# Difference between soft analysis and hard analysis

I have sometimes overheard people using the terms hard analysis and soft analysis.I am not a particularly well-read person in mathematics but I have wondered what that is all about.I hope there exists an explanation for someone with single-variable calculus background.

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Terry Tao has an excellent blog post on this topic. –  Bob Pego May 5 '12 at 20:16
This is more for those who already know the difference. I saw the following joke on the internet sometime in the late 1990s and used it in a MAA talk I gave on non-constructive proofs in 2001. Question: How many analysts does it take to screw in a light bulb? Answer: Three. One to prove existence, one to prove uniqueness, and one to devise a non-constructive way to do it. –  Dave L. Renfro May 7 '12 at 16:04

For example, Weierstrass constructed an example of a function $f \colon [0,1] \to \mathbb R$ that is continuous but nowhere differentiable. His proof involved computing inequalities to show his function was not differentiable. HARD
Nowadays a modern mathematician may consider the Banach space $C[0,1]$ and cite the Baire category theorem to show that there is a function $f \colon [0,1] \to \mathbb R$ which is continuous but nowhere differentiable. SOFT