[2] In 1934, Aleksandr Gelfond and Theodor Schneider independently proved the more general Gelfond–Schneider theorem,[3] which solved the part of Hilbert's seventh problem described below.
The square root of the Gelfond–Schneider constant is the transcendental number This same constant can be used to prove that "an irrational elevated to an irrational power may be rational", even without first proving its transcendence.
In 1919, he gave a lecture on number theory and spoke of three conjectures: the Riemann hypothesis, Fermat's Last Theorem, and the transcendence of 2√2.
He mentioned to the audience that he didn't expect anyone in the hall to live long enough to see a proof of this result.
[6] But the proof of this number's transcendence was published by Kuzmin in 1930,[2] well within Hilbert's own lifetime.