The analysis of approaches to mathematical knowledge correctness problem

The paper considers several approaches to mathematical knowledge correctness problem available in mathematical practice, mathematical and computer logic. It discusses mathematical knowledge correctness criteria: universal, intuitive, logical, logical-formal, and computerized ones. The paper shows that the computerized criterion provides potentially the most reliable way to ensure mathematical knowledge correctness, and that the man-machine systems for theorem proving are the most promising way of its application. It finally outlines future steps to solve the problem.