jl274

There are some reasonable points in here (problems with abstraction for abstraction's sake) but on the whole this reads as someone who simply cares about geometry and analysis, but not algebra or discrete mathematics.

Which is fine, he's entitled to his opinion. But the stronger argument that "mathematics is only good when it's tied to physics" argument is wrong and outdated -- belongs to the pre-computer, pre-information age.

Even on a purely mathematical level, some of his arguments don't hold. For instance, for all his complaining about how abstraction doesn't contribute anything -- Cayley's theorem on groups, Whitney's theorem on manifolds -- there ARE categories where the abstract definition is needed or is more natural, like algebraic varieties (which can't always be embedded in complex N-space for any N) and rings (I have no idea what better definition he'd be proposing).

To me, it sounds like he doesn't like or know much about the algebraic side of math, and resents how much it dominates in math today.