WellSpyder, on 2012-November-05, 09:06, said:
Ken, am I right in recalling you are a mathematician? It was through a maths lecturer that I was introduced to the concept of a "formal" proof, which I naively took to be a rigorous one. Apparently, it actually meant that he was just giving the "form" of the proof without the details, which is almost the opposite of what I thought it meant....
Yes I am a mathematician and I have never heard this approach referred to as a formal proof. At it's most extreme, I think of a formal proof as one that can be checked, or perhaps even done, by a computer. More often, it means a proof with little or no appeal to the type of argument where one says "Oh yeah, I don't doubt you can do it even if you have not written it all down". Formal proofs have detail. With a formal proof, one sometimes hears a person say "Line by line I see that it is true, but I don't understand it" meaning that it's hard to place it in a context.
I often think of Steve Smale as the master of the informal proof. He will talk about the ideas for a while, and then ask "Anyone see anything wrong with this?". If no one does, he moves on to the next result. You can cover a lot of ground that way,. With Smale it works very well. With some others, maybe less well.