I agree with everything you've said, but in general it is the result that advances mathematics, whereas very few proofs open up genuinely new fields of study or do things in a truly revolutionary way. For every proof like (for example) Wiles' of FLT (which is way over my head, but apparently...
@aikismos That couldn't hurt, thanks.
@fresh_42 In programming, even if you never write assembly, it can have a practical use to know how things compile for optimisation purposes. Not really applicable for maths though since the end result is in most cases the main point, rather than how...
I just want to understand the process from the ground up - kind of like in programming knowing assembly can give you some insight into coding with higher level languages, though this is more for interest than anything else. I expect I will learn a bit (possibly a lot) of set theory in the...
I am looking for a book that starts at the standard ZFC axioms and progresses to the point where some recognisable non-trivial mathematical statement is proved. By recognisable I mean something that you may encounter in school/early university level and is not purely set-theoretical (e.g...