数学发展过程中的三次危机及意义摘要 本文研究了历史上的三次数学危机及其意义。对三次数学危机发生的原因及所带来的影响进行了研究和分析。任何一门学科，只有当他充满大量问题时，他才算拥有生命力。缺乏问题则预示着这门学科发展的衰亡或终止。所以这三次数学危机就是因此而来。第一次危机呢是因为人们遇到了无理数的问题，而第二次则是因为人们遇到了微积分的问题，第三次是因为遇到了罗素悖论的问题。正是因为每次都遇到了新的问题，所以在每一次的危机中，数学这门学科都得到了新的发展。第一次改变了古希腊的数学根基，第二次则对微积分进行了严格的定义，而第三次则是使数学分析更加的严密化。所以最后我们得出这三次危机并不是真正的“危机”，反而是数学发展的三次契机，是一个让数学发展层层递进的过程。关键词 数学危机 无理数 微积分 无穷小Three crises in the development of mathematics and their significanceAbstract This paper studies three mathematical crises in history and their significance.This paper studies and analyzes the causes and effects of the three mathematical crises. Any subject has vitality only when it is full of many problems. The lack of problems indicates the decline or termination of the development of this discipline. So these three mathematical crises are the result. The first crisis is because people encounter the problem of irrational numbers, the second is because people encounter the problem of calculus, and the third is because of the problem of Russell's paradox. It is because of the new problems encountered every time, so in every crisis, the subject of mathematics has got new development. For the first time, it changed the mathematical foundation of ancient Greece, for the second time, it strictly defined calculus, and for the third time, it made mathematical analysis more rigorous.Therefore, we conclude that these three crises are not real "crises", but three opportunities for the development of mathematics...
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