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?
closed as off-topic by Ryan Budney, Daniel Moskovich, Qiaochu Yuan, Steven Landsburg, Nik Weaver Feb 12 '14 at 3:35
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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 first-order 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.