Abstract:
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.