> None of this is particularly controversial

Judging by the fact that most maths degrees are listed as science degrees, it's pretty clear that "mathematics is not science" is a controversial claim.

I don't think that's true. Certainly among the people in my department while I was doing my PhD in mathematics, it was universally agreed that mathematics is not a science (because mathematicians don't do experiments as a part of their work).

Even outside of math departments I see some evidence of that agreement -- for example, why else would the "STEM" acronym list Science and Math separately?

> Judging by the fact that most maths degrees are listed as science degrees

How colleges categorize their departments has an element of politics to it, so I wouldn't pay much attention to that. I've got both a math and science degree, and none of my professors or peers would consider math to be part of science -- even considering our math department was listed under our science department. I think OP is correct that this topic is not controversial at all, at least among the people who actually do math and do science. There's no question that math and science are completely separate things.

Isn't "self-serving narratives" an unobservable? Aren't you heading down the path of your self-described pseudo-science?

This is exactly why this kind of simplistic positivism is far from uncontroversial, and in fact saying that it is uncontroversial betrays an almost perfect innocence of epistemology. Once you subscribe to it, it becomes impossible to talk about very many things that we need to talk about.

> you can see by the downvotes how committed people are to their various self-serving narratives.

How can you see this purely based on downvotes?

He's positing the existence of a non-observable entity.

I've encountered this viewpoint before and it took me a while understand the nuance of the assertion - as it is so matter of fact it is easy to take "not a science" as a value judgement - especially as we often enshrine empirical thinking.

As with all things though, it comes down to definitions and with the more specific and academic understanding of science, it is easy to see how (pure) mathematics isn't a science. Indeed, a lot of computer science somewhat doesn't fit well as a science - like FP.

It's quite a controversial statement that can be construed as aggressive which is probably why you're getting downvotes but I think you're right to point out how confronting your own assumptions/axioms can bring out strange reactions.