Male Bastion Falls : Woman Wins the Fields Medal

The Fields Medal is often described as the “Nobel Prize in Mathematics” and regarded mathematics’ most prestigious award. Since its inception in 1936, not a single woman mathematician has featured in the awardees list. This however changed this year. The International Congress of the Mathematicians held at Seoul saw a woman, Dr Maryam Mirzakhani; walk up the stage to claim her Fields Medal. Dr Maryam is an Iranian and is currently the Professor in Mathematics at Stanford University. She has broken one of the most formidable male bastions and shattered the myth (once again) that women cannot excel in science and mathematics.

In March 1997, a few days before Nawroz, the Muslin New Year, a bus carrying some of the best young mathematical talent in Iran met with an accident. The occupants were students from the elite University of Sharif, who were returning from University of Ahvaz after attending a national mathematics competition. Six students were killed and amongst the injured was a girl aged 20 years - Maryam Mirzakhani. This girl would go on to make history by being the first woman to win the highest prize in mathematics - The Fields Medal. There was a chance this would have never been.

Maryam grew up in a middle class family in Tehran, with two other siblings. As a child she was a voracious reader and dreamt of being a writer. An average mathematics student in her elementary and middle school, there were no Field Medal traits at that time, unlike many other laureates who had been child prodigies. The recognition of the elegance of mathematics dawned upon Maryam when her elder brother told her about the Gaussian solution of adding 1 to 100. Maryam was fascinated with the elegance of the solution. And this launched Maryam on a career in mathematics.

It is to the credit of the Iranian High School system, that talents of the likes of her were nurtured and groomed. Maryam went to the Frazangan Girls High School in Tehran, a school for gifted students administered under the National Organization for Development of Exceptional Talents. In her first week at the new school, she made a lifelong friend, Roya Beheshti, who is now a mathematics professor at Washington University in St. Louis. As children, the two explored the bookstores that lined the crowded commercial street near their school. Browsing was discouraged, so they randomly chose books to buy.

The two girls during their spare time gave a shot at the previous year’s national mathematics competition question paper which would determine the students who would represent Iran in the International Mathematics Olympiad. Both the girls slogged for a numbers of days and could solve three of the six questions. An idea germinated - could they also try for the Iranian National Maths Olympiad Team. Never before had a girl made it to the national team. The two girls approached their principal with this nascent idea. The principal was a strong willed woman who decided to give the girls a fair chance and arranged for math problem solving classes like the ones being taught at the comparable high school for boys. She advised that it was worth trying for a place in the Iranian team, what if no girl has ever made it, there was always a first time.

In 1994, Mirzakhani and Beheshti made it to the Iranian math Olympiad team. In 1994 and 1995, Mirzakhani won gold medals in two consecutive International Mathematical Olympiads. In the 1995 Olympiad, she became the first Iranian student to achieve a perfect score and the first female Iranian student to win a gold medal. No doubt Maryam was headed for bigger things; her mathematical prowess was on display.

Maryam entered the elite Sharif Institute in the undergraduate program in Mathematics. Undergraduate admission to Sharif is limited to the top 1 percent of students who pass the national entrance examination administered yearly by the Ministry of Science, Research and Technology.

She enrolled in the graduate program at the Harvard University and worked on her doctorate at under the guidance of the 1998 Fields Medal recipient Curtis McMullen. During her initial days in Harvard she was all at sea with complex analysis, with which her fellow students with undergrad degrees from US Universities were largely familiar with. She persevered making copious notes in Farsi and visiting her research guide McMullen’s office with loads of questions and doubts. “She had a sort of daring imagination,” recalled McMullen in an interview, “She would formulate in her mind an imaginary picture of what must be going on, then come to my office and describe it. At the end, she would turn to me and say, ‘Is it right?’ I was always very flattered that she thought I would know.” Mirzakhani research interest was the mathematics of hyperbolic surfaces. In her doctoral thesis, completed in 2004, Mirzakhani developed a formula for how the number of simple geodesics of length L grows as L gets larger. Discussing the complex mathematics involved is beyond the mental abilities of the authors of this article. Mirzakhani’s thesis resulted in three papers being published in the three top journals of mathematics: Annals of Mathematics, Inventiones Mathematicae and Journal of the American Mathematical Society. Benson Farb, Mathematics Professor of the University of Chicago commenting on Dr Maryam’s thesis work remarked “The majority of mathematicians will never produce something as good, — and that’s what she did in her thesis.”

Maryam’s approach is slow but steady; there is no quick silver flash approach to mathematics, an approach many geniuses apply. She on the contrary mulls over mathematical problems over months and years and then produces path breaking work. Her research domain includes differential geometry, complex analysis and dynamical systems. Her research work and discoveries have been hailed by mathematicians globally as truly path breaking and elegant. She has broken through with solutions to some of the mathematics most persistent problems which have plagued mathematicians for decades.

Maryam is married to Jon Vondrak, alumnus of MIT and currently a theoretical computer scientist at IBM Almaden Research Center in San Jose, Calif. They have a 3 year old daughter Anahita.

Mirzakhani feels certain, that there will be many more female Fields medallists in the future. Despite her stupendous achievements, Dr Maryam remains humble. In an interview she said “to be honest, I do not think I have had a very huge contribution”. To this contention her fellow mathematicians vociferously disagree. When the email informing her of the Fields medal nomination arrived, Prof Maryam assumed that the email had come from a hacked account. It took some time to realise that the news was indeed true.

Mirzakhani since childhood has thought big, may that be competing at the Math Olympiad or going for cutting edge research at Harvard or her numerous challenging research projects. She contends that one has to learn how to ignore the low hanging fruits; it is a difficult and tortuous path she admits. She adds “life is not supposed to be easy”. Given her stupendous success we have no choice but agree with her. But may we add that the low hanging fruit did help one scientist- Isaac Newton.

Winning the Fields medal is difficult and can be slated akin to Federer winning his 17 Grand slam titles, or Anatoly Karpov’s ten year reign as the world chess champion. It takes the same amount of dedication, perseverance and talent, if not more.

In modern times there have been a number of brilliant women mathematicians including Sofia Kovalevskaya ( Cauchy-Kovalevskaya Theorem), Alicia Scott (described by Einstein as a mathematical genius) and Mary Somerville amongst others. Prof Maryam Mirzakhani is a member of this illustrious club.

And surely Prof Mirzakhani’s Field Medal is not only a celebration of top notch mathematical thought, it is also a celebration that women can be world beaters in esoteric subjects like mathematics. We would urge the readers of this article to share the story of Prof Maryam with young girls. Who knows a future Field’s medal winner might be a girl we know.