Recently, I issued a challenge (here) to the critical-race theorists to explain how a procedure that is obviously racially neutral – having applicants for symphony orchestras audition behind a screen – is somehow part of systemic racism. No one has bothered to explain, of course. And now here is another challenge: explain what evidence there is that mathematics is racist. This is the claim of the Mathematical Association of America. See here. It is one thing to claim that books, especially textbooks, on math are racist, or that teachers of math are racist. It is quite another to insist that math itself is racist. If so, then that is sad news for non-whites because there is nothing we can do about it.

Or is there? Here we get into what is perhaps the nerdiest of nerdy topics, not just math, but the philosophy of math. For those who don’t know about this, there are at least three possible positions on the status of number, and they correspond to the three positions on the existence of universals.

There is the Platonic, or realist, position that numbers exist independently of us.

There is the conceptualist position that numbers are invented or created by us.

And then there is the nominalist position that numbers don’t exist at all and that “mathematics is a game played according to certain simple rules with meaningless marks on paper.” That’s a quote from the mathematician David Hilbert.

Virtually no one really cared about any of this until the current madness settled upon us, and now we have people insisting that math is racist because “mathematics is created by humans and therefore inherently carries human biases.” This isn’t very persuasive. First, we have to assume that it is created rather than discovered, and second, we have to assume that human biases get in the way, somehow. But even if math is created rather than discovered, how do biases creep in? This isn’t really explained. If I say that the derivative of 2x is 2 or that of sin x is cos x, am I somehow biased? Are these statements somehow biased? These are about as far from anything related to skin color or ethnicity that I can imagine. I don’t see any reason for believing that the truths of calculus would be any different if “created” by non-whites rather than by Newton and Leibniz since it’s reasonable to think that they would create calculus in the same way Newton and Leibniz did. For that matter, think of how poorer the world would be if the French had reacted to the invention of calculus by saying it was an Anglo-German plot against the French? We would have missed out on Legendre, Lagrange, L’Hopital, Laplace, Cauchy, Fourier, Poincare, and so on.

Anyway, those who assert that math is racist claim that mathematical entities are invented and not discovered, so they take the conceptualist position. Not many actual mathematicians believe this, since they are realists. They believe that they are discovering truths about independently existing entities, not about human inventions. But the mathematician Leopold Kronecker declared that God made the integers and all else is the work of man (as it’s usually quoted). Of course, we can declare that fractions and irrational numbers and imaginary numbers are all somehow invented, but it’s hard to detect any difference here between integers and any of these others. They are all abstract entities. And if real numbers are real entities that we discover, then why not other entities, such as vectors, tensors, fields, rings, groups, and topologies?

Kronecker’s quote, incidentally, is repeated by a character in Dorothy Sayers’s *Gaudy Night* (p. 34 in my edition). I have never understood what it is doing there since it seems to have no relationship to what was being talked about. Anyone?

Anyway, what are we supposed to do if math is racist? If the realist view of numbers is correct, then there is nothing we can do. Bad luck for those of the wrong race, but they will just have to live with it. Suppose, then, that numbers are invented. Are we supposed to invent non-racist math? And what would that be like? Will the proofs be less rigorous? Will they come up with different results for derivatives or maybe even dispense with the concept altogether? Well, I for one don’t want to drive across bridges designed by engineers using some crazy, nonstandard math.

All of this seems like it is poorly thought out. I say, stick to saying that maybe some math books or teachers are racist and be done with it. Oh, and why not just admit that some ethnic groups in America don’t do well on math tests for no reason other than they aren’t interested in the subject?