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srn347 comments on Math is Subjunctively Objective - Less Wrong
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How would the world look different on each of those hypotheses? (Can you please taboo "fundamental" and "exists," too?)
You're confusing the map and the territory here. The Pythagorean theorem and pi are both mathematical features that fall out of a particular model of the world, namely Euclidean geometry, which is an inaccurate model for at least two historically major reasons (the Earth not being flat and relativity).
Actually, the pythagorean theorem and pi still apply regardless of what dimension of geometry the world obeys (3-dimensional newtonian physics, 4-dimensional relativistic spacetime, 11-dimensional string theory, etc).
I don't know what you mean by that.
The Pythagorean theorem doesn't apply to curved space, only to flat space (regardless of number of dimension). And pi is the number 3.14159..., which can be defined in ways that have nothing to do with geometry, so I'd put it as "in convex (concave) space, the ratio of a circumference to its diameter is less (greater) than pi", not as "in convex (concave) space, pi is less (greater) than 3.14159...)".