level 10
数学也是间接扎根于现实的,所以楼主的命题值得商榷。
2014年04月17日 01点04分
3
同意,数学基本都是为自然学科服务,当世界观发生变化,数学原理甚至会从根本上改变,最明显的例子就是欧氏几何与非欧几何
2014年04月17日 01点04分
回复@whykane:最典型的应该是19世纪数学家对于极限和微积分基础的思考。我相信现在没人会把无穷小当成幽灵了吧?
2014年04月17日 01点04分
但是数学是一种思想啊 一种逻辑体系
2014年04月17日 16点04分
level 11
How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality? [...] In my opinion the answer to this question is, briefly, this: As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.
—Albert Einstein
Physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover.
—Bertrand Russell
There is only one thing which is more unreasonable than the unreasonable effectiveness of mathematics in physics, and this is the unreasonable ineffectiveness of mathematics in biology.
—Israel Gelfand
2014年04月18日 11点04分
8