There is no Nobel Prize in Mathematics. And while the Norwegian government has managed to fund a separate prize called the Abel Prize with a similar monetary award and the Israeli government issues a coveted Wolf Prize in the discipline, no mathematical prize means more in mathematics or outside it than the Fields Medal. The monetary value is only $15,000 Canadian, but the prestige is priceless. This year, for the first time, the Fields Medal, which can be awarded to as many as four people every four years, was awarded to a woman, Maryam Mirzakhani, and awarded to a mathematician from the global south, Artur Avila. The press is making a big deal of the woman thing and not a big deal about the global south thing, which should not surprise anyone. The press is also trying to diminish the significance of a woman winning the Fields Medal by stating that no woman has yet won either the Abel or Wolf Prize in mathematics and talking statistics on the sex ratio of Ph.D.s in mathematics.
These prizes are all awarded for mathematical discovery in particular, not pedagogy, compilation of resources, or many of the other things that academic mathematicians do in their work. All but one recipient of the Fields Medal has been an academic. When you think about mathematical discovery, you think about a bunch of dead white guys having eureka moments in their bath tubs with a crown. And maybe, if you are the child of mathematicians like me who was the right age in 1994, you think about Andrew Wiles holing himself up in secrecy for seven years to prove Fermat's Last Theorem. And, if you read the news, you might also think of the one non-academic Fields Medalist Grigori Perelman, who proved the Poincaré conjecture. Even if you are the child of two mathematicians, you probably don't think about your mother running Maple calculations about complex manifolds while cooking dinner, or a young mathematician taking a break from writing a paper to nurse her child. And you don't think about how the ability of even a brilliant mathematician to devote the time and energy to amazing discovery and to get the resources she needs is dependent on her gender. Only 30% of mathematicians are women, and far fewer are tenured faculty at the world's top research institutions.
Before getting to the Fields Medal itself, let me push the other prizes to the side. The Wolf Prize has only existed since 1978, and it is a lifetime achievement prize. Its recipients are the authors of your college mathematical textbooks, the provers and conjecturers of Big Theorems, and the founders of new mathematical disciplines. Among its recipients are many Fields Medalists, and it has no age cap. This means that the gender bias in its recipients spans not just the last 20 years (assuming start of real mathematical work around age 20) but of the last 50 to 60 - Shiing-Shen Chern received the prize at age 73. So, when looking at a Wolf Prize awarded in 2014, we need to look at the gender biases in mathematics at least back to 1964. The Abel Prize has only been in existence since 2001, and despite its 6 million kroner ($1 million US) prize, is not discussed as a goal in mathematics. Its recipients are mainly winners of the other two prizes, and I think it is still working to establish itself as a legitimate prize, and picking winners helps in that. It is worth noting that my mother's thesis advisor, Isadore Singer, shared the prize with Sir Michael Atiyah in 2004 for the Atiyah-Singer Theorem, which won a Fields Medal for Atiyah but not for Singer, as singer was too old to win the prize at the time. Similarly there is no age cut off for the Abel Prize, which is also in the process of making up for its years of not existing. It is therefore not surprising that it has not yet been awarded to any women.
Now for the Fields Medal, which is awarded for outstanding discoveries by young mathematicians. For young mathematicians to succeed in quests for discovery, they need to be in the right environment and have support and the time to make their discoveries. This includes being in a research environment full of other talented mathematicians, usually ones in your own field, and having the support to do independent and collaborative research as well as teach. Additionally, being able to make mathematical discoveries is not usually a matter of Eureka moments but of extensive contemplation and research, something which taking the time to bear and raise children, even if not taking time off from academic teaching responsibilities, can severely hamper women's progress in mathematicians. While plenty of men mathematicians spend time raising children and caring for their families, they also have the option of having children later in life (which they do) and passing off care responsibilities to their partners in ways that are not acceptable for women. The consistent gender imbalance of faculty at elite institutions makes it even harder for women to get the resources they need to overcome these challenges. Top young women mathematicians are often given excellent positions at 2nd tier schools who are interested in attracting young mathematicians to keep and expanding which fields they have faculty in. They take these jobs because tenure is hard to come by and they are then set for life. But it makes incredible discovery harder.
I am hopeful with these latest Fields Medalists. The inclusion of a mathematician from the global south means that meaningful mathematical educational structures are developing there. The award going to a woman under 40 at a top American institution means that we are on the way to fixing the gender disparity in mathematics. If she can now get the support she needs at Stanford, others will be able to as well, and more women will want to become mathematicians. Programs will have to be more attentive to specific needs and concerns of women. And maybe fifty years from now, the Fields Medal, the Abel Prize, and the Wolf Prize in mathematics will all be able to be given to amazing mathematicians of many genders on a regular basis.
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