Maryam Mirzakhani

A mathematician who connected counting closed paths on surfaces with volumes and dynamics on moduli spaces. In 1994 Mirzakhani and Roya Beheshti became the first girls on Iran’s International Mathematical Olympiad team and won gold; Mirzakhani earned a perfect-score gold in 1995. Her 2004 Harvard thesis studied the growth of simple closed geodesics on hyperbolic Riemann surfaces, and its recursion gave a new route from Weil–Petersson volumes to Witten’s conjecture. She later studied dynamics of translation surfaces with Eskin and others. In 2014 she became the first woman to receive the Fields Medal, for the dynamics and geometry of Riemann surfaces and their moduli spaces. That institutional first matters, but her mathematics should not be reduced to gender or to her death from breast cancer in 2017; the route leads through actual problems about surfaces, geodesics, and orbit behavior.

This is a thought experiment about influence, not a verified historical fact.

Beginners draw nonintersecting loops on a sphere and a torus. Intermediate learners compare geodesics on hyperbolic surfaces of different genus. Advanced learners follow recursions for moduli-space volumes. Experts study the SL(2,R) action on translation surfaces and the Eskin–Mirzakhani measure-classification theorem.