“Naturally, man’s first knowledge of geometry was obtained by the inductive method from a very large number of observations and experiments. However, as the body of geometric knowledge grew, it was discovered that many truths could be obtained from others by means of deduction without resorting to observations or experiments. This idea occurred long ago to the geometers of ancient Greece, who began to develop a system of geometry in which the whole body of geometric truths known to them was deduced from a comparatively small number of fundamental propositions.”
– A. I. Fetisov (Proof in Geometry, 1963)
"I believe: Anything at all that can be the object of scientific thought becomes dependent on the axiomatic method, and thereby indirectly on mathematics, as soon as it is ripe for the formation of a theory."
– David Hilbert (Axiomatisches Denken, 1918)