Maryam Mirzakhani

#56/100 in #100extraordinarywomen

In 2014, Maryam Mirzakhani, then 37-years-old, a mathematician working at Stanford University, became the first woman, and only woman till date, as well as the first Iranian to win the Fields Medal since its inception in 1936. The Fields Medal is awarded to mathematicians under 40 who have made outstanding contributions to mathematics that hold future promise. She was one of four winners of the Fields medal, which is considered the mathematics equivalent of the Nobel prize. She was named for her work on complex geometry and dynamic systems. Her death, on July 14, 2017, due to breast cancer when she was only 40, saddened the entire mathematics community.

Maryam’s work straddled several branches of mathematics. She was intuitive and persistent. She would often take large sheets of paper and draw geometric patterns on them as she thought of the problem, prompting her daughter to think she was “painting again.” Manjul Bhargava of Princeton University remembers that Maryam was a “master of curved spaces.” As he explained in an email, “Everyone knows that the shortest distance between two points on a flat surface is a straight line. But if the surface is curved — for example, the surface of a ball or a doughnut — then the shortest distance [along the surface] between two points will also be along a curved path, and can thus be more complicated. Maryam proved many amazing theorems about such shortest paths — called geodesics — on curved surfaces, among many other remarkable results in geometry and beyond. Her work, and the research programmes she started, will have an impact on mathematics and physics for years to come.”

She had an uncanny intuition for geometric problems, Professor Bhargava said, which she would solve through drawings that looked like beautiful doodles “but were in fact profound geometric insights that she would then make rigorous later on.” Maryam was interested in complicated curved surfaces or hyperbolic geometry: for example, studying loops that don’t intersect; probing deeper to answer how many loops, which don’t intersect, are there of less than a given length on a curved surface. She worked with Alex Eskin to find a solution to the problem of understanding the trajectory of a billiard ball as it bounces around a table. In this, she generalised a work done by her doctoral adviser Curtis McMullen of Harvard University, also a Fields medallist.

A consequence of her work was to give an entirely new proof of a conjecture made by leading string theorist Edward Witten (a 1990 Fields medallist). The first proof of this conjecture was given by Maxim Kontsevich in 1992; it was such a difficult thing to prove that this work itself, in part, won him the Fields Medal in 1998. Maryam Mirzakhani’s proof of Witten’s conjecture was by relating it to an “elementary problem of counting the number of geodesics on individual surfaces.” She worked aggressively and went for deep and fundamental problems, never reaching for the “low-hanging fruit.” It was her strong geometric intuition and her fluency in a range of diverse techniques that made it possible for her to tackle these problems. In the words of Professor McMullen, “Maryam was a brilliant mathematician who has left us far too soon, and who will continue to inspire others to follow in her path.”

A tribute on the Stanford University website says she specialised in an area of mathematics that “read like a foreign language to those outside mathematics — moduli spaces, Teichmüller theory, hyperbolic geometry, Ergodic theory and symplectic geometry.” Each of these terms comes with a well-developed theory backing it and Maryam’s work was both breaking new ground and building a bridge across these areas. In an interview to Quanta magazine, her collaborator Professor Eskin said her doctoral thesis was such that you could immediately recognise that it belonged in a textbook.

An Iranian citizen, Maryam Mirzakhani was born on on May 3, 1977 in Tehran where she grew up in the post Iran-Iraq war period, “the lucky generation,” she said in a rare interview she gave to Quanta magazine. Her father Ahmad is an electrical engineer. She attended Farzanegan School there, part of the National Organization for Development of Exceptional Talents. In 1994, Maryam achieved the gold medal level in the International Mathematical Olympiad, the first female Iranian student to do so. In the 1995 International Mathematical Olympiad, she became the first Iranian student to achieve a perfect score and to win two gold medals. She obtained her B.Sc. in mathematics in 1999 from the Sharif University of Technology. She then went to the United States for graduate work, earning her Ph.D. in 2004 from Harvard University, where she worked under the supervision of the Fields Medalist Curtis T. McMullen. Maryam was a 2004 research fellow of the Clay Mathematics Institute and a professor at Princeton University. In 2008, she became a professor at Stanford University.

In 2005, Maryam married Jan Vondrák, a Czech theoretical computer scientist and applied mathematician who currently is an associate professor at Stanford University. They have a daughter named Anahita. Maryam was diagnosed with breast cancer in 2013. In 2016 the cancer spread to her bone and liver, and she died on July 14, 2017 at the age of 40 at Stanford hospital in Palo Alto, California where she lived with her family. During her lifetime, she had been celebrated with many awards and honours, like, AMS Blumenthal Award 2009; the 2013 AMS Ruth Lyttle Satter Prize in Mathematics (which is presented every two years by the American Mathematical Society and recognizes an outstanding contribution to mathematics research by a woman in the preceding six years); the Clay Research Award 2014; and of course the Fields Medal 2014. She was named one of Nature magazine's ten "people who mattered" of 2014. She was invited to be the plenary speaker at the International Congress of Mathematicians in 2014 and was elected as the foreign associate to the French Academy of Sciences and the American Philosophical Society in 2015; to the National Academy of Sciences in 2016; and to the American Academy of Arts and Sciences in 2017.

A private person, she was known to be humble and creative. Maryam originally dreamed of becoming a writer but then shifted to mathematics. When she was working, she would doodle on sheets of paper and scribble formulas on the edges of her drawings, leading her daughter to describe the work as painting. “We overlapped at Harvard University early in our careers, and became instant friends then… Her work has just been so remarkable then and ever since; it was indeed a great honour for me to receive [the Fields Medal] together with her,” said Professor Bhargava. 

Source: Google search and Wikipedia.