The Two Cultures of Mathematics
نویسنده
چکیده
In his famous Rede lecture of 1959, entitled “The Two Cultures”, C. P. Snow argued that the lack of communication between the humanities and the sciences was very harmful, and he particularly criticized those working in the humanities for their lack of understanding of science. One of the most memorable passages draws attention to a lack of symmetry which still exists, in a milder form, forty years later: A good many times I have been present at gatherings of people who, by the standards of the traditional culture, are thought highly educated and who have with considerable gusto been expressing their incredulity at the illiteracy of scientists. Once or twice I have been provoked and have asked the company how many of them could describe the Second Law of Thermodynamics. The response was cold: it was also negative. Yet I was asking something which is about the scientific equivalent of: Have you read a work of Shakespeare’s? I would like to argue that a similar sociological phenomenon can be observed within pure mathematics, and that this is not an entirely healthy state of affairs. The “two cultures” I wish to discuss will be familiar to all professional mathematicians. Loosely speaking, I mean the distinction between mathematicians who regard their central aim as being to solve problems, and those who are more concerned with building and understanding theories. This difference of attitude has been remarked on by many people, and I do not claim any credit for noticing it. As with most categorizations, it involves a certain oversimplification, but not so much as to make it useless. If you are unsure to which class you belong, then consider the following two statements.
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