量子奥秘 发表于 2012-6-14 23:44 
我也研究过弦论一段时候,它所用到的数学侧重微分复几何,准备知识是:微分几何,复分析(含复变函数) ...
你说的很有道理。但对于“不认为弦论的数学是21世纪的数学,相反弦论的数学只是20世纪数学瓶颈的体现”,我不能认同。不知你是否熟悉哈佛弦论专家Cumrun Vafa搞的那套数学(
http://www.physics.harvard.edu/~vafa/),那绝对是21世纪的。
Such an all-encompassing theory necessarily requires a tremendous amount of mathematical technology. In fact, most of the mathematics needed for string theory is not even yet developed. String theorists thus have the exciting task of building new mathematics as tools to explore new laws of physics. It is therefore not surprising that string theory is at the cross roads of many fields, including mathematics, particle phenomenology and astrophysics. Cumrun Vafa's research has involved essentially all these aspects. Together with his colleagues he has worked on topological strings, trying to elucidate some new mathematics originating from string theory (notably in his work on mirror symmetry) and using these techniques to uncover some of the mysteries of black holes, particularly the Bekenstein-Hawking entropy. He has also applied these ideas to particle theories by geometrically engineering quantum field theories, as well as solving the strong coupling dynamics of confining theories (using large N matrix model technology) and geometrizing string theory defects (in a limit of string theory known as F-theory). His recent work involves applying these ideas to come up with stringy predictions about what the Large Hadron Collider (LHC) at CERN may potentially discover in the near future.