Questions on the Culture and Philosophy of Mathematics
How are we affected by the difficulty communicating meaningfully between sub-fields? Is the problem comparable for other areas of science or humanities?
In what sense are mathematical objects real? Do mathematicians discover or invent these objects?
Is there an objective way to decide whether a proof is rigorous?
Why do we place more value on proofs that are simple and aesthetic?
How is our teaching of mathematics affected by our philosophy of mathematics? Do formalists teach differently than those who view mathematics as an imperfect and exploratory science?