[ggm]

Except for the corner cases. So the trivial one is "angles in a triangle add up to 180" which works in a plane but not on the surface of a sphere so navigation has to use more than trivial trigonometry functions for accuracy at scale.

The context is sometimes everything.

[giomasce]

That's not a corner case. Either you defined "triangle" and "angles" to mean a plane triangle and angles, or that is not a theorem. Within the theory you're looking at, the definitions are not part of the context, they are part of the theory itself. So you're not depending on the context.

[ggm]

Like the other response you basically said context is everything. You just prefer to call the context axioms. What is context free here is the arithmetic.

[giomasce]

Why should arithmetic be more or less context free than anything else? It's defined by axioms and definitions as much as the rest.

[_xnmw]

That's not a corner case, that's just more advanced math. No one ever claimed that triangulation on a plane is the same as triangulation on the surface of a sphere.

[ggm]

Like the other response you basically said context is everything. You just prefer to call the context axioms. What is context free here is the arithmetic.

[andrewflnr]

Arithmetic still depends on which ring/field axioms you're using. :) I think you would have to agree, though, that axioms are a much more tractable kind of context than "a whole honking physical situation with atoms and entropy", which I think is the real kernel of the article.