A professor's work on prime numbers could solve a 150-year-old puzzle in math

Shanghai-born Zhang Yitang is a professor of mathematics at the University of California, Santa Barbara. If a 111-page manuscript allegedly written by him passes peer review, he might become the first person to solve the Riemann hypothesis, The South China Morning Post (SCMP) has reported.

The Riemann hypothesis is a 150-year-old puzzle that is considered by the community to be the holy grail of mathematics. Published in 1859, it is a fascinating piece of mathematical conjecture around prime numbers and how they can be predicted.

Riemann hypothesized that prime numbers do not occur erratically but rather follow the frequency of an elaborate function, which is called the Riemann zeta function. Using this function, one can reliably predict where prime numbers occur, but more than a century later, no mathematician has been able to prove this hypothesis.

Who is Zhang Yitang?

Born in 1955, Zhang could not attend school and taught himself mathematics at the age of 11. He worked in the fields and factories for several years to make his way to Peking University, where he earned his master's degree in 1984.

Zhang then moved to the U.S. to get a Ph.D. in mathematics from Purdue University. Failing to get himself a job, Zhang then worked as an accountant, a restaurant manager, and even a food delivery person before getting a position to teach pre-algebra and calculus at the University of New Hampshire in 1999, the SCMP report said.

In 2013, Zhang shocked the world with his twin prime conjecture, which proposed that there were an infinite pair of prime numbers that differed by two. Prior to this, Zhang had achieved only one publication.

What has Zhang done now?

A manuscript that is allegedly written by Zhang has now surfaced in the mathematics research community and has proof related to the Riemann hypothesis. Although the paper has not been peer-reviewed or verified by Zhang himself, if found accurate by the mathematical community, it would mean the end of another famous mathematical hypothesis, the Landau-Siegel conjecture.

Named after mathematicians Edmund Landau and Carl Siegel, the conjecture speaks about the existence of zero points of type of L-functions in number theory. Simply put, the conjecture provides counterexamples to the Riemann hypothesis.

Zhang is expected to present his work at a lecture at Peking University today, and the publication could possibly enter the peer review process this month, the SCMP report said. The outcome of the process will be known in a few months' time, and if found accurate, could land Zhang a $1 million prize from the Clay Mathematics Institute.

This is not the first instance of a claim made for the Clay Institute's prize. Last year, media reports suggested that a mathematics professor in India had submitted such proof, while another famous mathematician Sir Michael Atiyah made similar claims in 2018. The Clay Institute has rejected both claims and confirmed that the Riemann hypothesis remains unsolved.

Will it be different this time around? The paper must pass peer review first.