🇮🇷Maryam
Mirzakhani

She wanted to be a writer. The girl growing up in Tehran in the years after the Islamic Revolution, reading voraciously, dreaming of novels, had no particular plan to become a mathematician. Mathematics, in her early telling, was something that happened to her rather than something she chose — a subject she encountered at the Farzanegan middle school in Tehran, recognized as her native language, and was then unable to set aside. By the time she was a teenager, she had become one of the most formidable mathematical competitors in the world. By the time she was thirty-seven, she had won the highest honor in mathematics — the first woman to do so in the sixty-year history of the Fields Medal. She was forty when she died, and the loss is the kind that mathematics has not yet found a way to calculate.

Maryam Mirzakhani was born on May 12, 1977, in Tehran. She grew up in a middle-class family in a city that was, in those years, simultaneously rebuilding itself after war with Iraq and redefining itself under the cultural policies of the revolutionary government. The Farzanegan schools — elite public schools for girls — were among the institutions that flourished in this environment, and Mirzakhani's was one of the best. She found her way to mathematics through a friend who introduced her to problem-solving competitions, and she took to the discipline with a completeness that surprised even her teachers. In 1994, at sixteen, she represented Iran at the International Mathematical Olympiad and won a gold medal. The following year, she returned and achieved a perfect score.

She completed her undergraduate degree at Sharif University of Technology in Tehran and then traveled to Harvard for her doctorate, where she worked under Curtis McMullen, himself a Fields Medalist. Her doctoral dissertation solved three long-standing problems in the geometry of Riemann surfaces — the curved surfaces that arise in complex analysis and topology. The dissertation was described by mathematicians who read it not as a student's work but as the work of a mature, original, already major mathematician. It was published as three separate papers in three of the most prestigious journals in mathematics.

Her research career after Harvard was centered on the geometry of Riemann surfaces and their moduli spaces — the mathematical structures that describe all the different ways a surface of a given topological type can be given a geometric structure. The questions she asked were beautiful and the tools she brought to them were original combinations of ideas from different parts of mathematics that no one had thought to combine before. She developed connections between hyperbolic geometry, complex analysis, and dynamical systems that shed new light on questions going back to the nineteenth century. Her 2013 paper with Alex Eskin, sometimes called the "magic wand theorem," solved a major conjecture about the dynamics of flat surfaces and was described by one of her colleagues as "the most important theorem in this area in the past twenty years."

In 2014, at the International Congress of Mathematicians in Seoul, she was awarded the Fields Medal — the first woman in the medal's history to receive it, and the first Iranian. The announcement produced a reaction that went beyond the usual careful congratulation of academic honors: newspapers in Iran, where women's images are subject to strict modesty requirements, printed her photograph uncovered, a recognition that her achievement transcended ordinary categories. She was photographed at the ceremony receiving the medal from the South Korean president, her daughter beside her. She had been diagnosed with breast cancer in 2013, a fact she kept largely private while continuing to work. The cancer spread to her bones. She died on July 14, 2017, at forty years old. Her daughter was six.