The first mathematical crisis was caused by Pythagoras, because he thought that any number could be expressed by fractions. However, he encountered difficulties in finding the diagonal of the unit square: 2 is not a complete square number, so he thinks that this number does not exist. Then the first mathematical crisis appeared. The first mathematical crisis caused a rift between arithmetic and geometry. With the development of mathematics, the differentiation between algebra and geometry is becoming more and more serious. It was not until Descartes founded coordinate system and analytic geometry that the crisis ended successfully.