《再絮叨几句》的评论

by: langfellow

Fri, 09 May 2008 12:46:52 +0000

感谢楼上朋友的关注，虽然是不同意我的观点。我们肯定都希望气氛友好地讨论这个问题。这一段英文我连蒙带猜基本能搞懂。对克莱因的《古今数学思想》前言，我看了，就是译者说对中国队数学的贡献没有提到，但是，译者也承认这仍然是目前最好的一本数学史著作，所以才集中了国内那么多数学教授们翻译这本书。
你推荐的应该是陶哲轩的文章吧，我这里打不开。我会多试几次。

by: antonin

Wed, 07 May 2008 20:42:03 +0000

Morris Kline’s book is not really a book of the history of mathematics. If you read the preface to his book, you would know that well. His point of view is sometimes considered contravertial, and he is not exactly a mathematician, rather an applied mathematician. Of course, there is a difference between the English word “mathematician” (which really means “someone works in mathematics” or “someone whose profession is teaching and research in mathematics”) and its Chinese counterpart, which is used in the sense of “an established mathematician” or “someone who made substantial contribution to mathematics”. But some ancient Chinese definitely made substantial contributions to mathematics, be it known to the western world at that time or not. And remember, when people did not have the algebraic expressions we have now, it was very difficult to perform even some simple computations like taking the square root. Actually even now without knowing the binomial theorem (which is a special case of the Taylor series), taking square root is not that easy. You have to be really smart (and perhaps even resilient) to achieve the goal of obtaining an approximation of \pi, or to solve a polynomial equation (imagine solving “only” a cubic equation). We can not assume that they did not have the right idea of the coefficients of the binomial expansion just because they only wrote down the case till n=7. We need proofs to make sure our conclusion is logically sound, but as an internationally renowned mathematician once said, to believe that the logical correctness is the main merit of mathematics, is no less that to believe that the main merit of Lu Xun’s work is that they are grammatically correct. We need proofs to make sure that there won’t be fatal mistakes in our work. But the central role is always played by genuine ideas. I suggest that you read a recent article “What is good mathematics” by Terrence Tau, Fields medalist and professor in UCLA. His article can be found at http://arxiv.org/abs/math.HO/0702396. You may get some ideas about how to judge mathematical work and mathematicians. Sorry for writing in English as I am using the computer in my office.

by: langfellow

Tue, 29 Apr 2008 02:45:15 +0000

我没有奉布尔巴基的说法为圭臬，文中不是修改了他们那么严格的说法了吗？但是他们作为一种重要的说法存在总不会成问题吧。

by: frank

Mon, 28 Apr 2008 22:43:16 +0000

Bourbaki is NOT God! So don’t blindly follow one citation or two from someone or some groups, then mistakenly think you see the light!

by: frank

Mon, 28 Apr 2008 22:37:03 +0000

Are you sure you know what you are talking about. I don’t think
what you said about Chinese mathermatics makes any sense.