Maryam Mirzakhani

Maryam Mirzakhani
Born	مریم میرزاخانی 12 05, 1977
Birthplace	Tehran, Iran
Died	Template:Death date and age Stanford, California, United States
Nationality	Iranian
Occupation	Mathematician, professor
Employer	Stanford University
Known for	Fields Medal (first woman and first Iranian recipient), research on Riemann surfaces and moduli spaces, magic wand theorem
Education	PhD, Harvard University (2004)
Spouse(s)	Jan Vondrák
Children	1
Awards	Fields Medal (2014), Clay Research Award (2014)

Maryam Mirzakhani (Template:Lang-fa; 12 May 1977 – 14 July 2017) was an Iranian mathematician and professor of mathematics at Stanford University whose work reshaped the understanding of the dynamics and geometry of curved surfaces. In 2014, she became the first woman and the first Iranian to receive the Fields Medal, often considered the most prestigious award in mathematics, for her contributions to "the dynamics and geometry of Riemann surfaces and their moduli spaces." Born and raised in Tehran, Mirzakhani demonstrated exceptional mathematical talent from a young age, winning gold medals at the International Mathematical Olympiad as a teenager. She earned her undergraduate degree from Sharif University of Technology in Tehran before completing her doctorate at Harvard University under the supervision of Fields Medalist Curtis T. McMullen. Her research encompassed Teichmüller theory, hyperbolic geometry, ergodic theory, and symplectic geometry, and her results connected seemingly disparate areas of mathematics in ways that opened new avenues of inquiry. Mirzakhani held positions at the Clay Mathematics Institute and Princeton University before joining Stanford in 2008, where she remained until her death from breast cancer at the age of 40. Her legacy continues to inspire mathematicians worldwide, and her name has become synonymous with efforts to promote the participation of women in mathematics and the sciences.

Early Life

Maryam Mirzakhani was born on 12 May 1977 in Tehran, Iran. She grew up during a period of significant upheaval in Iran, with the Iran–Iraq War (1980–1988) shaping her early childhood years. Despite the challenges of growing up in wartime, Mirzakhani's family provided a supportive environment for her intellectual development.

As a child, Mirzakhani initially aspired to become a writer rather than a mathematician. Her interest in mathematics developed gradually during her middle school and high school years. She attended the Farzanegan School in Tehran, a school for talented students affiliated with Iran's National Organization for Development of Exceptional Talents.

Mirzakhani's mathematical abilities became evident during her teenage years. In 1994, at the age of 17, she competed in the International Mathematical Olympiad (IMO) held in Hong Kong, where she won a gold medal. The following year, in 1995, she returned to the IMO held in Toronto, Canada, where she achieved a perfect score and won a second gold medal. These accomplishments were particularly notable given that she was among the first female members of Iran's IMO team. Her exceptional performances at the IMO brought her early recognition within the international mathematical community and signaled the extraordinary contributions she would later make to the field.

The environment of mathematical competition and camaraderie during these formative years proved influential in shaping Mirzakhani's career trajectory. She later recalled that her love of mathematics grew out of a desire to understand the deep structures underlying mathematical problems, a curiosity that would define her research throughout her career.

Education

Mirzakhani completed her undergraduate studies at Sharif University of Technology in Tehran, one of Iran's most selective institutions for science and engineering, earning a Bachelor of Science degree in mathematics in 1999. At Sharif, she studied under the guidance of mathematicians including Siavash Shahshahani and Ebadollah S. Mahmoodian, who served as early academic mentors.

Following her undergraduate education, Mirzakhani moved to the United States to pursue doctoral studies at Harvard University. She worked under the supervision of Curtis T. McMullen, himself a Fields Medalist (1998), who later described her as having an exceptional ability to see connections between different areas of mathematics. Mirzakhani completed her PhD in 2004 with a dissertation that addressed several longstanding problems in hyperbolic geometry and the geometry of Riemann surfaces. Her doctoral thesis was notable for its breadth and depth, with its results published in three papers in leading mathematical journals, including the Annals of Mathematics and Inventiones Mathematicae.

Career

Clay Mathematics Institute and Princeton University

Upon completing her doctorate in 2004, Mirzakhani was appointed as a research fellow at the Clay Mathematics Institute, a prestigious fellowship awarded to outstanding young mathematicians. During her fellowship, she was simultaneously affiliated with Princeton University, where she held a position as an assistant professor of mathematics. At Princeton, Mirzakhani continued to develop the research program she had begun in her doctoral work, producing results that deepened understanding of the geometry and dynamics of moduli spaces.

Her time at Princeton and the Clay Institute was characterized by a sustained output of original research. She explored problems at the intersection of geometry, topology, and dynamical systems, establishing connections that had not previously been recognized. This period of her career laid the groundwork for the major results that would later earn her the Fields Medal.

Stanford University

In 2008, Mirzakhani joined the faculty of Stanford University as a professor of mathematics. She was promoted to full professor in 2009, a position she held until her death in 2017. At Stanford, Mirzakhani continued to pursue her research on Riemann surfaces, Teichmüller theory, and the ergodic theory of the action of various groups on moduli spaces. Stanford provided an environment that supported her highly collaborative and interdisciplinary approach to mathematical research.

During her years at Stanford, Mirzakhani produced some of her most significant work, including contributions that established deep connections between different branches of mathematics. Her research style was noted for its geometric intuition; she was known to draw elaborate diagrams on large sheets of paper as she worked through problems, a process her young daughter reportedly described as "painting."

Research Contributions

Mirzakhani's research focused on several interconnected areas of mathematics, including Teichmüller theory, hyperbolic geometry, ergodic theory, and symplectic geometry. Her work was characterized by its depth and by her ability to bring together techniques from different mathematical fields to solve problems that had resisted previous approaches.

Riemann Surfaces and Moduli Spaces

Central to Mirzakhani's work was the study of Riemann surfaces — abstract mathematical surfaces with a particular type of geometric structure — and their moduli spaces, which are spaces that parameterize all possible geometric structures on a given surface. The moduli space of Riemann surfaces is a fundamental object in mathematics, with connections to algebraic geometry, number theory, topology, and theoretical physics.

In her doctoral thesis, Mirzakhani established a new formula for the volume of moduli spaces of Riemann surfaces with boundary, using hyperbolic geometry. She developed a novel recursive method to compute these volumes, which she then applied to obtain new proofs of several important results, including a new proof of the Witten conjecture (originally proved by Maxim Kontsevich) concerning intersection numbers on moduli spaces. Her approach also yielded a formula for counting the number of simple closed geodesics on a hyperbolic surface, solving a problem that had been open for decades.

Dynamics on Moduli Spaces

A second major strand of Mirzakhani's research concerned the dynamics of natural geometric flows and group actions on moduli spaces. In collaboration with Alex Eskin of the University of Chicago, and later with Amir Mohammadi, Mirzakhani proved a series of results about the action of the group SL(2,ℝ) on the moduli space of flat surfaces (also known as translation surfaces or Abelian differentials). Their work culminated in what has been called a landmark theorem, sometimes compared in significance to the celebrated theorems of Marina Ratner on unipotent flows on homogeneous spaces.

The Eskin–Mirzakhani–Mohammadi theorem demonstrated that orbit closures under the SL(2,ℝ) action on moduli spaces of translation surfaces are always algebraic varieties — a result with profound implications for the study of billiard dynamics in polygons and the behavior of geodesic flows on flat surfaces. The proof, published in a paper running to approximately 200 pages, required the development of new techniques in ergodic theory and algebraic geometry.

The Magic Wand Theorem

One of Mirzakhani's most celebrated achievements was the so-called "magic wand theorem," developed in collaboration with Alex Eskin and Amir Mohammadi. This result established a powerful structural theorem for the closures of orbits in moduli spaces, providing a tool that could be applied across dynamical systems, geometry, and topology. The theorem's name reflects its wide applicability — it functions as a unifying principle that connects multiple areas of mathematics and enables results in one domain to be transferred to others. The theorem has continued to generate new results years after Mirzakhani's death, with mathematicians building upon her framework to prove new theorems in areas she helped open up.

Subsequent Influence

In the years following Mirzakhani's death, her research has continued to inspire new mathematical developments. In 2025, Quanta Magazine reported on a new proof that extended Mirzakhani's work, describing it as cementing her legacy in areas of mathematics she helped pioneer. Her contributions continue to shape active areas of mathematical research, with new generations of mathematicians using the tools and frameworks she developed.

Personal Life

Mirzakhani married Jan Vondrák, a Czech-born theoretical computer scientist and applied mathematician who also held a faculty position at Stanford University. The couple had one daughter together.

In 2013, Mirzakhani was diagnosed with breast cancer. The disease eventually metastasized to her bone marrow, and despite treatment, her condition deteriorated. Maryam Mirzakhani died on 14 July 2017 at Stanford Hospital in Stanford, California, at the age of 40. Her death prompted an outpouring of tributes from the international mathematical community, with colleagues describing the loss as devastating for the field. Stanford University president Marc Tessier-Lavigne described her as "a brilliant mathematical theorist" whose influence would "live on for the many students and researchers she inspired."

Following her death, the Iranian president Hassan Rouhani issued a condolence message, and Iranian media published tributes. Her funeral was held privately in the United States. The response to her death extended well beyond the mathematical community, reflecting the broader cultural significance she had achieved as a symbol of intellectual achievement and perseverance.

Recognition

Fields Medal

On 13 August 2014, Mirzakhani was awarded the Fields Medal at the International Congress of Mathematicians held in Seoul, South Korea. She was the first woman to receive the award since its establishment in 1936, and the first Iranian mathematician to be so honored. The International Mathematical Union cited her "outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces." The announcement received extensive international media coverage, with news outlets highlighting both the mathematical significance of her work and the historic nature of the award.

Clay Research Award

In 2014, Mirzakhani also received the Clay Research Award from the Clay Mathematics Institute, in recognition of her joint work with Alex Eskin on the dynamics of moduli spaces of Abelian differentials.

Elected Memberships

Mirzakhani's contributions were recognized by election to several of the most distinguished scientific academies. In April 2015, she was elected a member of the American Philosophical Society. In 2015, she was also elected as a foreign member of the French Academy of Sciences (Académie des sciences). In 2016, she was elected to the National Academy of Sciences of the United States. In 2017, shortly before her death, she was elected to the American Academy of Arts and Sciences.

Invited Speaker

Mirzakhani was an invited speaker at the International Congress of Mathematicians, a distinction reserved for mathematicians who have made significant contributions to the field.

Legacy

Mirzakhani's legacy extends across both mathematics and the broader effort to increase the representation of women in science, technology, engineering, and mathematics (STEM) fields. Her achievement as the first female Fields Medalist has had a lasting symbolic impact, and her name has been attached to numerous initiatives aimed at supporting women in mathematics.

Maryam Mirzakhani New Frontiers Prize

In her honor, the Breakthrough Prize Foundation established the Maryam Mirzakhani New Frontiers Prize, awarded annually to outstanding early-career women mathematicians. The prize recognizes significant contributions by women at the beginning of their independent research careers and carries a monetary award. The creation of this prize has provided ongoing recognition for women in mathematics and has helped to maintain Mirzakhani's name as a symbol of mathematical excellence.

The 12 May Initiative

Mirzakhani's birthday, 12 May, has been designated as the date for celebrating women in mathematics worldwide through the "May 12th" or "12 May Initiative." The initiative was launched by organizations including the Committee for Women in Mathematics of the International Mathematical Union and aims to inspire women and girls around the world to pursue careers in mathematics.

Named Awards and Programs

Multiple institutions have created programs and awards in Mirzakhani's name. In 2025, San Francisco State University announced a major expansion of its Presidential Scholars Program, specifically honoring Mirzakhani by supporting STEM students through a gift from alumna Neda Nobari. The École Polytechnique in France awards the Maryam Mirzakhani Junior Prize to outstanding students in its Bachelor of Science program.

Tributes from the Mathematical Community

The American Mathematical Society has maintained a tribute page in Mirzakhani's honor, describing her as "a highly accomplished mathematician" whose work transformed the understanding of surfaces and their associated geometric structures. Mathematicians have continued to extend and build upon her work, with new results in 2025 demonstrating the ongoing vitality and influence of the research program she established.

Mirzakhani's life and career have become a source of national pride in Iran, where she is celebrated as a symbol of intellectual achievement. In 2025, the Tehran Times described her as "a scientific role model for Iranian girls" and "a source of honor for the global knowledge."