When Marin Alsop conducted the Last Night of the Proms, she said that she was “quite shocked that it can be 2013 and there can still be firsts for women”. The following year, Maryam Mirzakhani became the first woman to win the Fields Medal, awarded to mathematicians under 40 for their contribution to the subject. Now, after Mirzakhani’s sad death from breast cancer at the age of 40, I am struck by the stark reality that in the 80 years since the award was first given, there has still been only one female winner so far.

It is important to note that Mirzakhani was a pioneer in other ways too. She was the first Iranian Fields medallist. Her mathematical research on the geometry of complex surfaces was groundbreaking, and has opened up new horizons for others to explore. When she was awarded the Fields Medal, Mirzakhani immediately became an inspiration for many young mathematicians. I was delighted that, finally, a woman had won this prize, the highest accolade that the mathematical community awards. But I was also dismayed that it had taken so long.

For centuries, it was socially unacceptable, or even impossible, for women to study mathematics at the highest levels. As a young mathematician, I was inspired by the story of Sophie Germain, who taught herself maths under the bedclothes in the face of opposition from her parents. She went on to make substantial contributions to mathematicians’ understanding of one of the most famous problems in mathematics: Fermat’s Last Theorem.

In 1890, Philippa Fawcett was the highest performing maths student at the University of Cambridge. Yet women were not included in the main ranked list so the honour of Senior Wrangler (top student) went to a man, even though Fawcett scored higher. In the US in the 1940s, the mathematician Julia Robinson was not allowed to teach at the University of California at Berkeley, because her husband worked there and “nepotism rules” prevented them both working in the same department. She went on to play a major role in solving the tenth of Hilbert’s famous list of 23 problems.

Happily, things have moved on. These days, my own department and many others are actively seeking ways to improve gender diversity and inclusivity (as well as other forms of diversity). The Athena SWAN scheme provides recognition to universities and departments who are making serious attempts in this area.

It requires effort and active engagement to change culture. Progress is being made, albeit slowly. The “leaky pipeline” of academia (which sees women drop out at every level) means that even though gender diversity is improving amongst mathematics undergraduates, the balance is not great among postdocs and worse still among professors. Recent data from the London Mathematical Society showed that from 2014 to 2015 around 40% of UK mathematics undergraduates were female, but only 9% of UK mathematics professors were female.

Of course the same phenomenon occurs in many walks of life, not just academia. There is lots being done to try to understand why this is the case in mathematics. Recruitment practices are being improved, and academics are being trained in unconscious bias. Perhaps a problem that is distinctive to mathematics (and closely related subjects) is cultural. There is sometimes an unhelpful, and in my opinion incorrect, perception that one has to be some sort of genius to succeed in mathematics, and this can be off-putting.

## Signs of progress

Anecdotally, my impression is that there is more awareness now than say 15 years ago of the need to increase diversity within mathematics at all levels of seniority. At the same time, there is a danger that this might make the gender imbalance clearer to school students who might in turn feel inhibited in their desire to study mathematics. My personal hope is for all young people to experience the joys and frustrations, the creativity and the practicality of mathematics, so that those who wish to can take their mathematical studies further, regardless of gender or any other factor.

There are signs of progress in improving diversity in mathematics (of all forms, not just gender), but it’s taking a long time, and there are more firsts to come. We are still waiting for the first female winner of the Abel Prize, another major accolade in mathematics. Tragically, Mirzakhani died much too soon, but her mathematical contributions will live on, both in theorems and ideas that others can build on and also in inspiring future generations.

I look forward to the day when women winning the Fields Medal receive acclaim for their outstanding mathematical achievement, without reference to their gender. As Robinson wrote:

What I really am is a mathematician. Rather than being remembered as the first woman this or that, I would prefer to be remembered, as a mathematician should, simply for the theorems I have proved and the problems I have solved.