That sounds like a great idea. It might help reduce the Dunning-Krueger effect which says that people who don't know what they don't know are overly confident about the knowledge they (think they) possess.

Teaching the history of math would tell the students what they don't know and would no doubt motivate many to learn more.

I had a short course on History of Philosophy in high-school which I liked but which was kind of fuzzy because that's the way philosophy is. It was hard to discern any progress or direction in the study of philosophy over the centuries.

Whereas with math, there is no fuzziness about it, except in Fuzzy Logic of course.