The Two Cultures of Mathematics

WT Gowers:

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 understand- ing 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.

  • Article goes beyond answering its question to giving examples in somewhat sophisticated math. I find that engineers and physical scientists are trained to convert a principle into an equation and then search for a pre-solved equation type that will solve that problem. For example, many basic quantum theory problems are solved by using previously developed solutions to electric field problems, but adding the complicating issue of complex variables.
    Mathematicians seem to be more interested in knowing why the solution works.
    The other issue in the introduction is that most college science programs in a liberal arts college required the student to take 50% of their courses in non-science/non-math areas. Non-science majors will normally take 12-1/2 % of their courses in science and math. While the 2nd law of thermodynamics is presented in high school, it is often not applied until college chemistry and most non-science majors choose biology for their college science.