> Making my complaint more general: I find modern math is exploring areas that are interesting to mathematicians, but increasingly irrelevant to society.

Is it, or is it only the parts you hear about/pay attention to?

> People spent over a hundred years arguing whether a continuum approximation of a particle system would behave oddly. In the mean time, other folks went ahead and completely revolutionized the world of computational fluid dynamics (with multi-billion $$$ impact on society) by just doing better numerics (Kahn-style numerical analysis).

Yes, maybe famous solving famous conjectures is just trivia and trophy collecting and the real value is the intuition and techniques you develop along the way to solving them which you can then bring to bear on things like CFD.