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These two most-used foundations of mathematics originated almost "together" in ancient Greece.Thales of Miletus (c. 624-547BC) originated axiomatics for geometry. His pupil, Pyathagoras of Samos (c. 580-496BC), originated genratics for arithmetic.
Many centuries of popularity of The Elements of Geometry by Euclid of Alexandria (c. 450- 360) -- most published of books, excepting The Bible -- has made this the most-used foundation of the two.
However, the British mathematician, logician, philosopher, Bertrand Russell (x-y) had this to say: "Axiomatics has all the advantages over generatics that theft has over honest labor."
