本书是徐利治教授根据近两年来在大连、长春、武汉等地讲学用的提纲和讲义充实形成的。它主要是研究和讨论数学发展规律、数学的思想方法以及数学中的发明创新的法则和心智过程。作者精选了十来个公认为比较有趣的专题,对它们进行了分析和讨论;同时总结了一些历史上有过重大贡献的数学家成功的经验。这些对数学和哲学的科研工作者、爱好者和高校师生都有一定的参考价值。 This book is Professor Xu Lizhi based on the past two years in Dalian, Changchun, Wuhan and other lectures outline and handouts enriched the formation. It is mainly to study and discuss the law of mathematical development, mathematical thinking and mathematical innovation and the law of the process of mind. The author selected a dozen or so topics that were considered more interesting, analyzed and discussed them, and summed up the successful experiences of some mathematicians who had made significant contributions in history. These mathematical and philosophical research workers, enthusiasts and college teachers and students have a certain reference value.