Comment by potbelly83
3 hours ago
That's not what op is arguing. To use your example, coming up with singular examples of continuous non-differentiable functions is an example of "ugly" mathematics, whereas putting them into a nice framework where they can be analyzed as a whole (i.e. functional analysis, density of such functions, etc...) is an example "elegant and insightful" mathematics. The same with the monster group, on its own maybe nothing special, but then you have the connections with other branches of math. Tao seems so focused on the individual problems and not their connections/generalizations.
Well one does have to come up with continuous non-differentiable functions to begin with, right? Weierstrass had to shock the community with his weird series that's almost everywhere nondifferentiable before people could conceive of a nice framework that includes them. People do not invent whole encompassing abstractions out of nowhere
Great point, I think the argument you could make about Tao (fairly or unfairly) is he never tries to build that framework.