By Lillie Therieau 

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Although mathematics doesn’t have its own section of the Nobel Prize, there’s an international equivalent called the Fields Prize. In 2014, Maryam Mirzakhani shocked the mathematical world when she became the first woman and first Iranian to win the prestigious award. 

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Maryam was a very young, creative mathematician, whose work impressed her peers with its visionary prowess. Tragically, her life would be cut short by cancer soon after winning the Fields prize. However, Maryam’s influence and legacy live on, especially for young women breaking into the world of mathematics. 

Maryam Mirzakhani’s Path To Math’s Nobel Prize

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Maryam Mirzakhani was born in 1977, in Tehran, Iran. She came from a humble academic beginning, with one of her grade school teachers noting at the time that Maryam wasn’t particularly gifted in math class. However, in her junior and senior years of high school, she won mathematics awards at the Iranian National Olympiad. These wins allowed her to bypass traditional college entrance exams, and she began school at the Sharif University of Technology. During her college years, she became the first Iranian woman to win a gold medal at the International Mathematical Olympiad, and then the first Iranian to win two gold medals and receive a perfect score. 

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In 1998, Maryam was on a bus with other high-achieving Iranian Olympiad winners and academics en route to Tehran, when there was an accident and the bus rolled off of a cliff. Most of the passengers were killed and Maryam was one of the few survivors. The incident was considered a national tragedy in Iran, as many of the best and brightest young people in STEM programs were tragically killed. 

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After recovering from the accident, she graduated in 1999 with a Bachelor of Science in mathematics. During her undergraduate career, Maryam had received recognition from the American Mathematical Society for her work on a proof for one of Issai Schur’s theorems. After she graduated, she was invited to complete her graduate work at Harvard University. She earned a Ph.D. in mathematics from Harvard in 2004. 

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With her doctorate, Maryam worked as a professor at Princeton University until 2008. During this period she met and married her husband. Jan Vondrak, a Czech scientist, and mathematician. Together they had one daughter, named Anahita. In 2009, she received a professorship at Stanford University, when her husband worked as well. The family moved to Palo Alto, California, where Maryam would live and work for the rest of her life.

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In 2013, she was diagnosed with breast cancer. While undergoing treatment, she was working on the most groundbreaking research of her life, on the dynamics of complex geodesic surfaces. 

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In 2014, she was awarded the Fields Prize for that work, which is the most prestigious award in the world of mathematics. Maryam is the only woman and the first Iranian to be awarded the prize. She received the award in Seoul, South Korea, before an audience of revered international mathematicians. 

Maryam Mirzakhani, 2014, Image by Lee Young Ho—Sipa/AP Images via britannica.com

Maryam Mirzakhani’s Mathematical Creativity

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Maryam Mirzakhani called herself a “slow” mathematician. She worked at her own pace, letting ideas come together of their own volition. Her young daughter referred to her mother’s work as painting, watching the rhythmic and expressive strokes of her pen as she worked through proofs at her desk.

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Maryam’s work was largely focused on the field of geometry and specifically on the moduli theory of Riemannian surfaces. Riemannian surfaces can be defined as a complex two-dimensional surface that possesses the special property of being orientable.

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To be orientable, a geometric shape that is placed on the surface cannot be moved in a loop and end up in a flipped mirror image of itself. For instance, if a yin-yang symbol was moved in a loop around an orientable surface, it would have to end up facing the same way it started. 

Example of an orientable shape

Riemannian surfaces are interesting because they explore what happens when a complex plane is deformed and how the deformation changes the properties of the surface. There are three types of these surfaces: hyperbolic surfaces with a negative curvature, parabolic surfaces with a flat curvature, and elliptical surfaces with a positive curvature. 

Three examples of a Riemann Surface

Maryam began her work with hyperbolic surfaces, studying the way that a single line would traverse such a surface. On a flat plane, the shortest distance between two points is a straight line, something that most people learn in early geometry lessons. However, the shortest distance between two points on a curved plane is much more complicated. These lines are called geodesics and they’re a fruitful source of discovery and frustration for mathematicians throughout history. 

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Maryam won the Fields prize for her work on the subject of geodesics, finding that these lines were surprisingly regular in the way they traveled around hyperbolic Riemannian surfaces. It was a surprising discovery, as most people had previously theorized their properties on hyperbolic surfaces would be very irregular. 

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Maryam Mirzakhani’s Tragic Death and Enduring Legacy 

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In 2016, Maryam’s breast cancer spread to other areas of her body. Maryam Mirzakhani died in 2016 at the young age of 40. Her death shocked the world of mathematics and her home country of Iran. 

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The Iranian president and many other elected officials offered their condolences and remembrances of Maryam, celebrating the recognition she earned for the Iranian mathematics community. Obituaries poured out in the Iranian press, notably breaking protocol as they published photos of her with her hair uncovered. She holds an important place in the hearts and minds of the Iranian people, specifically for young girls interested in STEM subjects. 

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The International Council for Sciences has named May 12th Maryam Mirzakhani Day, in honor of her birthday. In 2020, she was named posthumously as one of the seven female scientists who have shaped the world by the UN Council For Women. 

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The Brilliant Lives of Famous Mathematicians 

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This article is the sixth in our series exploring the lives and achievements of famous mathematicians throughout history. (Our last article was about the Indian mathematician Brahmagupta!) 

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Through the lives of these brilliant folks, we hope you’ll find connections, inspiration, and empowerment. 

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And, be sure to check out the 2020 documentary about Maryam Mirzakhani, called Secrets of The Surface, to learn more about her remarkable life.