>An often reasonable way to ensure that you can mechanically apply a problem solving technique (which is related to, but absolutely not the same thing as unders

>An often reasonable way to ensure that you can mechanically apply a problem solving technique (which is related to, but absolutely not the same thing as understanding the maths) is to make a program that does it. What "problem solving technique"? There's no algorithm you can mindlessly remember and use it to create algorithms. Making a program that solves the problem is the highest possible understanding. >I don't even know what it would mean to write a program that "does" Riemann's geometry That's because it's an abstraction, not a problem to be solved. In the same way you can't write a program that 'does' functional programming, you can only program in a functional way. Well, I guess writing an AI which can solve problems in Haskell would be an exception. I bet you couldn't remember its code and execute it in your head, though.