Prime time

Author(s): Chris Adam
Photographs by: Provided

“He spent all of his free time thinking of mathematics.” That’s how T. T. Moh, professor of mathematics, remembers his former student, Yitang Zhang, who is now a mathematician at the University of New Hampshire and recently received worldwide attention for proving a spectacular result in number theory.

Yitang Zhang
Yitang Zhang

Moh describes Zhang as having been one of the top graduate students in mathematics in China, which is why Moh worked hard to get him and other talented Chinese students admitted into Purdue in 1985.

“Knowing that he had one published paper and training in the field of analytic number theory, I was happy to have a talented student,” Moh says. “I thought Zhang was an ambitious, intelligent and hard-working young man.”

Moh says he was surprised by Zhang’s request to work on the Jacobian Conjecture, which is a problem dealing with polynomials and variables, as his thesis topic. But Moh is no stranger to the subject — he has published an important paper on the Jacobian Conjecture.

“I felt it was odd for him to select such a difficult task,” Moh says. “After seeing his enthusiasm, I settled on it and did my best to guide him.”

After working with Moh, Zhang composed his thesis on the Jacobian Conjecture. Moh says Zhang’s thesis passed the committee with flying colors and he received his PhD in mathematics.

Moh says Zhang not only excelled in the classroom but also was active in student life on the Purdue campus.

“Some people believe that mathematicians are weird. I think differently,” Moh says. “All the mathematicians I know are quite normal. Zhang was a normal person for those seven years at Purdue. He was elected the president of the Chinese Student Club and served his community well.”

Moh says he sometimes regrets not pushing Zhang harder to find a position, but he says the process of tenure-track just did not feel like the right fit for Zhang.

“When I looked into his eyes, I found a burning bush, an explorer who wanted to reach the North Pole, a mountaineer who was determined to scale Mount Everest, and a traveler who would brave thunder and lightning to reach his destination,” Moh says. “I did not know what was the best thing for him, though I was sure of one thing — he could not survive the life of tenure-track. It was not his type.”

Though he’s not a tenure-track faculty member, Zhang has found success in academia. He works as a mathematician and lecturer at the University of New Hampshire.

It’s through Zhang’s research work as a mathematician that he has recently gained worldwide fame for proving what some experts call a “landmark result” in number theory. The result, announced in Nature in May, concerns the gaps between consecutive prime numbers. Zhang proved that there are infinitely many pairs of primes that are at most 70 million apart.

Mathematicians have called this a remarkable result because, despite the work by many top experts in the field over the years, very little has been known about gaps between consecutive primes. But Zhang was able to produce, for the first time, an estimate on the gap that did not grow to infinity: the gap is at most 70 million for infinitely many pairs of consecutive primes.

The gap between consecutive prime numbers is important not only to mathematicians but to applications outside mathematics as well. Factoring very large numbers into primes has been used to help secure the transmission of data, which is important to credit card transactions and other areas. Such work depends on the existence of very large prime numbers, and Zhang’s proof establishes that at least two primes exist within a 70 million range.

According to Simons Science News, Zhang made the discovery that led to his proof during a visit to Colorado in the summer of 2012. He had been working on the problem for three years with no progress, but then during the trip a solution suddenly came to him and he realized it would work.

Fellow mathematicians are now studying Zhang’s proof and his research to determine what might be next — including the possibility of narrowing the primes gap even more.

As for Zhang, he told Simons Science News that the glare of the spotlight has been somewhat uncomfortable.

“My mind is very peaceful. I don’t care so much about the money or the honor,” Zhang says. “I like to be very quiet and keep working by myself."

The Ulam spiral or prime spiral (in other languages also called the Ulam Cloth ) is a simple method of visual izing the prime numbers that reveals the apparent tendency of certain quadratic polynomials to generate unusually large numbers of primes. It was discovered by the mathematician Stanislaw Ulam in 1963: