Ramanujan, Nash, Turing, Mirzakhani

From a short review of a new documentary about the life and work of the Iranian mathematician Maryam Mirzakhani, September 9, 2022:

While there are other movies about real-life mathematicians such as Nash, Ramanujan and Turing, the special abilities of these individuals are often depicted as making them eccentric in their private lives. In contrast, Mirzakhani lived a “normal” life, was married with a child and simply loved math. I want people to know that mathematicians like her also exist.

The documentary powerfully conveys the attitude that there’s nothing women can’t do simply because they’re women, which makes it well worth watching from the perspective of diversity and gender.

This is well and good. I haven’t yet watched the documentary but will at the first opportunity. This said, the review raises a curious point about the impression that films, documentaries, etc. have created about John Nash, Srinivasa Ramanujan and Alan Turing. The reviewer, Prof. Yukari Ito of the Kavli Institute in Japan, has written that they have given us the impression that being a great mathematician requires one to be eccentric, or that contributing to mathematics at the highest level demands the sort of transcendental brilliance that a human mind may never fully comprehend. Ramanujan exemplified this sort of work by setting forth a very large number of axioms in number theory without specifying the steps in between the first principles and the final thing. When he asked, he said a goddess was working through him. It may well be that Ramanujan’s biggest contribution to the idea of mathematics was his incomprehensible mind. However, the stories of Nash and Turing are significantly different. Unlike Ramanujan, they both had formal training in mathematics that allowed them to think more clearly about their respective domains, and neither man attributed their work to any sort of divine intervention. They were eccentric men, sure, but unlike Prof. Ito, I prefer to think that they were distinguished by an exceptionalism that also attends to Maryam Mirzaklhani.

Specifically, Turing and Nash led normal lives too, in that they had families, they had homes and they had to work with the same quotidian constraints as many others of their generation (presumably minus misogyny, racism, etc. because they were white men). Sure, they were oddities in their respective social milieus, but I don’t believe that lends itself to the impression that mathematics and eccentricism are linked, at least in the cases of Nash and Turing. Nash was ill (he later developed schizophrenia) and Turing was gay well before the UK accepted homosexuality. It applies perfectly in Ramanujan’s case, of course. But by lumping the three men together, I fear that Prof. Ito’s review misidentifies the real nature of Mirzakhani’s achievement: not that she leads a ‘normal’ life but that she is a woman, and a woman from Iran. This is also what I meant by the exceptionalism that attends to Mirzakhani. Consider who the subjects of our films and documentaries are. Ramanujan, Nash and Turing had films made about them because they were eccentric – and Mirzakhani doesn’t escape this sampling bias as much as confirms it. There is a documentary about her because she hails from a country where women don’t have many of the rights that their counterparts in most other parts of the world enjoy, and because she was the first woman to be awarded the Fields Medal. There are several male and female mathematicians, and in fact mathematicians of other genders, who are perfectly brilliant as well as lead perfectly normal lives (in Prof. Ito’s definition). It’s just that their experiences may not make for a good movie. In fact, it may well be that what most people consider ‘normal’ hasn’t ever been the subject of a movie about a good mathematician.

The structural issues that Prof. Ito overlooks also include a significant part of what allowed the men she mentioned to be successful – the division of labour in society, within their homes, where as men they were free to focus on their work without contributing to helping their partners run the house or attending to any kind of tedious administrative work at their places of employment. This is as much an indictment of patriarchy as that attitude among prestigious institutes that continues to this day – that brilliant men’s ‘eccentricities’ should be excused so that they can keep bringing in the grants, the citations and the awards. Mirzakhani was not normal. I’m not familiar with her story (I really need to watch the documentary) but I’m certain that she had more barriers in her way to achieve the level of success that she did. That in turn elevates her achievements in a sad way, and might also inspire others to think that mathematics stands to benefit through more than just mathematical contributions. After all, aren’t we paying attention to Mirzakhani herself because of the Fields Medal committee’s disgraceful dismissal of women’s contributions for eight decades?