> as a low-dimensional topologist I'm not a mathematician Huh? How do you figure? > Symbolic proofs are sort of a lowest-common-denominator You are reading

> as a low-dimensional topologist I'm not a mathematician Huh? How do you figure? > Symbolic proofs are sort of a lowest-common-denominator You are reading the word "symbol" too narrowly here. What matters here is not so much the symbols but the existence of rules for manipulating them. Letters are symbols, and so are words, and so proofs written in natural language can be math if those proofs respect a set of precisely definable rules. I don't know much about low-dimensional topology, but I'd be surprised if it didn't adhere to that definition. (And if it turns out not to then I would have no qualms saying that it isn't math.)