I would argue that for a mathematician, the primary anchor is other mathematicians reading their proofs and complaining that it doesn't seem quite right. What a

I would argue that for a mathematician, the primary anchor is other mathematicians reading their proofs and complaining that it doesn't seem quite right. What anchors the mathematical community as a whole is applications - physics, cryptography, signal processing. The demand for applications is what keeps it from degenerating into some number-mysticism in the long term.