I still remember something you said at lunch around 2003 at Georgia Tech: in introductory real analysis, we work hard to prove things we already know, whereas in introductory complex analysis we work comparatively less hard to prove deep, useful things.
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It is a thought I’ve had for a long time. But as I get older, I’m starting to have more respect for the nuances and subtleties at the heart of real analysis.
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Dog is named Cauchy as it left remainder at every pole?
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It certainly left a residue!
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Walking sparks creativity research has shown - taking time off often gives the best maths ideas.
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Definitely!
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Had you been walking your dog around a tree, I'm guessing you would then have focused your thoughts on Rouche's theorem, right?
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An oldie but goodie!
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What is the study of mostly smooth, but not that smooth, functions called?
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Analysis. (I don’t know of any better name for it.) Some parts of analysis focus on the really pathological counterexamples. But other parts focus on functions with different amounts of smoothness and what that entails.
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