The reliability of mathematics comes from two levels
One is that the starting point of mathematical theory is based on axioms, which are universal, facts that have been tested by a large number of practices, and thus become the basis of mathematical reliability.
The second is that mathematical conclusions are based on people’s rational thinking and are the result of logical deduction. As long as the starting point is correct and logical reasoning is correct, the conclusion must be correct.
But there are also problems with the reliability of mathematics. That is, the axiom system itself cannot guarantee absolute perfection, and it cannot be claimed that all propositions can be proved or that they are unproven. This is exactly the conclusion after the third numerology crisis. From this it seems that the logic is reliable, but the axioms are not necessarily absolutely reliable, because the axiom itself is a limited choice of mankind, so the axiom is not absolutely perfect. Since it is not perfect, its reliability is limited.
Mathematics has existed and developed for thousands of years. It originated from practice, but also rooted in human reason. Mathematics has always been effective in the journey of human understanding of the world, and it must be effective in the future, because no learning is more rigorous, rational, and reliable than mathematics.
