The Number Theorist Who Solved the Unbounded Denominators Conjecture

Yunqing Tang became a leading arithmetic geometer through breakthroughs on modular forms, algebraic cycles, Galois representations and the unbounded denominators conjecture. She earned her bachelor’s degree at Peking University in 2011 and completed a Harvard doctorate under Mark Kisin in 2016. After appointments at IAS, Princeton and CNRS, she joined UC Berkeley in 2022. This documentary follows the work recognized by the SASTRA Ramanujan Prize, AWM Prize and 2026 Cole Prize. an enduring intell

Arithmetic geometry studies how algebraic equations encode subtle number-theoretic information. Tang's work revealed new structure in modular forms and helped settle the unbounded denominators conjecture, a problem linking power-series coefficients with hidden arithmetic symmetry. Her career also shows the rapid emergence of a new generation of researchers moving freely between geometry, representation theory and computation. This documentary explains how denominator growth can expose the true nature of a modular.