Why I Don't Like Math

A lot of mathematicians (Paul Halmos is one example) say that one way to make sure you understand your math is to see if you can re-express it in a different notation. So any time you try to rewrite a math problem to fit the notation you know best, you are aiding your understanding.

I think his point is more subtle than that. Informal paper math doesn't always neatly line up with formal, computer-processed math---such as numerical processing or theorem proving. This disconnect can be extremely frustrating: I want to believe paper proofs, but simply writing down the theorem statement in a rigorous way can require significant changes. It's the frustration of understanding something on the surface but then realizing that in fact it makes no sense.