> ... by the time you get to the frontiers of math, the words to describe the concepts don't really exist yet.

A friend of mine[0] once said that the act of doing research in math is the act of inventing a language in which you can talk about the problem. Once you have that, the solution tends to come. But inventing the right language is really, really hard.

This might explain why so many research mathematicians end up married to (or in long term relationships with) linguists. His wife is a PhD in Spanish and linguistics, my wife's first degree is in French and linguistics, and I know perhaps three or four others in my immediate circle.

Anecdata, of course.

[0] Andrew Lipson: https://www.andrewlipson.com/