I feel like this is a somewhat uncharitable reading. I am also a mathematician and I am perfectly aware that we use intuition and informal reasoning to do mathematics. However, it is no doubt one of the defining properties of mathematics, that agreeing on the validity of a proof is much easier than agreeing on the validity of an informal argument, not to mention intuition which cannot be put into words. In fact it is so easy that we have fully automatic proof checkers. Of course most mathematical proofs haven’t been translated into a form that an automatic proof checker can accept, but there’s no doubt that it can be done, and in principle doing so requires no new ideas but only lots of drudgery (modulo the fact that some published proofs will be found to have holes in the process).
As to whether mathematics is anthropocentric: it probably is, but it is very likely much less anthropocentric that natural language. Indeed, arguably the reason mathematics gained prominence is its ability to explain much of the non-anthropocentric aspects of nature. Much of the motivation for introducing mathematical concepts came from physics and engineering, and therefore those concepts were inherently selected for their efficiency in constructing objective models of the world.
I feel like this is a somewhat uncharitable reading. I am also a mathematician and I am perfectly aware that we use intuition and informal reasoning to do mathematics. However, it is no doubt one of the defining properties of mathematics, that agreeing on the validity of a proof is much easier than agreeing on the validity of an informal argument, not to mention intuition which cannot be put into words. In fact it is so easy that we have fully automatic proof checkers. Of course most mathematical proofs haven’t been translated into a form that an automatic proof checker can accept, but there’s no doubt that it can be done, and in principle doing so requires no new ideas but only lots of drudgery (modulo the fact that some published proofs will be found to have holes in the process).
As to whether mathematics is anthropocentric: it probably is, but it is very likely much less anthropocentric that natural language. Indeed, arguably the reason mathematics gained prominence is its ability to explain much of the non-anthropocentric aspects of nature. Much of the motivation for introducing mathematical concepts came from physics and engineering, and therefore those concepts were inherently selected for their efficiency in constructing objective models of the world.