As a woman in the male-dominated field of mathematics, I once opposed targeted efforts to help women succeed — what we now call diversity, equity and inclusion initiatives, which are currently facing fierce backlash. I wanted to be judged on the merit of my mathematics alone.
When I was admitted to the University of Cambridge as an undergraduate in math in 1994, I felt that I was a part of a clear minority. I struggled to keep up with some of the men in my class, many of whom had gone to elite boys’ schools where they had intense preparation. Yet I would progress to a Ph.D. and a career as a research mathematician.
As my career has advanced, what I’ve learned is that D.E.I. initiatives helped others see value in my abilities and experience that would have been missed otherwise. And it was through the lens of math that I came to understand this.
Math is not just a way of calculating numerical answers — it is a way of thinking, using clear definitions for concepts and rigorous logic to organize our thoughts and back up our assertions. Numbers can tell us about representation, but they often don’t tell the full story. The percentage of female math graduates in the United States has improved to around 42 percent; however, still less than 18 percent of university professors in mathematics are women. A 50-50 gender split might seem like “equality,” but not if it was achieved by lowering standards to let more women in. We need to be more careful than that. The nuance found in mathematics can show us a clearer understanding of how to think about equality.
Math is famous for its equations, but equations are more subtle than they first appear. A simple equation like 4+1 = 1+4 shows not just that two values are equal, but that there are two subtly different ways of adding the same numbers to produce the same result. A similar approach applies to more advanced and complicated forms of math, such as the study of shapes or paths through space. We make choices about how to determine equality.
This is relevant to how we evaluate what people have achieved, and make predictions about how well they will do in the future. We can get some insight into how we should make these evaluations from a mathematical field called metric spaces.
A metric is a way of measuring the distance between two points, but not necessarily physical distance — it could be how much time it takes with traffic as a factor, or how much energy will be expended depending on whether you’re going uphill or downhill. A distance cannot be measured based on the position of a single point; it requires the effort of measuring the distance between two points. This may sound redundant, but it’s an important clarification: Metrics can be measured only by taking into account the starting point and ending point, as well as relevant features of the journey — the whole story.
When we evaluate people we could do the same. Instead of looking at just what they have achieved, we could also look at where they started, and be clearer about how we are measuring the metaphorical distance they have come, and whether we are taking into account the support they had or the obstructions they faced.
If we were selecting sprinters for a track team we might look at their best times for the 100-meter dash. But if someone had, for some reason, only ever run races uphill, or against the wind, it would make sense to take that into account and not compare that runner’s times to others’ directly. We would be treating those people differently but only because their paths were different; really we’d be evaluating their paths fairly relative to their contexts.
Other forms of achievement are not as straightforward to measure, but the idea is analogous. If someone achieved a certain SAT score after months of tutoring, and someone else earned the same score having never seen an SAT before, it would be reasonable to be more impressed with the latter result and think that the second test taker has more potential. We should think of D.E.I. efforts as the best versions of this, and aim to design systems that can measure the fuller picture of someone’s professional journey, not just the end result.
It took me a long time to realize that when I began my career, I had probably already worked much harder than I might have done if I had a different identity. I had to work against people telling me I would never be able to succeed. When I attended conferences, I dealt with inappropriate behavior from men senior to me. I had to find my way in my career having no mentors who looked at all like me. I am grateful for the support of some senior mathematicians, and I now realize that it wasn’t “extra help” because I was a woman — it was help in overcoming the extra obstructions I faced as a woman.
It shouldn’t be called sexist to help people overcome sexism, and it shouldn’t be called racist to help people overcome racism, but if we give this help too crudely then we leave ourselves open to these criticisms. Math teaches us that D.E.I. initiatives should be about carefully defining the metrics we use to measure how far people have come, and thus how far they have the potential to go. They should be about uncovering when some people are constantly running uphill or against the wind, which can inform us how to give everyone an equal tailwind and an equal opportunity to succeed.
Eugenia Cheng is a mathematician and the author, most recently, of “Unequal: The Math of When Things Do and Don’t Add Up.”
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