Timeline for Proofs that require fundamentally new ways of thinking
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Dec 19, 2010 at 16:57 | comment | added | Zsbán Ambrus | I'd generalize this answer to include the observation that transfinite induction (or the axiom of choice) can simplify proofs of statements that don't actually require them. This is similar to how probabilistic arguments can sometimes be simpler than constructions. Here's an example statement for which all three kinds of proof exists: there exists a set $ A \subseteq [0,1]^2 $ that is dense everywhere on the unit square [0,1]<sup>2</sup>, but for every x, A contains only finitely many points of form (x, y) or (y, x). | |
| Dec 17, 2010 at 13:21 | comment | added | dvitek | I think that Ax-Grothendieck can be lumped with this in a sort of "unexpected model-theoretic arguments" category. | |
| Dec 13, 2010 at 0:34 | comment | added | Pietro | I'm pretty sure the model-theoretic approach is due to model theorist Abraham Robinson. Of course completeness and decidability of Th(R,+,*,0,1,<) goes back to Tarski. | |
| Dec 11, 2010 at 11:06 | history | answered | Andreas Thom | CC BY-SA 2.5 |