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Or does it...? Case in point, the fifth axiom of geometry, attributed to Euclid, that through a point there is exactly one line parallel to a given line has bee
by mitko 7y ago
Or does it...? Case in point, the fifth axiom of geometry, attributed to Euclid, that through a point there is exactly one line parallel to a given line has been shown to be unprovable, and Lobachevski and Rieman have built alternative geometric theories assuming that axiom wrong.
I find it hard to believe that Math is that different from physics or other sciences in its robustness.
Some advantages that math has had over other sciences is low resource consumption (pen and paper), easier reproducibility(thinking), and it has gotten a long head start of 2-3 thousand years.
- doubleunplussed 7y agoAxioms shouldn't be provable (other than from themselves) - if the fifth axiom of geometry had turned out to be provable from something else, then it would be have just been renamed a theorem instead of an axiom.
- fao_ 7y agoThat's the wrong way to think about it, I think. It's more correct to think of axioms as being preconditions. We say, "Here is what happens if these things are true", and then specify what happens, but that doesn't deprive us from independently checking whether those conditions are true. Just because something has been proven does not stop it from being an axiom. It's contextural.