How he did it: Tiep worked intensively on Brauer's Height Zero Conjecture for the past decade, although he thought about it for most of his career. "A conjecture is an idea that you believe has some validity," he told Rutgers Today. "But conjectures have to be proven. I was hoping to advance the field. I never expected to be able to solve this one." Tiep solved the conjecture in partnership with Gunter Malle of Technische Universität Kaiserslautern in Germany, Gabriel Navarro of Universitat de València in Spain and Amanda Schaeffer Fry, a former graduate student now with the University of Denver. Meanwhile, Tiep, along with Robert Guralnick of the University of Southern California and Michael Larsen of Indiana University, also addressed a longstanding problem in the Deligne-Lusztig theory, solving a crucial issue related to the traces of matrices. Both breakthroughs advance a subfield of algebra called representation theory of finite groups. They may further our understanding of symmetries of structures in nature, as well as long-term behavior of random processes arising in fields such as chemistry, physics, engineering, computer science and economics.