Maryam Mirzakhani

Iranian mathematician Maryam Mirzakhani. Photo courtesy of Mirzakhani

Mirzakhani became the first woman and the first Iranian to win the Fields Medal in 2014 at age 37, while serving as a mathematics professor at Stanford University.

Established in 1936, the Fields Medal is awarded every four years by the International Mathematical Union (IMU) to up to four mathematicians under 40, recognizing both major achievements and future promise. Until 2014, all 52 recipients had been men.

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

According to IMU, she received the award for her outstanding contributions to understanding the dynamics and geometry of Riemann surfaces and their moduli spaces. Her work centered on geometry and dynamical systems, especially the properties and symmetries of curved surfaces such as spheres and doughnut-shaped forms. Though theoretical, it also had applications in physics and quantum field theory.

"It was bound to happen," Ingrid Daubechies, former president of IMU and the first woman to lead the organization, told Scientific American in a 2017 interview. "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."

Born in Tehran on May 3, 1977, Mirzakhani first wanted to become a writer before discovering a passion for mathematics in high school. She later won gold medals at the 1994 and 1995 International Mathematical Olympiads, earning a perfect score in the latter.

"It is fun – it’s like solving a puzzle or connecting the dots in a detective case," she told Stanford University. "I felt that this was something I could do, and I wanted to pursue this path."

After receiving a bachelor’s degree from Sharif University of Technology in Iran in 1999, she completed her PhD at Harvard University in the U.S. She later taught at Princeton University before joining Stanford in 2008.

In a 2014 interview with Quanta Magazine, Mirzakhani, who described herself as a "slow" mathematician, said she often chose the harder route when tackling mathematical problems. "You have to ignore low-hanging fruit, which is a little tricky," she said. "I’m not sure if it’s the best way of doing things, actually — you’re torturing yourself along the way."

While traveling to the International Congress of Mathematicians (ICM) in Seoul, South Korea, in 2014, where the medal was presented, Mirzakhani was in the midst of her first battle with cancer, though she kept it private at the time. The disease later returned, and despite aggressive treatment, it spread to her liver and bones.

She died on July 17, 2017, at age 40. She continued working until shortly before her death, and colleagues said she faced her illness with both realism and hope. She was survived by her husband, Jan Vondrák, and their daughter, Anahita.

Her death was "a big loss and shock to the mathematical community worldwide," Peter C. Sarnak a mathematician at Princeton University and the Institute for Advanced Study, told The New York Times.

"She was in the midst of doing fantastic work. Not only did she solve many problems; in solving problems, she developed tools that are now the bread and butter of people working in the field."

Curtis McMullen, her doctoral advisor, said her work "opens new frontiers of research that are just starting to be explored," adding that her questions would continue to shape the field.

Maryna Viazovska

Ukrainian mathematician Maryna Viazovska. Photo courtesy of EPFL

Viazovska became the second woman to receive the Fields Medal on July 5, 2022, at age 37, during a ceremony at Aalto University in Helsinki, Finland.

"I feel sad that I’m only the second woman," Viazovska said in a statement. "But why is that? I don’t know. I hope it will change in the future."

A specialist in number theory, she was honored for solving the sphere-packing problem in eight and 24 dimensions, showing the most efficient way to arrange spheres in space. The question had remained unsolved for more than 400 years.

Mathematician Henry Cohn, who gave the official ICM talk celebrating her work, said Viazovska "manages to do things that are completely non-obvious that lots of people tried and failed to do," adding that she does them by "uncovering very simple, natural, profound structures, things that nobody expected and that nobody else had been able to find."

Born in Kyiv on Dec. 2, 1984, Viazovska developed an interest in mathematics at an early age. "I've liked mathematics since my schooldays," she said in a 2022 interview with Swiss research institute École Polytechnique Fédérale de Lausanne (EPFL). "It always seemed like the most straightforward subject."

She earned her undergraduate degree from Taras Shevchenko National University of Kyiv, completed a master’s degree in Germany, and received her PhD from the University of Bonn in 2013. She later joined EPFL, becoming a full professor at 33.

"Studying pure mathematics is bit like reading a book with illustrations," she said in a 2022 interview with EPFL. "The images are linked to the text, but they don’t match the written word exactly." She said problem-solving felt like "doing a jigsaw puzzle," while abstract ideas helped her connect concepts and identify practical applications.

The 2022 ICM was originally scheduled to take place in St. Petersburg, Russia, but was moved to Helsinki and held virtually after Russia attacked Ukraine. In her acceptance remarks, Viazovska spoke about the war’s effect on her life and work.

"Ukraine is my native country, and seeing how it's being destroyed, how many lives are lost ... of course, it's all very difficult," she said, adding that teaching math allowed her to "forget about this fear and pain" she felt about her home country being attacked.

"In February, my life changed forever, And not only for me, but for everyone in the world and especially the people in my country," she said. "Whenever we have something good in our life, often we take that for granted. And peaceful is what I always took for granted."