When you get good at math, it also feels like language. Mathematicians see expressions like `|x-y|` and the read it as synonymous with "distance" just as they would "distancia". Physicists pick out fragments of large equations and say "this term acts sort of like an 'effective' mass", etc. There is a sort of vocabulary to mathematical patterns.

Picking up a skill without intentional study is great, but you still learned the skill. Programming languages are formal languages. Most mathematicians don't study foundations either.

Professional programming doesn't often make use of specific advanced mathematical knowledge, but I find it makes everyday use of the skills.