【摘要】 数学史上出现的三次数学危机,与其说是“数学的危机”,不如说是“数学哲学的危机”.解决的办法只有依靠哲学.三次数学危机的共性是在于数学家们研究数学的过程中执拗于恶无限性,也由于思维把一个对象的实际上联结在一起的各个环节彼此分隔开来考察.三次数学危机给我们的反思:自然科学家力图建立无所不包的庞大理论体系行不通;单靠形式逻辑不能解决危机;一直到现在,数学家们仍重犯恶无限性毛病,数学的演进始终是在离散与连续相互作用和相互补充的矛盾中.更多还原

【Abstract】 Three mathematic crises in mathematics history is philosophic mathematic crisis rather than mathematic crisis.The solution is only to depend on philosophy. the generality of three crises lies in the process through which the mathematicians have wilfully studied the vicious infinite. It is also caused by the thinking method which led the mathematicians to study separately the a:tually linked, subject. From looking back the crises, we should wake up: it is im-possible for natural scientists to try to et up a huge theoretical system which consists of everything;it is not enough to depend on formal logic to solve the crises; until now, the mathematicians still repeat the mistake of the vicious in-finite,and the mathematic progress has always been made in the contradiction of the separate and continuous interaction and complement.更多还原