再絮叨几句
(2 votes, average: 5 out of 5)
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关于什么是数学家，一般没有严格的定义。但是行家能知道本行的那些人可以是数学家，那些人不是数学家只是数学教师或者数学工作者。布尔巴基学派的迪厄多内有本法语汉译了的《当代数学：为了人类心智的荣耀》，书中对数学家的定义是“至少发表过一条非平凡定理证明的人”，其中的要点是“发表”和“证明”，而“平凡的工作”意思是说“从熟知的定理中引出明显的结果”，这样基本可以准确地理解什么是数学家了。自然这是当代数学家的定义。当代的标准不能套用到古人身上。但是，古代的数学家也不能随便封吧，得有个现代标准的雏形才行啊。考虑到中国古代不重视数学和科学，所以，我们可以去掉“发表”这一项。“证明”总不能去掉了吧？刘剑查了很多资料还是得出了第一个结论，中国古代有数学家，而且不止一位。那就是不要证明，不要发表，也不要不平凡，我们就胜利了，“不战而屈人之兵”，完胜！刘剑给出的第一个数学史网站我也常看，我还统计出了这个网站上各国数学家人数的排名，斑竹如果不发，可以到我博客上察看。总之按最严格定义，中国古代没有数学家，放宽要求就不止一位了，就看你采取什么标准了。至于刘剑的《答什么是“爱国主义”兼谈两种读书人》我认为没有什么价值。不过它有作用，就是按照“习惯法”我理解为他和我的争论结束的意思。我刚好也想说，我所有想说的就这么多了。看不看，懂不懂，褒不褒，贬不贬，都由你了。
关于祖冲之计算圆周率的值，他不是使用割圆术的世界第一人，也不是使用割圆术的中国第一人，他有前人的工作可以参考。似乎（没有确切的证据）掌握了一种简化的算法，得到了很好的结果。如此而已。说他独立地发现割圆术的方法的人，肯定没有好好利用网络的资源。
至于说中国数学是“一个不同于逻辑主义的理论流派”，我看不懂你在说什么。中国古代数学没有脱离实际应用而完全独立出来，也不注重证明，你就说它是理论？还“流派”？这可不能自封啊！查查我们选择翻译了的目前最好的数学史书《古今数学思想》四卷本，看看它上面有没有这个“理论流派”！
04月 29th, 2008 at 7:37 am
Are you sure you know what you are talking about. I don’t think
what you said about Chinese mathermatics makes any sense.
04月 29th, 2008 at 7:43 am
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!
04月 29th, 2008 at 11:45 am
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。
05月 8th, 2008 at 5:42 am
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.
05月 9th, 2008 at 9:46 pm
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。