In mathematics, the Gel'fond-Schneider theorem is the following statement, originally proved by Aleksandr Gelfond :
- If α is an algebraic number (with
and 
), and β is an irrational algebraic number, then αβ is a transcendental number.
This statement implies that 
(the Gelfond-Schneider constant) and 
(see nonconstructive proof) are transcendental numbers.
The Gelfond-Schneider theorem is a partial answer to Hilbert's seventh problem.
