In this wikipedia article on the foundations of mathematics, it says:
In practice, most mathematicians ... do not work from axiomatic systems
Is this correct? If so, what is an example of this?
In this wikipedia article on the foundations of mathematics, it says:
Is this correct? If so, what is an example of this? 

closed as offtopic by Ryan Budney, Daniel Moskovich, Qiaochu Yuan, Steven Landsburg, Nik Weaver Feb 12 '14 at 3:35This question appears to be offtopic. The users who voted to close gave this specific reason:



It's correct in a sense, but it makes me want to rewrite that Wikipedia section. If you replace the preposition "from" with "in", you have a foundational question. Most mathematics is not done in axiomatic systems. As a trivial example, consider a typical MathOverflow post: it is in English, is not in a formal language, and does not specify an axiom system. The more important claim is different: $\ $ Most mathematics can be readily formalized in axiomatic systems, and it's sometimes useful to do so. If you insist on the preposition "from", you have a more psychological question. I would say mathematicians work more from intuition than from axiomatic systems. Most mathematicians would have difficulty writing out the axiomatic system for ZFC  it would require writing out rules for firstorder logic, being precise about bound and free variables in quantifications. Perhaps they could do it, but they would find it a strange request and one irrelevant to their ordinary mathematical work  which shows that they are probably not working from the formal system in the first place. 

