Humans See Truth Penrose believes that human mathematicians can directly see whether a theorem is true or not. This is a form of neo-Platonism. He is almost certainly mistaken in his view. Mathematicians frequently make mistakes.

Penrose believes that human mathematicians can directly see whether a theorem is true or false. This is a form of neo-Platonism. He is almost certainly mistaken in his view. It is a common experience of mathematicians that they think they have a proof of a theorem, only to subsequently discover that the proof is false. In some branches of mathematics, particularly applied mathematics, it is sometimes possible to have a diagram which represents the basic structure of the proof. In this sense, when the mathematician first thinks about the proof in a pictorial manner, one can say that he can see the truth of the theorem. However, this type of reasoning could also be done by a machine, and the proof will only be valid if a more rigorous demonstration can be given.