# MARYAM MIRZAKHANI

A prized #Iranian #mathematician, the first woman to receive a #Fields Medal... and an #artist, according to her daughter Anahita.

Featuring artwork & words by Dr. Eleonora Adami, Sci-Illustrate Stories. Set in motion by Dr. Radhika Patnala

Maryam had a very peculiar approach to tackle complex mathematical problems. She would lay on the floor of their Stanford house with huge pieces of papers and would start doodling, sketching diagrams, and writing questions working through her math — “painting” according to the daughter. In an interview she said “It is like being lost in a jungle and trying to use all the knowledge that you can gather to come up with some new tricks, and with some luck you might find a way out.” Maryam was humble yet very ambitious; defined herself as slow, while others saw her as a virtuoso and exceptionally bright.

Born in Tehran (Iran) in 1977, she initially wanted to become a writer and only as a teenager started to see the beauty of math (she won A NUMBER of gold medals at mathematical olympiads). After completing her studies at the Sharif University of Technology, she moved to Harvard for her PhD, earned in 2004 under the supervision of the Fields Medalist C. McMullen. She then was a research fellow at Princeton and obtained full professorship at Stanford University.

Her PhD work concerned the theory of moduli spaces of hyperbolic Riemann surfaces. You can think about these as Pringles-like surfaces, but with holes (like multiple bagels, pineapple rings, donuts — yes I’m hungry as I’m writing this). She set out to answer this question: on a given surface how many simple loops (closed curves/geodesics) are there of less than a given length? She solved the problem finding a relationship to volume calculations in moduli space. A space is a set of points, describing one of the shapes that the surface can take.
This result was something most mathematicians would not achieve in a lifetime and led to a new proof of the Kontsevich theorem, which had implications in quantum field theory.

In her late work, she focused on the “billiard ball dynamics”, a point mass moving in a polygon. When a ball touches the edge of a billiard table and bounces back, how many different routes could it take, provided it would never lose velocity? Would paths eventually repeat? How do they look like?Embedding billiard tables into larger moduli spaces or “translation surfaces”, mathematicians can better analyse and understand orbits and the system’s dynamics in general. Her work on the dynamics of Riemann surfaces with Eskin is now referred to the “magic wand theorem”, with far reaching implications in engineering, physics and beyond.

In 2014, for all her “outstanding contributions in geometry and dynamics of Riemann surfaces in their moduli spaces” Maryam was the first woman and first iranian mathematician to be awarded the Fields Medal.
At that time, Maryam had just undergone a cycle of chemotherapy to treat breast cancer and was unsure whether she could be well enough not only to receive the award, but — most of all — to face the press. Six fellow distinguished women mathematicians, the “MM Shield” devised a plan to help her celebrate and enjoy that important recognition, despite her fragile health status. Two of them were with her at any time: one to intercept and deflect the attention of journalists while the other would facilitate Maryam’s escape.

Maryam passed away in 2017, but her legacy continues to blend the imaginary boundaries we set between scientific fields.

ARTIST’s NOTE

Why Maryam? I was fascinated by this young and determined woman who accomplished so much, sadly in such a short time (she died at 40). I was also very intrigued by her way of reasoning and solving problems. I saw videos in which she was doodling on the floor geometric shapes and surfaces that for me were flowers and pringles. I never saw a mathematician working this way, you’d agree with me. That’s why I decided to include this doodles in the background of the portrait.

# About the author and artist

## DR. ELEONORA ADAMI

Content editor and contributing artist
Women in Science, Sci-Illustrate Stories

Eleonora is a proud descendant of ancient Romans. Besides that, she is currently a postdoctoral research fellow at Duke-NUS in Singapore, working in the cardiovascular and metabolic diseases area. She has a biotechnology (BSc) and functional genomics (MSc) background, and has obtained her PhD in molecular biology and genetics in Germany before going to the far east.

Eleonora thinks of herself as a carrier pigeon, always on the go, trying to find new adventures and challenges. Ok, maybe pigeons are not very adventurous, but they were once useful to deliver important messages. One of the messages she likes to bring across is that we need more art in scientific practices. Creative thinking benefits both disciplines.
A passion for illustration has always accompanied her and percolates in her scientific work. She started the collaboration with the Sci-Illustrate team after attending their course on scientific illustration.

# About this series:

Not enough can be said about the amazing Women in Science who did and continue to do their part in moving the world forward.

Every month, through the artwork & words of the Sci-Illustrate team, we will bring to you profiles of women who touched our hearts (and brains) with their scientific works, and of many more who currently hold the flag high in their own fields!

-Dr. Radhika Patnala, Series Director

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