I'm aware of the categorical revolution, since I'm young enough to have been (mathematically) raised on that perspective. Some of the more abstract algebraic ge

I'm aware of the categorical revolution, since I'm young enough to have been (mathematically) raised on that perspective. Some of the more abstract algebraic geometry is actually coming back to computational applications. See, for example: http://www.researchgate.net/publication/226664601_From_Oil_Fields_to_Hilbert_Schemes http://www.researchgate.net/publication/226664601_From_Oil_F... To say that something is not applicable is hard to argue. And besides giving examples of when it is applied (and you claiming it's still an unimaginably small fraction of mathematics) all I can say is that the understanding of some object can provide insights and applications in unexpected ways. Dynamical systems inspire computer graphics, Mobius bands inspire carburetor belt design, category theory inspires Haskell... I just don't think it's fair to ask for the immediate applications of any given theorem because the ultimate application is understanding what's going on. But thanks for the great discussion! :)