The problem with this theory is: what is the part of a geometric proof which cannot be described or validated using a classical, discrete computer? There is no such step. All parts of mathematics which mathematicians are able to agree on can be so described. There is no scope for our brains taking in an analog measurement, doing an analog measurement step on it, and using it to confirm the truth of a mathematical statement.

Of course, this is not an argument that our brains are absolutely finite and classical. Perhaps analog computations is required for an appreciation of beauty, or quantum physics is necessary for us to fall in love. But we seem to be able to check math proofs without them.