A mathematical proof is a series of steps each of which the listener is confident they could prove to be correct. The more difficult or surprising a result the

A mathematical proof is a series of steps each of which the listener is confident they could prove to be correct. The more difficult or surprising a result the more steps you will have to add to convince the listener. Similarly when you are writing a program you don't know the exact inner workings of every function you call. You should, however, be confident that they work and that you could understand them if you need to. The source for a computer program omits plenty of contextual information thats needed to make it meaningful. The only completely unambiguous interpretation of the program is the machine code which is analogous to the proofs in the principia mathematica. Its nice to know how it works in principle but you dont want to work with it unless you really have to.