In 1900 David Hilbert posed his famous collection of problems. The seventh of these, and one of the hardest in Hilbert's estimation, asked about the transcendence of numbers of the form "a""b" where "a" and "b" are algebraic, "a" is not zero or one, and "b" is irrational. In the 1930s Alexander Gelfond and Theodor Schneider proved that all such numbers were indeed transcendental using a non-explicit auxiliary function whose existence was granted by Siegel's lemma. This result, the Gelfond–Schneider theorem, proved the transcendence of numbers such as "e"π and the Gelfond–Schneider constant.