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In Enderton's Elements of Set theory, the author writes:

The axiomatic method has been useful in other subjects as well as in set theory. Consider plane geometry, for example. It is quite possible to talk about lines and triangles without using axioms. But the advantages of axiomatizing geometry were seen very early in the history of the subject.

What are advantages of the axiomatic method anyway?

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Trying to summarize 2 and half millenia of mathematics and logic ...


For a "gentle introduction" to axiomatic method, see :

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  • $\begingroup$ Tarski is a good one. $\endgroup$ – user384011 Nov 15 '16 at 19:47
  • $\begingroup$ Yeah, they did some really fantastic stuff. $\endgroup$ – user384011 Nov 15 '16 at 19:50
  • $\begingroup$ Why did you delete your comment about Gödel and Tarski? $\endgroup$ – user384011 Dec 2 '16 at 18:15