Informally, an example of this problem is calculus class. A kid who's interested in programming, and takes calculus, can dream up a program that computes the de

Informally, an example of this problem is calculus class. A kid who's interested in programming, and takes calculus, can dream up a program that computes the derivative of any expression. But now try doing that with the anti-derivative. And to be sure you can write an expression in multiple ways, but the core problem remains. Disclosure: I was that kid. My program was a mess, but good enough for a proof of concept.