UC Merced Magazine | Commemorative Chronicle

e discovery is but one example of trailblazing and transformative research performed at UC Merced. In Spring 2025, the university was named one of the nation’s best for research, earning R1 status by the Carnegie Classi cation of Institutions of Higher Education. Less than 10% of eligible institutions in the U.S. have earned this distinction. In the “eureka” moment study, the researchers video-recorded six Ph.D.-level mathematicians as they wrestled, chalk in hand, with notoriously tough problems from the William Lowell Putnam Mathematical Competition. e annual event is considered the world’s premier university-level math exam. A sample question from the examination: For which real polynomials p is there a real polynomial q such that p(p(x)) – x = (p(x) – x) q(x) for all real x? e researchers tracked more than 4,600 blackboard moments, such as writing, pointing, erasing and shi ing attention. ey used information theory — a branch of mathematics that measures how surprising or unpredictable an event is — to calculate “surprisal,” which rises when someone makes an unexpected move compared to their recent pattern. is research draws on theories about early warning signals in complex systems, where small changes in stability can foreshadow sudden shi s — such as ecosystems tipping or weather patterns breaking. In this case, the system was the mathematician’s ow of thought, expressed through gestures and writing. e resulting discovery belongs to all those disciplines and to none of them. It's its own thing.

UCMERCED MAGAZINE 18