> Algorithms can actually produce a real physical result, whereas mathematics exists beyond pen and paper You are confusing the algorithm, which is an abstract

> Algorithms can actually produce a real physical result, whereas mathematics exists beyond pen and paper You are confusing the algorithm, which is an abstract procedure with no physical existence, with the set of possible processes that can implement it. > Algorithms that we (programmers) construct usually aren't done in terms of Turing machines or the lambda calculus. Therefore they're not purely mathematical Sloppy math is still math. Any program that an interpreter or compiler will accept is a mathematical object. If it weren't, it couldn't be parsed. That said, it is possible for a mathematical statement to be undefined, ambiguous, or erroneous.