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chonglitoday at 2:02 AM1 replyview on HN

No, they're saying that what is true in mathematics is contingent, not absolute. It all depends on which set of axioms use, what assumptions you make.

The area of a triangle doesn't have 1 unique formula, it has many, depending on the system you use. A triangle in plane geometry has a different area than a triangle in spherical geometry, and different again in hyperbolic geometry.

When you get to studying the geometry of manifolds, you realize the area of a triangle can be any damn thing you want, depending on how you construct the manifold you embed it in.


Replies

cman1444today at 1:03 PM

This is a needless qualifier for the argument at hand.

A proof can just be "assuming these axioms.....the area of a triangle is X"