# Cheering for Yitang Zhang

If you Google the name of “Yitang Zhang” recently, you will find many entries with keywords such as “twin primes”, “twin prime conjecture”, “bounded gaps between primes”, along with “University of New Hampshire”. Here’s three of the entries: UNH professor solves ancient mathematics riddle; UNH lecturer stuns the math world; The Beauty of Bounded Gaps. Here’s a piece from New York Times: Solving a Riddle of Primes. The reason for all this attention from the mainstream media that normally don’t pay attention to math? Mr. Zhang made a huge breakthrough toward solving an ancient problem about prime numbers. This is a brief account of his achievement.

_________________________________________________________________

A prime number is an integer greater than 1 that has no divisor other than 1 and the number itself. For example, 3 is a prime number because 1 and 3 are the only positive integers that evenly divide 3. However 6 is not a prime number since 3 evenly divides 6 in addition to 1 and 6. The first several prime numbers are: 2, 3, 5, 7, 11, 13, …

A pair of prime numbers are twin primes if they differ by 2, for examples, 3 and 5, 5 and 7, 11 and 13, 17 and 19 and so on.

The Greek mathematician Euclid gave the oldest known proof that there are infinitely many prime numbers around 300 BC. Euclid also conjectured that there are infinitely many pairs of twin primes.

The statement that there are infinitely many pairs of twin primes is called the Twin Prime Conjecture. Note that the Twin Prime Conjecture is saying that there are infinitely many pairs of primes such that the gap within each pair is exactly 2. Many great mathematical minds since ancient time had been trying to prove this conjecture but to no avail. But there were incremental progress throughout the twentieth century and in the first decade of the new century.

Mr. Yitang Zhang did not prove the Twin Prime Conjecture. He proved that there are infinitely many pairs of prime numbers such that the gap within each pair is bounded is at most 70,000,000 (70 millions). In other words, Mr. Yitang Zhang proved the Bounded Gaps Conjecture.

The gap of 70 million seems like a large number and may not seem all that significant to non-mathematicians. Now that there is now a proof that the gaps between pairs of primes do not have to increase without bound (as some mathematicians had suspected), mathematicians can work on narrowing the gaps (may be even reducing the gaps down to 2).

Indeed, since the announcement of Mr. Yitang Zhang’s result in May, some mathematicians had narrowed the gaps down to mere millions (in one case down to hundreds of thousands)!

_________________________________________________________________

His achievement is even more impressive considering the background of Mr. Yitang Zhang. Mr. Zhang did earn a PhD in mathematics in 1991 from Purdue University. In the tough academic job market after graduation, he could not find any academic position. He worked as an accountant for a period. He even made sandwiches at a Subway shop at one point. He is currently a part-time math lecturer at the University of New Hampshire, a nice school for sure, but far from the elite club of mathematicians working at places like Harvard, Princeton and Stanford.

Some people have this notion that monumental math problems such as the Twin Prime Conjecture are the domain of young math whiz. Mr. Zhang is over the age of 50.

Another handicap for Mr. Zhang is that he is not in the math specialty of number theory, which would be the specialty of the mathematicians who work on problems like Twin Prime Conjecture.

The last academic publication of Mr. Yitang Zhang is from the year 2001. So he is considered an inactive researcher by many in the math community.

Given his background, no one in the math community expects great results from Mr. Yitang Zhang. Apparently he was oblivious of his supposedly “handicaps”. He certainly did not make any excuses for himself. He just kept plugging away, building upon the advances made by other mathematicians.

The story of Yitang Zhang is remarkable in two fronts. One is his mathematical work. The other is the human dimension of the story, which makes his achievement all the more remarkable. Mr. Yitang Zhang is an inspiration to us all.

_________________________________________________________________

More information about Yitang Zhang can be found on the Internet. Here’s a few more entries from an Internet search.