Being a woman means many things.

Many of those things really have nothing at all to do with being a woman—they are contrived, invented, imposed, conditioned, unnecessary, obstructive, damaging, and the effects are felt by everyone, not just women.

How can mathematical thinking help?

As I am a woman in the male-dominated field of mathematics, I am often asked about issues of gender: what it’s like being so outnumbered, what I think of supposed gender differences in ability, what I think we should do about gender imbalances, how we can find more role models.

However, for a long time I wasn’t interested in these questions. While I was making my way up through the academic hierarchy, what interested me was ways of thinking and ways of interacting.

When I finally did start thinking about being a woman, the aspect that struck me was: Why had I not felt any need to think about it before? And how can we get to a place where nobody else needs to think about it either? I dream of a time when we can all think about character instead of gender, have role models based on character instead of gender, and think about the character types in different fields and walks of life instead of the gender balance.

This is rooted in my personal experience as a mathematician, but it extends beyond that to all of my experiences, in the workplace beyond mathematics, in general social interactions, and in the world itself, which is still dominated by men, not in sheer number as in the mathematical world, but in concentration of power.

I worked hard to be successful, but that “success” was one that was defined by society. It was about grades, prestigious universities, tenure. I tried to be successful according to existing structures and a blueprint handed down to me by previous generations of academics.

I was, in a sense, successful: I looked successful. I was, in another sense, not successful: I didn’t feel successful. I realized that the values marking my apparent “success” as defined by others were not really my values. So I shifted to finding a way to achieve the things I wanted to achieve according to my values of helping others and contributing to society, rather than according to externally imposed markers of excellence.

In the process I learned things about being a woman, and things about being a human, that I had steadfastly ignored before. Things about how we humans are holding ourselves back, individually, interpersonally, structurally, systemically, in the way we think about gender issues.

And the question that always taxes me is: What can I, as a mathematician, contribute? What can I contribute, not just from my experience of life as a mathematician, but from mathematics itself?

Most writing about gender is from the point of view of sociology, anthropology, biology, psychology or just outright feminist theory (or anti-feminism). Statistics are often involved, for better or for worse: statistics of gender ratios in different situations, statistics of supposed gender differences (or a lack thereof) in randomized tests, statistics of different levels of achievement in different cultures.

Where does pure mathematics come into these discussions?

Mathematics is not just about numbers and equations. Mathematics does start with numbers and equations, both historically and in most education systems. But it expands to encompass much more than that, including the study of shapes, patterns, structures, interactions, relationships.

At the heart of all that, pumping the lifeblood of mathematics, is the part of the subject that is a framework for making arguments. This is what holds it all up.

That framework consists of the dual disciplines of abstraction and logic. Abstraction is the process of seeing past surface details in a situation to find its core. Abstraction is a starting point for building logical arguments, as those must work at the level of the core rather than at the level of surface details.