# Gelfond's theorem

Gelfond's theorem, also known as the Gelfond-Schneider theorem, asserts that *a ^{b}* is a transcendental
number if (1)

*a*is an algebraic number and not equal to either 0 or 1, and (2)

*b*is algebraic and also an irrational number. Gelfond's theorem enables the seventh of David Hilbert's famous problems to be solved.