Our Daily Story #6: A Subway Sandwich Mathematician Zhang Yitang 张益唐

Zhang is the typical demonstration of pure perseverance of traditional Chinese mathematicians: knock harder and harder until the truth is finally cracked.

His work is based on the prior half-way proof by 3 other mathematicians “GPY”:


Gap between Primes:

Let p1 and p2 be two adjacent primes separated by gaps of 2N:

p1 – p2 = 2 (twin primes)
eg. (3, 5), (5, 7)… (11, 13) and the highest twin primes found so far (the pair below: +1 and -1)

p1 – p2 = 4 (cousin primes)
eg. (7, 11)

p1 – p2 = 6 (sexy primes)
eg. (23, 29)

p1 – p2 = 2N

Euclid proved 2,500 years ago there are infinite many primes, but until today nobody knows are these primes bounded by a gap (2N) ?

Zhang, while working as a sandwich delivery man in a Subway shop, kept trying alone for 7 years with the GPY method, finally in 2013 he found the bounded gap: \boxed {2N <  70,000,000,000}

Recent mathematicians (Terrence Tao’s Polymath Project and others) follow his technique to narrow 2N down from 70 million to, hopefully, 16.

At age above 50, Zhang (1955 -) has shown that Mathematics is not limited to only young minds – as GH Hardy had set 35 the age limit for any great math achievements.


Part 1:

Part 2:



2. 张益唐(中文) 伯克利大学演讲记:

3. Euclid’s Proof of Infinite Primes:


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