Overcoming misogyny

Yassamine Mather tells the story of a woman whose achievements were made against all the odds

Maryam Mirzakhani: claimed by all Iranian factions

Maryam Mirzakhani, who died on July 14 at the age of 40, was a professor at Stanford University, a mathematician who obtained the quadrennial Fields Medal in 2014. The award, which is often compared in stature to the Nobel Prize, was given to Mirzakhani for her work in theoretical mathematics.

Sanaz Moazezi, writing on the website of the Organization for Defending Victims of Violence, has this to say about her childhood in Iran:

She wanted to be a writer. She read any book she could get her hands on … Their house was near a street filled with bookshops. She was not allowed to look through the books because she ended up turning the bookstore upside down until she got the book that she wanted, and would make the proprietor angry ...

Her brother was the one who got her interested in science ... One day he told her a story about a German mathematician called Carl Friedrich Gauss, who when he was a student had in just a few seconds got the answer to the total of the numbers 1 to 100 in an ingenious way. This was the first time that she found the joy of getting a beautiful answer …1

Her school principal stressed the importance of her female students having equal opportunities with the boys and, with her interest in mathematics aroused, Maryam went on to become a student first at Farzanegan School and then at one of Iran’s best universities, Sharif University in Tehran.

The Iranian government has always claimed that her achievements are testimony to the country’s educational system, while the opposition points out that in order to pursue her studies as she wished she had to leave the country. The reality is that for the kind of innovative work she was involved in very few institutions, even in Europe and the United States, would have been able to accommodate her. That is why she did her doctorate in Harvard, then moved on to Princeton and since 2008 has worked in Stanford.

The achievements of pupils from Farzanegan School (where most are from middle class families) only highlights the inequalities in the Islamic republic’s educational system; and the fact that most, if not all, of those who qualify at the school and then graduate at university end up working outside Iran is testimony to the country’s serious deficiencies when it comes to research in institutions of higher education.

There is also controversy regarding Maryam Mirzakhani’s portrayal in the media inside Iran. She was married to a fellow academic - a Czech-US citizen - and has not been photographed wearing a hijab outside Iran. Yet the official media (with the exception of a photo shown on the Twitter account of president Hassan Rouhani in 2014) insist on using images that have been Photoshopped to cover her hair, or in the case of some newspapers showing her head against a dark background so you cannot see she is not wearing a headscarf - an insult to the intelligence of the Iranian people.

A campaign is now underway over the citizenship of her daughter, Anahita. Children born to Iranian women married to non-Iranians do not get Iranian citizenship, and there has been much speculation, inside and outside Iran, about Anahita’s nationality. There are reports of a petition signed by over 60 members of the Majles (Islamic parliament) to grant her Iranian citizenship - while at the same time keeping in place the misogynistic regulations for the thousands of other Iranian women married to non-Iranians.

Before Iranian royalists try to claim superiority over the current clerical dictators in Iran, let us remind everyone that (1) women’s legal rights, such as the right to travel abroad granted only with the consent of a husband or guardian, were no different under the shah; and (2) during the latter years of his rule state propaganda seemed to have one aim: to encourage girls to become Miss Universe contestants.

For all its many misogynistic laws, probably the one and only positive thing one can say about Iran’s Islamic Republic is that it has saved young Iranian women from sexist US cultural imports such as Miss Universe pageants, whereas the shah thought women were clearly “inferior to men”, as they had “not produced a decent chef”!2

The royalist nostalgia, repeated ad nauseam this week, for the good old days of the shah, when women held ministerial and managerial posts, is also nonsense. All such women were from the ruling circles - to give one example, the less than talented sister-in-law of the shah’s minister for agriculture was appointed a deputy minister, who revealed her ignorance of basic geography every time she was interviewed. The same thing occurs under the Islamic republic, where female relatives of senior clerics are promoted - very few hold such posts on merit.

Research

When Maryam Mirzakhani won the Fields award in 2014, fellow mathematician Jordan Ellenberg explained her research as follows:

Her work expertly blends dynamics with geometry. Among other things, she studies billiards … She considers not just one billiard table, but the universe of all possible billiard tables. And the kind of dynamics she studies doesn’t directly concern the motion of the billiards on the table, but instead a transformation of the billiard table itself, which is changing its shape in a rule-governed way; if you like, the table itself moves like a strange planet around the universe of all possible tables ...

This isn’t the kind of thing you do to win at pool, but it’s the kind of thing you do to win a Fields Medal. And it’s what you need to do in order to expose the dynamics at the heart of geometry.3

In the last few days everyone has been asking about the practical use of her work - as if advances in mathematics are supposed to be like waving a magic stick. The reality is such advances are multifaceted and it will take a long time before physicists and experts in dynamics will be able to put her equations to practical use, so we might not benefit from her discoveries in the short term. However, we have to remind ourselves that every time we get in a car, take a train or fly in a plane we are benefiting from the work of mathematicians and physicists who devised the equations making the various dynamics possible. In other words, it might take a few years - or even decades - before her mathematical discoveries are put to practical use, but there is no doubt that hers were ground-breaking formulations.

Mirzakhani’s PhD work dealt with hyperbolic geometry - the study of curved surfaces. Mathematicians are fascinated by these surfaces and study curves (simple loops) that sit upon them. Her PhD thesis dealt with one question: on a given hyperbolic surface, how many simple loops are there of less than a given length? Her supervisor, professor Curtis McMullen of Harvard University, recalls that, a few weeks after finding a solution,

she came to him with a surprising announcement: she had used her work to find a new proof of the Witten conjecture - an important result in string theory. Maryam was one of the rare mathematicians who combined outstanding problem-solving skills with the insight and curiosity of a mature scientist.4

Princeton mathematician Manjul Bhargava, who also won a Fields award in 2014, said of Mirzakhani that she “was a master of curved spaces”:

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 ... 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.5

Mirzakhani’s unique approach to geometry and dynamical systems covered a number of specialised fields in mathematics, from hyperbolic geometry and complex analysis to topology and dynamics.

She studied and developed theories around Riemann surfaces, which are considered the natural setting for studying the global behaviour of functions - especially multi-valued functions, such as the square root and other algebraic functions, or the logarithm. Mathematicians are interested in Riemann surfaces because they can be arranged topologically, by a single number following g (the genus of the surface).

Her work will be of great significance for decades to come and she will be a source of inspiration to many young female students. However, the reality is that in Iran - and indeed the rest of the world - from a very young age girls are discouraged from studying mathematics and physics, to the detriment of us all. No fewer than 94% of maths professors in British universities are men. The group, Women in Mathematics, which holds annual events to encourage women to take up mathematics, has set itself the goal of achieving 18% participation by women in its programmes (currently they make up just 13%). Males also dominate undergraduate degrees in engineering and technology (86%) and in computer science (83%).

But Maryam Mirzakhani proved through her own example that things do not have to be like that - even if you were brought up in a clerical dictatorship.

Notes

1. www.odvv.org/blog-583-From-Dreams-of-Writing-to-Getting-the-Fields-Mathematics-Prize.

2. https://newrepublic.com/article/92745/shah-iran-mohammad-reza-pahlevi-oriana-fallaci.

3. www.slate.com/articles/life/do_the_math/2014/08/maryam_mirzakhani_fields_medal_first_woman_to_win_math_s_biggest_prize_works.html.

4. www.quantamagazine.org/maryam-mirzakhani-is-first-woman-fields-medalist-20140812.

5. www.newyorker.com/tech/elements/maryam-mirzakhanis-pioneering-mathematical-legacy.