I continue with the recent posts about mathematics, which so far have been as follows.
- “What Mathematics Is”: As distinct from the natural sciences, mathematics is the science whose findings are proved by deduction. I say this myself, and I find it at least implicit in an address by Euphemia Lofton Haynes.
- “More of What It Is”: Some mathematicians do not distinguish mathematics from physics.
- “Knottedness”: Topologically speaking, there is a sphere whose outside is not that of a sphere. The example is Alexander’s Horned Sphere, but it cannot be constructed physically.
- “Why It Works”: Why there can be such a thing as the horned sphere.
When I first drafted the first post above, I said a lot more than I eventually posted. I saved it for later, and later is starting to come now.
Polytropy 