alt Hacker NewsArguments about beauty don't lead anywhere constructive because they are too observer- and context-dependent. Poincaré himself was decrying continuous non-differentiable functions as abominations. The monster group is, well, just like that. What feels intellectually ugly for one generation is natural for the next, and the field moves on
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Ygg2 • today at 5:08 PM
According to legends Pythagoreans tried to surpress existence of irrational numbers because they couldn't be expressed as ratio of natural numbers
Supposedly even drowned their member that divulged their existence.
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.