Also the mathematicians wouldn’t decline to give an answer.

Are you sure? I only minored in math, but even I would struggle to provide an answer to this. It would have to be something incredibly vague, like “a number is a mathematical object that has certain consistent properties relevant to the field of study.” Because otherwise you get situations like “is infinity a number?” and you can’t answer categorically, because usually it’s not, but then you look at the transfinite numbers where you can indeed have omega-plus-one as a number. And someone asks if you can have an infinite number of digits to the left of the decimal place, and you say “well, not in the reals, but there are the P-adic numbers…” and folks ask if you can have an infinitely small number and you say “well, in the reals you can only have an arbitrarily small number, but in game theory there are the surreal numbers, where…”

So yeah, I’m not sure “what is a number” is even a math question. It’s more a philosophy question, or sometimes a cognitive science question (like Lakoff and Nuñez’s “Where Mathematics Comes From”).

Obligatory XKCD: https://m.xkcd.com/1428/