17606 | Axioms reveal the underlying assumptions, and reveal relationships between different areas |
Full Idea: The axiomatic method ....revealed precisely what assumptions underlie each branch [of mathematics] and made possible the comparison and clarification of the relationships of various branches. | |
From: Morris Kline (Mathematical Thought from Ancient to Modern Times [1972], p.1027), quoted by Penelope Maddy - Defending the Axioms 1.3 | |
A reaction: I take this to be the 'fruitfulness' which marks out the discovery of the essence of something. |