Timeline for Proofs that require fundamentally new ways of thinking
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 22, 2017 at 20:27 | comment | added | Andrés E. Caicedo | @FawzyHegab Yes, Paul du Bois-Reymond. See here. | |
| Jan 3, 2017 at 18:58 | comment | added | Michael Hardy | @MathsLover : I don't know of any use of such arguments before Cantor; I just wanted to make clear that that's not relevant to this answer. | |
| Jan 3, 2017 at 16:55 | comment | added | FNH | Is there any one who used diagonal arguments before Cantor? | |
| Jul 3, 2013 at 9:28 | comment | added | Alexandre Eremenko | Anyway, this was perhaps the most radical change of the way of thinking in the whole history of mathematics. | |
| Aug 11, 2012 at 21:51 | comment | added | Michael Hardy | @RoySmith : Was Cantor really the one who proposed to encode all of mathematics within set theory? Certainly he developed cardinals and ordinals and lots of theorems about them, and proposed the continuum hypothesis, and applied set theory to trigonometric series, but I'm not sure he was the one who proposed to make everything into set theory. | |
| Dec 13, 2010 at 17:55 | comment | added | roy smith | Cantor's whole idea of casting mathematics in the language of set theory is now so pervasive we don't even think about it. It dominated our subject until the category point of view. So to me these are the two most basic insights, viewing mathematics in terms of sets, and then in terms of maps. Etale topologies are just one example of viewing maps as the basic concept. | |
| Dec 10, 2010 at 3:15 | comment | added | Emerton | While Cantor's argument is amazing, and certainly produces scads, Liouville didn't have to work that hard; his approach is also very natural, and doesn't rely on much more than the pigeon-hole principle. | |
| Dec 9, 2010 at 22:07 | comment | added | Gerry Myerson | I vote yes. Look how hard Liouville had to work to find the first examples of transcendental numbers, and how easy Cantor made it to show that there are scads of them. | |
| Dec 9, 2010 at 17:25 | history | answered | Michael Hardy | CC BY-SA 2.5 |