If you are a professional mathematician and you are asked whether 2 + 2 = 4, the only answer you should give is “Yes, obviously.”

Of course, in mathematics the symbols are arbitrary and can be used to mean whatever you choose. And of course, there are countless settings where the addition and equality symbols are reused to mean something other than the addition and equality of integers. When you write your next paper on commutative unital semirings, you can tell us all about how 2 + 2 can equal 5.

But we are already living in a time when respect for experts is low. Now is not the time for this kind of pointless sophistry. Mathematics is already misunderstood by the general public, but they at least have a fuzzy sense that it provides a bedrock of absolute truths; an indisputable foundation used by all the natural sciences. This is a reputation worth protecting.

Allowing basic arithmetical facts to seem up for debate, even when they obviously aren’t, risks destroying this image. The 2 + 2 = 5 ruckus began, as far as I can tell, from an argument about to what extent mathematics is a purely cultural product. There is something worth discussing here, but the way some working mathematicians twisted into knots to defend 2 + 2 = 5 was genuinely reckless. It is not hard to find tweets from people who are dismayed that “the rot of academia has even reached mathematics”.

This is not the only recent example of this kind of carelessness with the credibility of mathematics. In her book “x + y”, Eugenia Cheng uses analogies with category theory to explore gender and gender relations. The problem with mathematical analogies is that it doesn’t take much effort to make them support whatever position you like.

For example, one gloss on the Yoneda lemma is that we can study an object by studying how it is “seen” by every other object: there are no intrinsic properties of the object that can be missed by doing this. Recklessly spinning that out into an analogy with gender, we can argue that there is no such thing as “an innate sense of one’s gender identity”; the only thing that matters is how you present to other people. Not a very progressive conclusion!

The lesson is: just stop doing this. Mathematics does not choose sides in issues of human values. Trying to convince people that it does makes you look unserious, but worse, makes mathematics itself look unserious.