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I think this is written from the perspective of a continuous mathematician or physicist, and the examples of discrete maths they have have in mind are numerical
by penteract 3y ago
I think this is written from the perspective of a continuous mathematician or physicist, and the examples of discrete maths they have have in mind are numerical simulations, which are certainly harder to reason about than their continuous counterparts.
I also suspect that this is a fairly orthodox attitude among mathematicians - in "The two cultures of mathematics" (https://www.dpmms.cam.ac.uk/~wtg10/2cultures.pdf https://www.dpmms.cam.ac.uk/~wtg10/2cultures.pdf) Tim Gowers says with more authority than I could:
> the subjects that appeal to theory-builders are, at the moment, much more fashionable than the ones that appeal to problem-solvers.
This isn't precisely the discrete/continuous split, but it's mostly aligned and the article puts combinatorics is firmly in the latter category.
- Tainnor 3y agoI'm not sure that the "two cultures" split aligns with continuous vs. discrete maths. There's theory-building in continuous mathematics (abstract spaces, e.g. topological, metric, Banach, ... spaces) and in discrete mathematics (theory of finite fields), whereas both areas also have computational / problem-solving aspects (proving specific inequalities in the continuous case, or proving theorems about particular kinds of graphs in the discrete case).