Chapter 72: The Grandmaster

Although the Chinese side had done sufficient work to conceal Chen Jingrun’s background,

it was not enough.

Some more fundamental things are hard to hide.

Harvey Cohen had suspicions about the origins of this young Chinese-American named Chen Dehui, suspecting he came from China.

His foundation in number theory was solid, and his understanding of sieve methods showed originality, but his knowledge was too narrow, with a serious disconnect from contemporary mathematics.

Just from the interview and casual conversations, Harvey Cohen sensed that the techniques Chen used were very similar to those of the Chinese mathematician Hua Luogeng, who had already returned to China.

Hua Luogeng had been a visiting scholar at the Institute for Advanced Study in Princeton in the 1940s, then spent two years as a visiting scholar at the University of Illinois before returning home; Harvey Cohen had crossed paths with Hua Luogeng at academic conferences.

The similarity in technique to Hua Luogeng was one point; another was the use of sieve methods to tackle the Goldbach conjecture.

The sieve method Chen Jingrun mentioned clearly bore the imprint of the Hungarian mathematical master Alfred Renyi.

Alfred Renyi had already used sieve methods to study the Goldbach conjecture as early as 1948, proving with the large sieve that there exists a number K such that every even number is the sum of a prime and a number that is the product of at most K primes.

Chen Jingrun’s subsequent Chen’s Theorem was a further strengthening of Alfred Renyi’s work.

Clearly, Chen Jingrun had encountered Alfred Renyi’s work and deeply understood and mastered it, because Hungary and China were currently in the same camp, allowing academic achievements to flow between them.

It was like in a wuxia novel: every move you make reveals which sect you belong to; even if you mask your face and try every trick to conceal your origin, a top master can still see through you at a glance.

Mathematics is the same.

You can perfect your identity and background, but the traces of your mathematical techniques cannot be hidden from a master.

In other words, this was also Lin Ran’s fault: during the Xiangjiang seminar, Lin Ran had taught little number theory, focusing entirely on harmonic analysis and algebraic geometry, constantly trying to slip in his own private knowledge to Chen Jingrun, causing Chen to immediately betray himself before Harvey Cohen.

Fortunately, Lin Ran had carefully selected Chen’s advisor—Harvey Cohen would not care whether you came from China; he even wanted to help Chen conceal his origins.

Helping Chen plug the gaps in other fields was also an implicit suggestion: learn more techniques from other sects; I, your master, can help you conceal your roots, but if others find out, they may not help you.

“Also, Chen, sieve methods are powerful tools—Brun used them to prove the convergence of the sum of reciprocals of twin primes, and Selberg used them to achieve much more precise upper bounds.

But they have clear limitations: on one hand, sieve methods rely on combinatorial techniques rather than deep function analysis, making them somewhat crude.

Do you understand? It’s hard to control the error terms—when we handle prime number problems, the error accumulates as the sieve range expands.

I don’t deny they’re effective tools, but they need to be combined with more methods to achieve greater power.

Selberg’s sieve, for example, incorporated analytic tools—he introduced the Riemann zeta function and Dirichlet L-functions, using analysis of sums of squares to optimize upper bounds.

Only by integrating with other mathematics can sieve methods be enhanced; you must also read more frontier papers and improve the methods...”

Harvey Cohen spoke with earnest concern; his underlying message was: learn more techniques from other sects, so your origins can be concealed.

But since they had just met, Harvey Cohen couldn’t directly state his true thoughts.

Lin Ran was about to take up a post at the White House; if he revealed it now, who knew what trouble might arise.

Harvey Cohen didn’t care whether Lin Ran worked for China; from the Manhattan Project to NASA, how many top American scientists had worked for the Soviet Union?

Even if Lin Ran truly worked for China, so what?

Still, Harvey Cohen didn’t believe Lin Ran actually worked for China; he could smell China’s scent in Chen Jingrun’s moves, but from Lin Ran himself, he could only smell the scent of a master.

Every move, every technique, perfectly natural, the demeanor of a grandmaster, unmatched.

Earlier, during the seminar, people had joked about submitting to him—it sounded exaggerated—but Harvey Cohen knew it was not exaggerated at all.

Because Randolph Lin’s most bizarre trait was that not only had he produced Fields Medal-level results one after another, but after reading his papers, no one could find any way to improve them.

Usually, when a master produces a result, others can build a series of results along that direction.

The easiest way is to improve the master’s paper.

For example, Wiles’s proof of Fermat’s Last Theorem was later reduced from 130 pages to 50 pages—that too was progress.

But Lin Ran’s papers were unimprovable; the published version was already perfect, at least no one could find any way to improve it at present.

Moreover, Lin Ran didn’t just solve the problem himself and create a general method—he even came up with a new conjecture for you.

It was truly too bizarre.

Thus, during the New York number theory seminar while Lin Ran was absent, everyone privately discussed him as if he were a celestial being, unable to imagine how Göttingen could have let such a talent slip away.

Siegel, former head of Göttingen and a master of number theory, had previously come to New York and been invited by Harvey Cohen to attend the number theory seminar, but he couldn’t bear being constantly asked why Göttingen had let Lin Ran go.

Siegel had originally planned to spend six months as a visiting scholar at Columbia University, but after being silenced by the questions, he returned to Göttingen after only one month.

It was far easier to go back and face only Doering than to stay in New York and be mocked by everyone.

For this reason, the twenty-something mathematical master Harvey Cohen instinctively wanted to protect him, and also didn’t believe Lin Ran was truly Chinese—he merely sympathized with China.

This was perfectly normal in America.

America’s academic circles were full of Jewish scientists who had come from Germany; many of them supported Germany’s development in various ways; so why would it be strange for Chinese-Americans to sympathize with China and want to help?

The academic climate of the 1960s was still quite open.

“Appointing Randolph Lin as Special Assistant for Aerospace Affairs

Be it known that Randolph Lin is hereby appointed Special Assistant to the President for Aerospace Affairs, responsible for aerospace matters. Mr. Lin shall report directly to Vice President Lyndon Johnson, with duties including providing policy advice to the President on aerospace matters, overseeing the implementation of NASA-related work, and participating in aerospace-related affairs.

This appointment shall take effect on March 1, 1961.

Signed: John F. Kennedy

United States of America”