[coldtea]

>These statements are simply false. The vast majority of pure mathematics research done today does not involve category theory at all, and does not benefit from it. An even greater majority (like 99%+) of mathematics done in industry and in national labs does not involve category theory. Numerical analysis, probability, statistics, partial differential equations, dynamical systems, harmonic analysis, even lots of modern differential geometry – no category theory to be seen!

They might not think of it consciously, but they sure exploit and use properties of sets, rings, groups, and so on all the time in their calculations...

[btilly]

The properties of sets, rings, groups and so on that they most often use were established prior to the invention of category theory in the 1940s. Therefore the fact that they use subjects that category theory tried to find abstractions in no way suggests that they are based on category theory.