High Quality Content by WIKIPEDIA articles! In transcendence theory, a mathematical discipline, Baker`s theorem gives a lower bound for linear combinations of logarithms of algebraic numbers. The result, proved by Alan Baker (1966, 1967a, 1967b), subsumed many earlier results in transcendental number theory and solved a problem posed by Alexander Gelfond nearly fifteen years earlier. Baker used this to prove the transcendence of many numbers, and to derive effective bounds for the solutions of some Diophantine equations, and to solve the problem of finding all imaginary quadratic fields with class number 1.