Well, I don’t know if I can comment on Kant or Hegel because I’m no real philosopher in the sense of knowing what these people have said in any detail so let me not comment on that too much.
Roger PenroseI imagine that whenever the mind perceives a mathematical idea, it makes contact with Plato's world of mathematical concepts... When mathematicians communicate, this is made possible by each one having a direct route to truth, the consciousness of each being in a position to perceive mathematical truths directly, through the process of 'seeing'.
Roger PenroseAnd these little things may not seem like much but after a while they take you off on a direction where you may be a long way off from what other people have been thinking about.
Roger Penrose