"Programming isn't analogous to math" I think it's analogous to math in the sense that a programming language is a formal system, just like any logical system.

"Programming isn't analogous to math" I think it's analogous to math in the sense that a programming language is a formal system, just like any logical system. The syntax is defined by formal rules, it semantics if not defined formally is strictly defined by the compiler implementation or hardware. Actually, the link between programming and proving as been characterized by the "curry-howard isomorphism" that says that a program is a proof of his type. In that sense, programming = writing a proof. For instance, in ML : the program "fun (x,y) -> x" is a proof of the proposition "A and B => A". This idea can be extended to more complex types/propositions (see the Coq proof assistant for instance). That being said, writing programs usually require different set of skills than doing mathematics. The best programmers are not always the best mathematicians and conversely. To me difference shows especially for big complex software, rather than smart algorithms in programming contests for instance.