数学发展的矛盾运动

On contradictory movement of mathematics development

用唯物辩证法研究数学发展中的矛盾运动,考察数学体系内部的矛盾如何导致了数学史上重大变革的产生.以非欧几何、群论和集合论的诞生为例说明数学理论与现实世界的矛盾运动,进而用历史的、逻辑的方法说明数学理论能否充分发展最终取决于生产实践和科学实验的发展程度,实践始终是检验数学理论真理性的唯一标准.

This paper researched the contradict movement inside mathematics development with materialistic dialectic and has reviewed the inner antinomy of mathematics system how to cause important change of the mathematics history. This paper accounted for contradict movement of mathematics theory and realistic world by using non-Euclid geometry, the group theory, and set theory. This paper explained that mathematics theories can be developed further to be decided by development degree Of producing practice and science experiment by historical and logistic method. The practice should always be unique examine standard of the true reasonableness of mathematics theories.