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Results tagged with mathematical-philosophy
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user 3634
Philosophical aspects of logic and set theory; truth status of mathematical axioms; Philosophy of Mathematics; philosophical aspects of mathematics in general; relation of mathematics to philosophy; etc. Consider also posting at http://philosophy.stackexchange.com/, where philosophy-of-mathematics is one of the most popular tags.
115
votes
Nontrivial theorems with trivial proofs
The additivity of expected value is absolutely trivial to prove, but (I think) mind-blowing that it is true.
Also, the fact that (finite) sums/products of vector spaces are isomorphic. Extremely eas …
7
votes
The impact of large cardinals in mathematics
I guess this is relevant to Question 4: In the paper
Implications of large-cardinal principles in homotopical localization. Adv. Math. 197 (2005), no. 1, 120–139. by Casacuberta, Carles; Scevenel …
- 12.5k
58
votes
Can a mathematical definition be wrong?
I was involved in such a case. My thesis advisor (S. Husseini) and his coauthor (E. Fadell)
defined the "category weight" of a cohomology class in a way that allowed them to prove the theorem they wa …