Does mathematics carry human biases?

This week, a conversation flared up on Twitter on whether mathematics can carry human biases, and what such a possibility could even mean.

The spark was a statement by the Committee on Minority Participation in Mathematics of the Mathematical Association of America (MAA), responding to actions the Trump administration has taken to disparage and de-fund the academic discipline of Critical Race Theory. The committee's statement pointed out that the attack on Critical Race Theory has a potentially chilling effect on all academic disciplines, including mathematics:

As mathematicians, we notice patterns - this is something we are all trained to do. We bring these Executive actions to our community’s attention for several reasons: we see the pattern of science being ignored and the pattern of violence against our colleagues that give voice to race and racism. We need to fight against these patterns. As educators, we also recognize the threatening pattern of banning education and withdrawing education funding to suppress conversations on race and racism, extending from elementary to postsecondary institutions to the workplace and research spheres.

 The MAA tweeted out this statement, highlighting the following quote:

"It is time for all members of our profession to acknowledge that mathematics is created by humans and therefore inherently carries human biases. Until this occurs, our community and our students cannot reach full potential." -CMPM #MathValues https://t.co/vVBUnXf1TL

— MAA (@maanow) October 3, 2020

The resulting conversation appears to have focused in particular on the idea that "mathematics is created by humans and therefore inherently carries human biases", largely disregarding the rest of the committee's statement. One biologist in particular felt so provoked by this statement that she felt it should be disqualifying for the whole field:

If you truly believe that math is created by humans, you have no business in math.

The ways that we *describe* math are, no doubt, a social construct, but math itself is the discovery of underlying reality. https://t.co/z5ce8hLCTZ

— Heather E Heying (@HeatherEHeying) October 3, 2020

First off, let me say clearly: Dr. Heying's tweet is reprehensible.  No one should be dictating who does or does not have business in math, let alone someone from outside the field.  She also seems completely ignorant of the centuries-old debate on whether mathematics is discovered or invented (most mathematicians feel it's some combination of both). And while I do not know if her comment was intended to be racist, the fact that she is saying the Committee on Minority Participation in Mathematics has "no business in math" is absolutely racist in its effect. She should apologize immediately, but instead she is doubling down.

Leaving aside Dr. Heying's offensive remark, the statement itself raises some interesting questions.  What could it mean for mathematics to "carry human biases"? I think part of the issue here is that the word "mathematics" could be understood in several different ways:

1. Mathematics as a collection of relationships (discovered or not) among numbers and other mathematical objects,
2. Mathematics as the human body of knowledge regarding these relationships,
3. Mathematics as a discipline and profession devoted to understanding and describing these relationships

For an example of mathematics in the first sense, let's take the theorem that there are infinitely many primes among the natural numbers. This is one of the most famous results in elementary number theory, with a number of beautiful proofs dating back to Euclid in ancient Greece. Within the universe of math, such a statement is not contestable. This is the point--and the beauty--of proofs in mathematics: they reveal truths that are universal, regardless of who discovers or uses them.

Many of those responding to the committee's statement assumed that they were using "mathematics" in this first sense, as if theorems like the inifinitude of primes could carry human bias. But I see this as an exceedingly ungenerous interpretation, with no support in the rest of their statement. Indeed, the people leaping to this interpretation seem to be all too eager to paint the committee's statement in the worst possible light, as if any statement calling for greater diversity and inclusion in mathematics is automatically considered suspect.

If "mathematics" is understood in the third sense, as a discipline and profession, then absolutely it can carry human bias. Ronald Fisher, who pioneered the study of statistics, was a notorious racist and eugenicist, and he was not alone in these views. Moreover, until recent decades, women and minority groups were systematically excluded from studying and practicing higher mathematics. Because of this systematic exclusion, most of the "great figures" of Western mathematics are white men, and this perception that "math is for white men" becomes self-reinforcing. This is not merely a historical legacy: nonwhite mathematicians continue to face bias and isolation, and in some cases harassment.

What about the second sense, mathematics as a human body of knowledge? Could this carry bias? Here I think the question is much more nuanced, but the example of negative numbers is instructive. They first appeared in the Han Dynasty of ancient China (202 BC - 220AD). It has been suggested that the idea of duality in Chinese philosophy made negative numbers more intuitive for them. Indian mathematicians in the 7th century AD were using negative numbers to represent debts.  Yet in Western mathematics, negative numbers were dismissed as absurd and nonsensical until calculus came along in the 18th century.

I like the example of negatives, because it shows that what gets accepted as legitimate mathematics is indeed a social construct. Cultural biases can come into play when determining which ideas gain legitimacy, even in the abstract world of pure mathematics.  Relationships among numbers are not biased, but our process of understanding and discovering these relationships may be. And I agree with the committee's statement that understanding how human biases influence our thought--even within the ivory tower of mathematics--is key to achieving greater inclusion and equity for all people.