Barkley Rosser wrote:  
> Well, you are correct that the use  
> of axioms in 20th century math and physics  
> involved matters far from obvious, but   
> from a history of thought perspective the  
> concept of an axiom does date back (at least?)  
> to Euclid, for whom they were assumptions  
> thought to be obvious from internal analysis,  
> even if later his axioms (or at least some  
> of them) came to be viewed as synthetic   
> propositions capable of empirical testing.  
>  
>    
  
   
Be very careful about using Euclid to make such a case. The Elements   
were primarily a teaching device, demonstrating for the children the   
rules of deductive inference. The geometric "results" were generated by   
the system in the same way that we teach the fundamental theorem of   
calculus using Rolle's Theorem, and "leading up" to that through   
formalisms about real numbers, functions, etc. This way of teaching (per   
Lakatos's Proofs and Refutations) confounds doing mathematics with   
teaching it to students. This was the reconstruction of geometry that   
Hilbert saw as symmetric with physics -- the theorems or rather   
conjectures come first, the demonstrations or proofs, as Hardy once   
noted, are primarily "rhetorical froth designed to affect psychology".    
Axiomatization as a "research program" involves seeking interesting   
axiomatizations that entail the desired result, be it the Pythagorean   
Theorem or Maxwell's Equations. It is thus a category mistake to ask   
whether one "believes the axioms", or whether the axioms are   
"realistic"; one might though inquire if, for the desired theorem the   
axioms suffice, or are redundant, or inconsistent, etc.  
  
E. Roy Weintraub