Conception of understanding in mathematical proof

The article analyzes the role of the concept of understanding in mathematical proof. Understanding seems to be a natural and necessary characteristic of proof, interpreted as an argument in favor of the established result. It is shown that in general two traditions in the treatment of mathematical proofs can be distinguished, going back to Descartes and Leibniz. It arguments for conceptual treatment of category of understanding which is not connected with individual mental acts are resulted. The prospect of achieving conceptual understanding in the computational interpretation of mathematical proof is problematized