From the American Mathematical Society:
"Baker was awarded the Fields Medal for generalizing the Gelfond-Schneider theorem, the theorem that solved Hilbert's seventh problem. The generalization, now known as Baker's theorem, generated new transcendental numbers and gave bounds on how transcendental, and how irrational, certain numbers are. In addition to the Fields Medal, Baker received the Adams Prize from the University of Cambridge, was elected to the Royal Society of London, and was an inaugural Fellow of the AMS. He received his PhD from the University of Cambridge in 1964 under the direction of Harold Davenport, and spent his career at Cambridge but also held many visiting positions at prestigious universities and institutes worldwide."
Fields Medalist, 1970