二十世纪之初,数学家对于数学之基本问题曾致深湛之注意,例如如何使数学合理化,数学之象是什么等问题乃当时众目之的。于时乃有所观念论与实在论之对峙,前言可学举 Hilbert 与 Hadamard 为代表,此派主张,只要理论上之公理系统,由始至终,无所牴牾,即认该种数学为合理的,其对象其得谓之存在,后一派之主张则不然,即一一数学不具有形势上的意义,且须具有内容的意义,而数学之对象 At the beginning of the twentieth century, mathematicians had paid great attention to the basic problems of mathematics. For instance, issues such as how to rationalize mathematics and what are the maths of mathematics were all at the time. At that time, there was a confrontation between idealism and realism. The preface can be represented by Hilbert and Hadamard. This school holds that as long as the theoretic axiom is from beginning to end, Reasonable, its object has its own existence, the latter group of propositions are not, that is, one by one, mathematics does not have the significance of the situation, and must have the meaning of the content, and mathematical objects