Maryam Mirzakhani and the Art of Unfolding
Some people change the world not with loud declarations or sweeping movements, but through quiet, persistent dedication to what they love. They follow their curiosity with discipline, shaping the future in ways that feel almost invisible—until history looks back and realizes the magnitude of their work. Maryam Mirzakhani was one such person. Through her deep engagement with mathematics, she transformed the field. In doing so, she broke multiple barriers: becoming the first woman, the first Iranian, and the first Muslim to win the Fields Medal, mathematics' highest honor. Her legacy lies not only in the concepts she explored, but in the glass ceilings she shattered by relentlessly following what she was curious about.
![]() |
Maryam Mirzakhani © Courtesy Stanford News Service |
Born in Tehran in 1977, Maryam Mirzakhani grew up during a turbulent period in Iran’s history, yet found solace in stories and books. As a child, she imagined herself becoming a writer, not a mathematician. But her path began to shift in high school, when she discovered an unexpected fascination with mathematics, despite early discouragement and uninspiring classroom experiences.
Mirzakhani’s talent soon became undeniable. In 1994, as a junior, she became one of the first Iranian women to qualify for the International Mathematical Olympiad, where she earned a gold medal. The following year, she returned and achieved a perfect score—securing a second gold medal and international recognition. She went on to study mathematics at the prestigious Sharif University of Technology in Tehran.
She became deeply intrigued by the strange and beautiful geometry of curved spaces—specifically, hyperbolic surfaces. Unlike flat, Euclidean geometry where the angles of a triangle always add up to 180°, hyperbolic geometry describes spaces that curve like the surface of a saddle or the ruffled edge of a kale leaf. In such a space, triangles have angles that sum to less than 180°, and through a single point, infinitely many lines can run parallel to a given one. This unusual geometry captivated her.
To understand these surfaces, mathematicians study curves that lie on them—especially simple closed curves, which loop around without crossing themselves. Mirzakhani became intrigued by these loops and the challenge of counting how many of them exist on a given surface, up to a certain length. This seemingly simple question turns out to be incredibly difficult because the surfaces she studied don’t exist neatly in our three-dimensional world—they twist and curve in ways that defy easy visualization.
After graduating in 1999, she moved to the United States to pursue a Ph.D. at Harvard University. There, under the mentorship of Fields Medalist Curtis McMullen, she delved into the world of hyperbolic geometry and Riemann surfaces—abstract and often visually elusive topics that she made sense of through intricate doodles and deep intuition.
![]() |
Fields medal (top), hyperbolic surfaces (bottom left) and Mirzakhani talking about it (bottom right) |
Using a concept known as moduli space—which organizes all possible shapes of a given type of surface—she found a groundbreaking way to count these curves. Her work revealed that properties of the moduli space could predict the number of simple closed geodesics (the shortest paths on a curved surface) on a hyperbolic surface. She treated these mathematical objects almost like living characters, often describing them with emotion and enthusiasm.
After earning her doctorate, Mirzakhani served (2004–08) as a Clay Mathematics Institute research fellow and an assistant professor of mathematics at Princeton University. In 2008, she became a professor at Stanford University. She continued to explore connections between geometry, topology (the study of spaces that can be stretched or twisted), and dynamical systems (how things move or change over time). Her work was deeply theoretical but had powerful implications, even helping to solve a long-standing problem in string theory, a field in physics.
Later in her career, she began investigating what a 'typical' hyperbolic surface looks like. Most mathematicians build very specific, controlled examples—but Mirzakhani wanted to study random surfaces to understand the bigger picture. As her former student Alex Wright put it, “A hyperbolic surface is like a puzzle you can piece together locally, but never complete in our universe.” Despite this, Mirzakhani brought clarity to this puzzling world, leaving behind a toolkit that others continue to explore.
Maryam Mirzakhani approached mathematics not as a set of rigid rules but as a creative and exploratory art. “I can see that, without being excited, mathematics can look pointless and cold,” she once said. Her young daughter, watching her fill long sheets of paper with sprawling diagrams, thought that her mother was an artist. In many ways, she was—an artist of abstraction, drawing beauty from spaces most of us cannot even imagine. Through her joyful curiosity and quiet brilliance, she showed that mathematics can be full of wonder, warmth, and imagination.
In 2014, she was awarded the Fields Medal—the most prestigious honor in mathematics—becoming the first woman, the first Iranian, and the first Muslim to receive the award. Her work was not only groundbreaking in its technical achievement but also symbolically powerful, challenging long-held assumptions about who belongs in mathematics. The citation for her award recognized “her outstanding contributions to the dynamics and geometry of
Iranian President Hassan Rouhani said the “unprecedented brilliance of this creative scientist and modest human being, who made Iran’s name resonate in the world’s scientific forums, was a turning point in showing the great will of Iranian women and young people on the path towards reaching the peaks of glory … in various international arenas”. Her photo without a headscarf was published in Iranian media—a rare move prompted by a tweet from Iran’s president, carrying deep symbolic resonance.
Maryam Mirzakhani passed away in 2017 at the age of 40, after a battle with breast cancer. Yet her legacy endures—not just in the theorems that bear her name, but in the doors she opened for future generations of women and underrepresented groups in science and mathematics.
She once said, “The beauty of mathematics only shows itself to more patient followers.” For Mirzakhani, patience was not passive—it was a "fearless ambition" for understanding, a willingness to sit with complexity until it revealed its form. Maryam Mirzakhani’s life was brief, but her impact was vast. She left behind not just theorems and proofs, but a vision of how to explore with depth, persist with grace, and break barriers simply by doing what you love—with patience, passion, and purpose.
Written by Janaky S. and edited by Parvathy Ramachandran @ThinkHer
References:
1. https://www.britannica.com/biography/Maryam-Mirzakhani
2. https://www.scientificamerican.com/article/mathematics-world-mourns-maryam-mirzakhani-only-woman-to-win-fields-medal/
3.https://www.quantamagazine.org/years-after-the-early-death-of-a-math-genius-her-ideas-gain-new-life-20250303/
4. https://news.stanford.edu/stories/2017/07/maryam-mirzakhani-stanford-mathematician-and-fields-medal-winner-dies
👍👍👌👌
ReplyDelete<3
Delete