Mathematics and Creativity

2010年好像是1月份在法国召开了一个关于Grothendieck的会议,其中包括一些大数学家,很会议中讨论了为什么Grothendieck能够如此地有创造力,并分析了他的创造力的来源,特别分析了他的家庭对他的影响。这个会议本来在网上很好找到,但是我找了一通,没有找到。但是还可以找到会议的文集。其中第一章的内容非常有意思,对于不学数学的人也会很有启发。这篇文章的题目就是:《Mathematics and Creativity》全文可以在这里下载:



All of the aspects of Grothendieck’s mathematical approach discussed here: the slow, broad approach, the search for the essence, the embrace without reticence of a problem as its own solution – all will be illustrated by numerous cases and examples from his research in the coming chapters.

One might ask what it is that makes it so hard, or so rare, for other mathematicians to react this way. Grothendieck suggests that the answer is undoubtedly a form of fear; fear that the unfamiliar will not bend docilely to the mathematician’s will, fear that confronting the unknown will lead to unfortunate mathematical accidents such as error or total lack of progress, fear of not obtaining recognizable results. If there is one feature of Grothendieck’s personality to which he attributes his ability to have explored and constructed so much that no one else had done before him, it is a total lack of this kind of fear.


“Perhaps the very crux of the matter is that creativity, for Grothendieck, is identified with the accepting and comprehending observation of the mysterious ways of nature – observation made with respect and love, absolutely devoid of judgment – thisis creativity, and it is completely independent of whether anything material is actually produced.”


In fact, Grothendieck’s spontaneous reaction to whatever appeared to be causing a difficulty – nilpotent elements when taking spectra or rings, curve automorphisms for construction of moduli spaces – was to adopt and embrace the very phenomenon that was problematic, weaving it in as an integral feature of the structure he was studying, and thus transforming it from a difficulty into a clarifying feature of the situation.


About kongliang

I am a mathematician interested in quantum field theory.
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