*This article is a preview from the* *Winter 2018 **edition of New Humanist*

In the film *The Man Who Knew Infinity* (2015) the young Indian prodigy Srinivasa Ramanujan travels from his home in Madras to Cambridge to work with some of the brightest minds in pure maths. All men, of course, but then this was 1916. One hundred years on, Cambridge University’s Department of Pure Mathematics is still the desired destination for many brilliant young mathematicians. Amongst the renowned algebraists, geometers and analysts on its permanent academic staff, there are now four women. The other 39 are men. Other centres of mathematical excellence across the world have similar ratios – or worse. Mathematics in 2018 is not an equal opportunities profession nor, at the present rate of progression, does it seem likely to be.

This summer in Brazil, four winners of Fields Medals were announced at the International Congress of Mathematics. The Medals, seen as the Nobel Prize of mathematics, are awarded every four years. Amongst the dozen mathematicians being talked about as possible winners this year were two women: the Ukrainian Maryna Viazovska, known for her work in the geometry of sphere-packing, and Sophie Morel, a French mathematician who specialises in number theory. Neither won; the medals were awarded to Peter Scholze, Alessio Figalli, Akshay Venkatesh and Caucher Birkar. There have now been 62 recipients of Fields Medals since they were first awarded in 1936. Of these, 61 have been men.

Over a dozen years ago, one of the most prominent British Fields Medallists, Sir Timothy Gowers, argued that the small number of top female mathematicians was both “puzzling” and “regrettable”. Despite Gowers’s concern, and despite initiatives in the UK like the Equality Challenge Unit’s SWAN programme, established in 2005 to encourage women’s careers in science and mathematics, change is frustratingly slow. The London Mathematical Society’s most recent report into gender and mathematics concludes that there are still a “surprisingly small proportion of women studying for a PhD and worryingly few promoted to professor”. The latest research suggests only one in ten maths professors in Britain are female.

This does not appear to be due to direct discrimination. In her 18 years as a research mathematician, Colva Roney-Dougal, Professor of Pure Maths at St Andrews University, cannot think of any occasion when she was treated differently because of her gender, at least not on the surface. “I have got used to being the only woman in the room, and am comfortable with that, to be honest,” she says.

But Roney-Dougal wonders if she really did have the same chances as male colleagues. “The common criticism of female mathematicians is that we’re quite good at all the plodding stuff but we don’t come up with the big connecting, surprising ideas,” she says. “In my first few years as a mathematician, I did quite a lot of what is seen as classic female work, building data bases, which you have to get right. It’s not easy but if you work hard you will get there in the end. Had I been more arrogant about my ability I might not have spent all those years on those projects.”

This lack of professional confidence seems to be crucial. A recent American study showed that women are still under-represented in academic disciplines where people believe innate talent or brilliance is required to succeed. And there is no academic subject that values innate talent and natural brilliance more than mathematics.

“These days there are hardly any tangible obstacles to a woman’s career in maths,” says Julia Wolf, reader in Pure Maths at Bristol University, “but a lot of small things come together to make it more difficult for women to succeed.”

One of those “small” things that young male students seem to have, and young women don’t, is bluster: the courage to take risks, the confidence to bluff. “I’m a personal tutor for first-year students, and when something is hard, the boys say, ‘It’s fine’, whereas girls say, ‘I don’t think I can do this’. Yet there’s no difference in their ability,” Wolf continues. “When I was an undergraduate at Cambridge, we had around 25 per cent women in the first year in maths. But in the third year, on courses that were considered difficult, all of a sudden, I was on my own. All of the girls had disappeared to easier options. I found myself alone amongst dozens of men in a lecture about Hilbert spaces.”

A Hilbert space is a vector space equipped with some notion of length and angle that is complete in the sense that a Cauchy sequence of vectors always converges to a well-defined limit within that space. To understand all that, of course, you need to know how the words “vector”, “limit” and “space” are used in mathematics and what is so crucial about a “Cauchy sequence”. That’s why contemporary mathematics is so difficult. To grasp one concept, you have to know many, many others.

Hilbert spaces are one of many daunting peaks in an undergraduate degree in maths and they make studying the subject at university as precarious as rock climbing. Many male students, with the learned arrogance of their gender, saunter into this treacherous terrain and assume they will find the right path as they go along. The best of them scramble up with an effortless cleverness, throwing down a challenge to those below. Female students often appear to conclude they don’t have the same talent to survive. What they don’t recognise is that being able to scale peaks with little effort is not always a predictor of future success. “People who came across as the smartest students when I was studying for my first degree at Cambridge didn’t necessarily go on to become the best research mathematicians,” Wolf points out.

To push the boundaries of mathematical research requires patience as much as cleverness, determination as well as technical skill, the ability to collaborate as well as the concentration to work out answers on your own. Yet these qualities are down-played in a mathematical culture that can be as vicious as a boxing match, even if the struggle is between competing minds rather than bodies.

This competition starts early – the junior Mathematical Olympiad in Britain is open to 11-year-olds – and never really stops. It is not just number theorists who rank their colleagues in descending order of merit. “Mathematicians I know say there are Fields Medallists and there are good Fields Medallists,” says Alison Etheridge, a professor at Oxford University. “Some years ago I was at a meeting with people I hadn’t seen for 10-15 years and I was struck by how unpleasant the behaviour of some of them was. I’m now tough enough to deal with it but, when I was starting out, it wasn’t so easy to cope with this very aggressive, very competitive style.”

This style can be traced back to the real hero of *The Man Who Knew Infinity* – not Srinivasa Ramanujan but Godfrey Harold Hardy, the maths professor who brought Ramanujan to Cambridge. Hardy, still a towering influence in British mathematics even though he died in 1947, lived in a world of men. He viewed the ideal mathematician as a mental athlete who does his best work in his 20s and 30s. “More than any other art or science,” he wrote, “mathematics is a young man’s game.” It still is. Fields Medals are only awarded to mathematicians under the age of 40.

The obsession with youth in mathematics works against women. The American mathematician Claudia Henrion collected studies and personal testimony that suggest that women do their best maths after the age of 40, not least because many take time off to bring up children and cannot complete the three post-doc research posts around the world which are almost a requirement today. “You finish your PhD and then you are mobbing around from continent to continent,” says Roney-Dougal. “Some mathematicians I have heard of have had to work in three continents in five years and to still be doing that in your 30s is remarkably tough. It’s not too bad for me because I haven’t got kids and don’t want them but I’ve known female friends with family commitments who couldn’t do all that moving, and so they gave up maths. We are losing many of our best mathematicians.” Indeed, research in America which looked at the hiring of staff in maths-based sciences showed that, if anything, women were more likely to be successful at interview than men. The problem was that fewer women applied for jobs in the first place.

The main challenge to achieving a healthier gender balance in mathematics is no longer the need to persuade more girls to study maths at university, but to find ways to ensure the brighter female maths students stick with the subject and make it their profession. One obvious reform is to develop career paths in mathematics that take children into account. Another is to break with the expectation that post-docs must turn themselves into intellectual nomads roaming the mathematical world before they are rewarded with a secure job. Yet another is to arrange more female-only gatherings in areas of maths where there are few or no women. All these are important not just for the future health of mathematics but because the existence of this discrimination at the heart of British science and life allows us all to think there are some things that men are just better at than women.

But there is something else that is as crucial and without which these practical remedies will never succeed. It is to start changing the culture in which mathematics is practised. The world of elite mathematics still prizes youthful brilliance above slow, steady development and does not seem to mind that this brilliance often brings with it an emotional immaturity that is expressed in lack of concern for colleagues. It is an immaturity that would not be entertained in other academic disciplines but is seen in mathematics as the price of genius. And it is glorified by the veneration of Hardy and films like The Man Who Knew Infinity whose message could be read as “if you haven’t done your best work when you are young, you might as well give up”.

The result is a culture that, from competing for an Olympiad medal at 11 to achieving that elusive Fields Medal before you are 40, rewards male competitiveness and tolerates what often comes with it: rudeness and lack of empathy. And it says to many bright young women that a career in mathematics is not for the likes of you.