Grapevine

In double breakthrough, mathematician helps solve two long-standing problems

A Rutgers University-New Brunswick professor who has devoted his career to resolving the mysteries of higher mathematics has solved two separate, fundamental problems that have perplexed mathematicians for decades.

The solutions to these long-standing problems could further enhance our understanding of symmetries of structures and objects in nature and science, and of long-term behavior of various random processes arising in fields ranging from chemistry and physics to engineering, computer science and economics.

Pham Tiep, the Joshua Barlaz Distinguished Professor of Mathematics in the Rutgers School of Arts and Science's Department of Mathematics, has completed a proof of the 1955 Height Zero Conjecture posed by Richard Brauer, a leading German-American mathematician who died in 1977.

Proof of the conjecture—commonly viewed as one of the most outstanding challenges in a field of math known as the representation theory of finite groups—is published in the Annals of Mathematics.

"A conjecture is an idea that you believe has some validity," said Tiep, who has thought about the Brauer problem for most of his career and worked on it intensively for the past 10 years. "But conjectures have to be proven. I was hoping to advance the field. I never expected to be able to solve this one."