Timeline for Use of Conjectures to Prove a Theorem
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 24, 2010 at 19:26 | comment | added | Will Jagy | Live and learn. $$ 2^{\sqrt 2} $$ was first proved transcendental by Kuzmin in 1930, so it was a near thing. en.wikipedia.org/wiki/Gelfond%E2%80%93Schneider_constant which also discusses David's example. | |
| Jul 24, 2010 at 19:21 | comment | added | Will Jagy | $$ 2^{\sqrt 2} $$ is transcendental by Gelfond-Schneider. Therefore $$ {\sqrt 2}^{\sqrt 2} = \left( 2^{\frac{1}{2 }} \right)^{\sqrt 2} = \left( 2^{\sqrt 2} \right)^{\frac{1}{2 }} $$ is transcendental. en.wikipedia.org/wiki/Gelfond%E2%80%93Schneider_theorem $$ $$ On this and related topics, I really like "Irrational Numbers" by Ivan Niven, available in paperback from the M.A.A. Gelfond-Schneider and Hermite-Lindemann are proved, history given etc. | |
| Jul 24, 2010 at 12:55 | comment | added | Lennart Meier | But it's cool, anyhow. | |
| Jul 24, 2010 at 7:45 | comment | added | Martin Brandenburg | I don't think that this conjecture is not solved. | |
| Jul 24, 2010 at 3:29 | history | answered | David Spivak | CC BY-SA 2.5 |