Lakatos's [Proofs and Refutations](http://www.worldcat.org/oclc/258084194 http://www.worldcat.org/oclc/258084194) is good background on the mathematical ideas t

Lakatos's [Proofs and Refutations](http://www.worldcat.org/oclc/258084194 http://www.worldcat.org/oclc/258084194) is good background on the mathematical ideas that Stepanov is alluding to. The short version is that you don't start with axioms, because they are generally uninteresting. You start with interesting theorems and if necessary revise the set of axioms needed to prove those theorems.