer sat in Bauhaus-style brown leather armchairs, the sunlight streaming through New York's classic iron-framed grid windows to illuminate the round teak coffee table situated between them.
The sunlight fell precisely upon the latest issue of *Advances in Mathematics* brought by Siegel, casting a spotlight on Randolph Lin's name.
"Max, you rascal, you've put me in such a terrible position that I can barely remain at the University of Göttingen anymore. Why didn't you tell me sooner that Randolph had proven Fermat's conjecture? My colleagues at Göttingen now regard me as a traitor who no longer cares about the university's future simply because I've retired."
Before Dossin, Siegel had been the one on the defensive; now, before Horkheimer, the roles were reversed, and it was Siegel's turn to play the accuser.
"I apologize, but science inherently knows no borders. No matter where Randolph is, he remains your student, and he is also a graduate of the University of Göttingen, isn't he? Whatever achievements he makes, one can never detach them from the fact that Göttingen nurtured him," Horkheimer argued eloquently.
"Just as a philosopher should not merely serve the development of a specific discipline, but rather safeguard the negative dimension of thought, a mathematician works for all humanity, not for any single university. A mathematician is not a quantifiable output."
("Treating thought as a quantifiable 'output' is precisely the symptom of the self-destruction of Enlightenment rationality." — Max Horkheimer, *Dialectic of Enlightenment*)
Siegel was about to lose his temper: "You fellow..."

Being reprimanded by Dossin was one thing, but what irritated Siegel even more was realizing that despite being in the right, he was completely unable to outargue his opponent.
When it came to debate, mathematicians seemed genuinely helpless against philosophers.
"No, this is deception!" Siegel simply could not endure it.
Horkheimer raised an eyebrow: "How is it deception? Is Randolph a mathematical genius or not? Is he qualified enough to earn a Ph.D. in mathematics from your University of Göttingen?"
Back when Horkheimer brought Lin Ran to Göttingen, he had given his word of honor that Lin Ran was more than qualified.
Invoking his reputation, their old friendship, and their shared identity as German Jews, Horkheimer had barely managed to persuade Siegel.
Siegel was struck speechless; he simply could not bring himself to say no, for if Lin Ran were not qualified, then no future doctoral students in mathematics would ever graduate from Göttingen.
"No, the deception I'm talking about is that you didn't explain the full context of the matter to me. Einstein proposed a grand unified theory in physics; Randolph has proposed a grand unified theory in mathematics. Compared even to Einstein, his greatest advantage is his youth—he is the mathematician most likely to approach Gauss since Gauss himself, and he might actually realize the grand unified theory."
Siegel took a deep breath before continuing: "You never made it clear to me that Randolph's talent far transcends what the word 'genius' can describe. Countless geniuses exist in the mathematical world, but he is the unique one. In the realm of number theory, I can boldly conclude that he *is* already Gauss. Mathematics has no borders, and mathematical achievements constantly flow, but mathematicians do. If Randolph stays at Göttingen, Göttingen might just be able to recreate the glory of Gauss's era."
Having said this, Siegel let out another long sigh, comforting himself, as falling out with Horkheimer would hardly help his cause in bringing Lin Ran back to Göttingen:
"Sigh, Max, I can't entirely blame you. Indeed, what you said is correct—at the very least, Randolph is a graduate of the University of Göttingen, and no one can alter that fact. Göttingen produced Gauss, Riemann, and Hilbert, and now it has Randolph as well; that is not a bad thing after all. But when he returns shortly, you must help me persuade him to take up a teaching position at Göttingen."
This was precisely why Professor Horkheimer had summoned him back to the university in such a fiery haste.
Siegel was waiting for this.
"Professor, Professor Siegel, good afternoon. These are some specialty pastries I brought back from Hong Kong; please have a taste." Lin Ran placed the pastries he was holding onto the coffee table between the two men, then took a seat in a chair.
"Ah, wonderful. Randolph, I read the paper you wrote. It is exceptionally well-written. The more I ponder the ABC conjecture, the more fascinating I find it.
Fermat's Last Theorem can indeed be viewed as a corollary of the ABC conjecture.
Certain exponential equations possess only a finite number of solutions, which aligns with the high-quality triple sparsity predicted by the ABC conjecture you proposed.
The growth of $ ext{rad}(abc)$ correlates with the prime factor distributions of $a$, $b$, and $c$.
The linear forms in logarithms theory you introduced can, in turn, be applied to analyze logarithmic relations involving prime factors.
For instance, with certain triples, one can estimate whether the expression $log c - log ext{rad}(abc)$ approaches zero; lower-bound estimates can help demonstrate that such proximity is strictly limited, thereby supporting the sparsity judgment of your ABC conjecture.
Fermat's Last Theorem, Fermat's Diophantine theorem, the theory of linear forms in logarithms, and the ABC conjecture have been pieced together by you into a magnificent, comprehensive puzzle.
Extending new problems from past problems, and summarizing new theories from past problems.
This grand puzzle you have constructed faintly converges with your very own Randolph Program.
It is truly marvelous."
A mathematician who can solve problems is formidable; a mathematician who can pose problems is even more formidable.
Why is the lineage of mathematical mentorship so crucial? Because under the guidance of a master, one's intuition can perceive which problems are fertile ground for results, and those approachable problems can then be handed over to students.
It is akin to a grandmaster helping you locate lesser monsters so you can train on them first, gradually progressing from minor foes to the ultimate boss—a cultivation path that is exceptionally clear.
Otherwise, confronting the boss straight away would strip away both one's ability and confidence.
Furthermore, defeating minor foes allows one to publish papers, which in turn helps secure an academic post and establish oneself in the scholarly community.
The entire journey from minor foes to the boss also helps cultivate top-tier mathematical taste.
Following a grandmaster provides a stable career, systematic training, and refined mathematical taste.
For the mathematics department of any university, a mathematician of Gauss's caliber is sufficient to elevate it into a global center of mathematics. Need one be reminded that Russian mathematics lived off Euler's achievements for two centuries?
In Siegel's view, the Randolph standing before him, barely in his early twenties, was already a mathematician of that exact caliber.
*Why on earth do I feel more regret the more I talk about it?* Siegel thought to himself.