Kronecker explains the need for fundamental concepts in a most fascinating way as follows: “Clearly, when a reasonable master builder has to put down a foundation, he is first going to learn carefully about the building for which the foundation is to serve as the basis. Furthermore, it is foolish to deny that the richer development of a science may lead to the necessity of changing its basic notions and principles. In this regard, there is no difference between mathematics and the natural sciences: new phenomena overthrow the old hypotheses and replace them by others."

Vladimir Arnold: "Mathematics - a servant of science, and it must explain every science that really makes this science."

关于数学的摘抄