where all four unknowns are algebraic, the αs being neither zero nor one and the βs being irrational. Finding similar lower bounds for the sum of three or more logarithms had eluded Gelfond, though. The proof of Baker's theorem contained such bounds, solving Gauss' class number problem for class number one in the process. This work won Baker the Fields medal for its uses in solving Diophantine equations. From a purely transcendental number theoretic viewpoint, Baker had proved that if α1, ..., α"n" are algebraic numbers, none of them zero or one, and β1, ..., β"n" are algebraic numbers such that 1, β1, ..., β"n" are linearly independent over the rational numbers, then the number