Mirzakhani broke a nearly eight-decade tradition when she became the first woman among 53 recipients since the prize's establishment in 1936. She remains one of only two women ever to receive the distinction.

"This is a great honor. I will be happy if it encourages young female scientists and mathematicians," Mirzakhani said at the time. "I am sure there will be many more women winning this kind of award in coming years."

Awarded every four years by the International Mathematical Union (IMU), the Fields Medal, often described as the "Nobel Prize of mathematics," recognizes mathematicians under 40 for outstanding achievements and future potential.

According to the IMU, she received the award for her contributions to understanding the geometry and dynamics of Riemann surfaces and their moduli spaces. Her work explored the behavior and symmetries of curved surfaces, advancing mathematics while influencing fields including physics and quantum theory.

"It was bound to happen," Ingrid Daubechies, former president of the IMU and the first woman to lead the organization, told Scientific American in 2017. "There are excellent young women mathematicians. Many times they have been on the short, short list, but it had so far not happened. I was very, very happy that it happened on my watch."

Iranian mathematician Maryam Mirzakhani. Photo courtesy of Stanford University

From aspiring writer to pinoneering mathematician

Born in Tehran on May 12, 1977, Mirzakhani did not initially plan to become a mathematician. An avid reader, she once dreamed of becoming a writer and spent much of her childhood immersed in books.

Her path to mathematics was not straightforward. During elementary school, she struggled with the subject and lost confidence after a teacher suggested she lacked talent. At that age, "it's so important what others see in you," Mirzakhani told Quanta Magazine in 2014. "I lost my interest in math."

A more encouraging teacher the following year helped restore her confidence. "Starting from the second year, she was a star," recalled Roya Beheshti, Mirzakhani's lifelong friend from elementary school who is now a mathematics professor at Washington University in the U.S.

While attending the all-girls Farzanegan High School in Tehran, Mirzakhani and Beheshti challenged themselves with problems from Iran's national Olympiad selection exam. Encouraged by their progress, they persuaded their principal to arrange advanced mathematics training, despite no Iranian woman ever having represented the country at the International Mathematical Olympiad.

Mirzakhani later said her principal's belief that "you can do it, even though you'll be the first one" helped shape her outlook on life.

In 1994, at age 17, she and Beheshti earned places on Iran's Olympiad team. Mirzakhani won a gold medal that year and returned in 1995 to achieve a perfect score. What began as a test of her abilities evolved into a deep love of mathematics. "You have to spend some energy and effort to see the beauty of math."

After earning a mathematics degree from Sharif University in Tehran in 1999, Mirzakhani moved to the U.S. for graduate studies at Harvard University. There she attended seminars led by Curtis McMullen, who later became her doctoral adviser and a major influence on her career.

At Harvard, she developed a fascination with hyperbolic geometry, a branch of mathematics that studies curved spaces whose properties differ from those of ordinary geometry. During her doctoral studies, she solved several longstanding problems that had challenged mathematicians for decades, revealing new connections between geometry, topology and theoretical physics.

Her work also produced a new proof of a famous conjecture proposed by physicist Edward Witten. The problem was so difficult that an earlier proof by mathematician Maxim Kontsevich contributed to his Fields Medal in 1998. Experts have said that each of the major problems Mirzakhani solved during her doctorate would have been a notable achievement on its own.

Her thesis generated three papers published in Annals of Mathematics, Inventiones Mathematicae and the Journal of the American Mathematical Society, among the field's most prestigious journals. After receiving her doctorate in 2004, she joined Princeton University as an assistant professor and became a research fellow at the Clay Mathematics Institute before moving to Stanford University in 2009.

Recognition followed quickly. Popular Science magazine named her to its Brilliant 10 list in 2006. She received the American Mathematical Society's Blumenthal Award in 2009, the Satter Prize in Mathematics in 2013 and the Clay Research Award in 2014. In 2016, she was elected to the U.S. National Academy of Sciences, one of the country's highest scientific honors.

Despite her growing acclaim, Mirzakhani remained modest. When she received an email in February 2014 informing her that she had won the Fields Medal, she initially assumed the sender's account had been hacked.

A self-described "slow" mathematician, she became known for pursuing problems others considered impossibly difficult. McMullen said her willingness to tackle ambitious questions distinguished her from her peers. "Her work opens new frontiers of research that are just starting to be explored," he told Scientific American. "She approached new mathematics with fearless ambition."

Rather than seeking easier problems, Mirzakhani often gravitated toward the hardest ones. She worked by covering large sheets of paper with diagrams, formulas and notes. Her young daughter once described the process as "painting."

In an interview with The Guardian after receiving the Fields Medal, Mirzakhani said many students never give mathematics a genuine chance because the subject can seem "pointless and cold" without curiosity or engagement. Drawing on her own experience of struggling with math in middle school, she said, "The beauty of mathematics only shows itself to more patient followers."

A legacy that lives on

Mirzakhani died on July 14, 2017, at Stanford Hospital after battling breast cancer. She was 40. She is survived by her husband, Jan Vondrak, and their daughter, Anahita. Her birthday May 12 has become International Women in Mathematics Day after it was proposed in July 2018 by the Women’s Committee of the Iranian Mathematical Society at the World Meeting for Women in Mathematics in Rio de Janeiro, Braziland officially celebrated for the first time in 2019.

Her death was deeply felt throughout the mathematics community. "Women mathematicians all over the world are e-mailing each other, trying to comfort each other," Ingrid Daubechies, a mathematics professor at Duke University, said. "It is heartbreaking that we had to lose a gifted mathematician and wonderful role model so soon."

Stanford President Marc Tessier-Lavigne told Stanfod Report that her influence would extend far beyond her own research. "Maryam is gone far too soon, but her impact will live on for the thousands of women she inspired to pursue math and science."

Mirzakhani's influence continues to be felt worldwide years after her death.

Her birthday, May 12, became International Women in Mathematics Day after the Women's Committee of the Iranian Mathematical Society proposed the celebration in 2018. It was officially observed for the first time in 2019.

In February 2025, mathematicians Nalini Anantharaman of the College de France and Laura Monk of the University of Bristol built on Mirzakhani's research to prove a major new result about hyperbolic surfaces, a class of geometric objects that she spent much of her career studying.

Their work showed that properties once thought to be rare are in fact typical. "This is a landmark result," Peter Sarnak, a mathematician at Princeton University, told Quanta Magazine. "There'll be a lot more that will come out of this."

The breakthrough highlights the enduring reach of Mirzakhani's ideas. Although Monk said she has never watched Mirzakhani's recorded lectures or heard her voice, she feels connected to her through the mathematics she left behind. "When you read the works of someone in detail, you end up understanding things beyond the sheer content of the work, about how they were thinking."

Monk said she was honored to help extend Mirzakhani's legacy. For many mathematicians, the result is also a reminder of what Mirzakhani might have achieved had she lived longer. "I'm sad she can't see it," mathematician Alex Wright, one of her former students, said.

"She was supposed to be there to appreciate this," said Anton Zorich, a mathematician at the Institute of Mathematics of Jussieu in Paris. "I have no doubt she would be extremely happy."