Another smart Chinese-American returned to China. Yitang Zhang born February 5, 1955 is a Chinese-American mathematician primarily working on number theory and a professor of mathematics at the University of California, Santa Barbara since 2015. In 2025, he was appointed a professor at Sun Yat-sen University. 又一位聰明的美籍華人回國了。張益唐（1955年2月5日出生）是一位美籍華裔數學家，主要研究數論。自2015年起，他擔任加州大學聖塔芭芭拉分校數學教授。 2025年，他被聘為中山大學教授.

Mathematical prodigy 张益唐 Zhang Yi Tang returns to China
https://www.youtube.com/watch?v=eKUSDltccd8

Zhang was a self-taught mathematical prodigy, born in Shanghai (family from Pinghu) in 1955. He entered and graduated from Peking U despite not receiving a proper tertiary education. He went on to Purdue University on a full scholarship to do a PhD in Math, obtaining it in 1991.

After graduation, his extraordinary talents were discounted and he drifted for nearly a decade doing manual and low wage labor (hotel receptionist, delivery driver, subway sandwich technician). Later, he managed to get a small part time position as an adjunct (a temporary position, equivalent to being a migrant laborer on the academic plantation).

Then in 2013, out of nowhere, he submitted a limiting proof of the twin prime conjecture in the Annals of Mathematics. While the paper was being refereed, news circulated like wildfire in the mathematical world that a complete unknown, working alone, had solved one of the hardest and oldest problems in mathematics. Many dismissed it as rumor–these things just don’t happen–and it was only when it was published that the mathematical world came to grips with his accomplishment: fire from heaven.

The twin prime conjecture, hundreds of years old, is one of the great unsolved problems in mathematics, a seemingly simple but unresolvable koan. It conjectures that there are an infinite number of prime numbers that are separated by a certain number (in the classical conjecture, by 2, (such as 3 & 5, 11 & 13, etc.)).

It is seemingly intuitively correct:
Infinity is, well, infinite, so there are obviously an infinite number of numbers.
Of them, the number of prime numbers is also infinite (this was proven 2300 years ago), so it’s highly likely that there would be an infinite number of primes with a bounded difference (prime numbers that are separated by a fixed number).

Simple as the conjecture was, it turned out impossible to prove. Part of the challenge is that as numbers get larger, prime numbers become more and more scarce, like flowers at high altitude. If you have an infinitely tall mountain, will the flowers–the ones separated by a finite distance–vanish as you go higher?

Also, primes tend to appear randomly (there is no discernible pattern to their appearance (other than they get sparser (“prime number theorem”)) but on the other hand, they also don’t like to repeat the same last number as before. So curiosities abound with primes. They are the elemental numbers–numerical atoms that cannot be subdivided–yet they are very poorly understood or mapped.

The twin prime conjecture is considered one of the holy grails in number theory. It touches on the fundamentals of what it means to count, how to count/measure, and how to prove something that involves wrapping your mind around both bounded limits and infinities.

It was originally conjectured in its modern form in 1849 by Alphonse de Polignac, but no progress had been made in a century and a half.

Zhang was able to prove, beyond any mathematical doubt, that there were an infinite number of primes that had a gap of a number that was less than 70 million. Now, 70M may seem large, but it is finite–it is proof of the shortest finite gap between consecutive primes that is repeated infinitely.

Once the proof for that bounded number was demonstrated, it was a watershed breakthrough. It shows that primes–prime gaps–have been tamed. Other mathematicians were able to jump on his proofs, and they now show that that gap can be as small as 246. It’s approaching 16 ( or 12 or 6) as we speak.

To go back to our infinite mountain analogy, this finding means, no matter how high long and how high you climb this infinite mountain toward the heavens, Zhang’s proof guarantees that you will always find a flower before you take another 70 million steps. The flowers (primes) will never disappear; they are infinite, but more importantly, the distance to the next prime is bounded (70 M) and guaranteed, into infinity. It is a mind-bending discovery, given the random nature of primes.

As a result of his proof, Zhang received 4 major mathematical prizes in short order, as well as tenure.

Zhang’s proof involves the use of sieve theory (GPY; pigeonhole principle) which simplifies this discernment of infinity to generate a provable assertion.

Now Zhang is taking his mathematical genius back to China to nourish a new generation of young Chinese mathematicians. It’s just as well. Tacit but clear in the secretive way he was ferried out is that he is leaving because of the political persecution of Chinese scholars in the US. But even before then, he spent nearly a quarter century in the wilderness wasting his talents–making sandwiches and teaching undergraduate math–the academic equivalent of making sandwiches.

A lesser talent would have remained there or just given up. Even more impressive in this regard is that mathematics is considered a young person’s game–like boxing or gymnastics: it is mostly young scholars that make significant mathematical discoveries, and mathematicians consider that as they age, they are less likely to generate new breakthroughs: it is a hyper-competitive cognitive battle where young talents train non-stop.

In that respect, Zhang is like a grizzly 55-year-old boxer/kung Fu master who trained by himself without a gym, then stepped into the ring to win the world heavyweight boxing Champion. In your fifties, it rare to do original, ground-breaking work. Only through sheer mathematical Kung Fu–the raw force of his genius honed and applied with decades of determined practice, did he break out of the neoliberal purgatory that discards and wastes human talent on an industrial level.

Now he is returning to his motherland, with every deserved honor. This is a great moment in intellectual history.

Short educational video explaining his math accomplishment
https://www.youtube.com/watch?v=vkMXdShDdtY&t=2s
More detailed (18 mins)
https://www.youtube.com/watch?v=D4_sNKoO-RA
Good short explanation of the twin prime conjecture with James Maynard
https://www.youtube.com/watch?v=QKHKD8bRAro
Mechanics of the proof: pigeonhole principle (3 mins)
https://www.youtube.com/watch?v=Vr48Odw3dbk
Explained mathematically
https://www.youtube.com/watch?v=D4_sNKoO-RA
YTZ’s own lecture: notice how clear his lecture is, even for non-mathematicians
https://www.youtube.com/watch?v=Z5zvhqyO7IM&t=17s
Terence Tao on prime gaps
https://www.youtube.com/watch?v=LikuKTZzgoU

This is his slimeball advisor’s side of the story.
https://www.math.purdue.edu/~ttm/ZhangYt.pdf