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.

How do we mourn human civilization?

2019 was a lot of things. But for what I want to say here, 2019 was the year that I realized we might not save ourselves.

Just on its face, 2019 was a terrible year if you care about climate change. Arctic permafrost may have reached a tipping point. Antarctic ice melted at record pace. The Amazon burned. Meanwhile, carbon emissions continued to rise, and COP-25, the major UN forum for international climate policy, ended with essentially no progress.

But for me personally, 2019 was the year I allowed myself to consider that we might not work it out.  Not only will we not stop the first effects of climate change, we might not even stop any of them.  Faced with an existential threat to our entire civilization, we might just drive ourselves right off the fucking cliff.

Surely we will do something to stop it. Consciously or not, this thought had always been in the back of my head when thinking about climate change. Yes, the science looks bleak, the politics look intractable, and some level of crisis is probably unavoidable. But surely, at some point, human civilization will come together, face the danger ahead, and do something to stop it.

This year, I allowed myself to pluck this voice from the back of my head, hold it to the light, and examine it. Will we do something to stop it?

Well, what does our track record show? Climate change was officially identified by NASA as a severe global threat in 1988. Since then, we've had 31 years of scientific research, policy debates, and international agreements. Every international scientific and policy-making body recognizes climate change as an urgent and existential threat. And yet emissions have continued to rise, essentially without pause. 

I'm an optimist at heart. I always try to look at things in the best possible light. But at this point, it's starting to look like, if we were going to save ourselves, we would have done it by now.

Surely we will stop it. We might not stop it. What if we don't stop it?

What happens if we don't take drastic action? Here is where I think that the scientific and journalistic institutions have failed to properly communicate the danger. Because the headline numbers—3 or 4 degrees Celsius, 2 meter sea-level rise by 2100—might not sound that bad at first. Why, exactly, are these numbers so scary?

First of all, with a 4°C temperature rise, 74% of the Earth's population would experience deadly heat waves every year. Multi-breadbasket failures are possible, leading to mass famine. As much as 5% of the world's population could be flooded every year by 2100. These and other catastrophes could lead to as many as a billion climate refugees by 2050.

What would this level of disruption mean for human civilization? With one tenth of the world's population displaced, can nations still maintain their borders or their identities? Can governments survive if they can't provide food or freshwater to their people? When "natural disasters" turn into commonplace occurrences, will the collective fiction known as "money" retain its value?

Questions like these defy quantitative predictions, but based on these an other considerations, researchers have described increase of 5°C or more as posing "existential threats to the majority of the population".  And while it is probably still possible to avoid this level of warming, doing so would require unprecedented economic transitions and global cooperation—and our track record so far does not give much reason for optimism.

We might not stop it.

2019 is the year I started to mourn. The year I let myself consider that the civilization we have right now might be—likely will be—the best we will ever get. That our current society—for all its wonders and flaws—could be revealed as fossil-fueled mirage that collapses before we ever build something better to replace it. That, even if homo sapiens as a species survive, what we know of as human civilization could go up in smoke, fire, and water.

Of course, the destruction will not be spread evenly, nor fairly. The countries most vulnerable to climate change, such as Bangladesh and Haiti, are among those least responsible for creating it. Still, there is reason to doubt that the political and economic systems of the West will survive extreme climate change. Already, mass migration from the Middle East and Central America (driven in part by climate change) have fueled the rise of the Far Right in Europe, Brexit in the UK, and the election of Donald Trump in the US. Currently, the US is holding thousands of these migrants in concentration camps, forcibly separated from their families. What will happen when migrants swell to 10% of the world's population, compounded with greatly increased fires, flooding, hurricanes, epidemics, and food shortages? How much strain, exactly, can our political and economic institutions take?

What had you pictured for yourself and your loved ones in 2050? I had hoped to be rounding out my career as a mathematician, with a satisfying record of scientific accomplishment and well-taught students behind me. I had hoped to be watching my son thrive in the world with at least some of the advantages that had helped me succeed. But now I'm letting myself ask, what if my college, the university system, the country, the entire economy, are gone by then? What if all we leave the next generation is a command to survive, survive at all costs?

I am not telling you to despair. Despair saps the will to act, and there is too much work to be done.  The difference between 2°C vs 3°C, or between 3°C vs 4°C, is so great that we must be out in the streets causing disruption, fighting for our futures and our lives. We must also join with each other to become resilient, to form networks of preparedness, to help the most vulnerable, and to strategize how we will adapt to whatever change will come. I am not telling you that we cannot make a difference. I believe we can and we will, and I invite you to join me, and help me, in this struggle.

But I also invite you to mourn. We can't truly grasp the urgency for action unless we emotionally grapple with the consequences of inaction. What, in human civilization, will you miss most? What will you wish we had fought harder to preserve? What imagined future will you be most heartbroken to discard?

I wish you a joyous 2020, but also a mournful one. We must be clear-eyed about what we will lose, if we are to fight to preserve what we can.