Proofs and Refutations is essential reading for all those interested in the methodology, the philosophy and the history of mathematics. Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors ce...
Proofs and Refutations is essential reading for all those interested in the methodology, the philosophy and the history of mathematics. Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or creativity. Imre Lakatos is concerned throughout to combat the classical picture of mathematical development as a steady accumulation of established truths. He shows that mathematics grows instead through a richer, more dramatic process of the successive improvement of creative hypotheses by attempts to 'prove' them and by criticism of these attempts: the logic of proofs and refutations.
isaachan
复旦大学出版社2007版
哲夫成城
上海译文出版社1987版
hmev
复旦大学出版社2007版
kengo
复旦大学出版社2007版
1 有用 mondain 2014-01-02 21:59:55
因为干老牛逼
2 有用 君 2021-04-30 10:41:28
对话读起来太有意思，实在太少有书我能在每一段旁边写yes！ ps：学习数学就是学习所有的希腊字母
1 有用 淇厚生 2015-05-13 22:12:45
Lakatos对于形式主义以及数学研究中由概念驱动的创造非常不以为然，尽管后者是数学中非常重要的方法。他无法找到庞加莱证明的漏洞，亦不能像数学家那样理解它的意义。而且，由它衍生出的代数拓扑在物理中确实是有用的。
2 有用 君 2021-04-30 10:41:28
对话读起来太有意思，实在太少有书我能在每一段旁边写yes！ ps：学习数学就是学习所有的希腊字母
1 有用 淇厚生 2015-05-13 22:12:45
Lakatos对于形式主义以及数学研究中由概念驱动的创造非常不以为然，尽管后者是数学中非常重要的方法。他无法找到庞加莱证明的漏洞，亦不能像数学家那样理解它的意义。而且，由它衍生出的代数拓扑在物理中确实是有用的。
1 有用 mondain 2014-01-02 21:59:55
因为干老牛逼