His research centers on diophantine approximations and diophantine equations. Among his work are articles on simultaneous approximation to algebraic numbers, normality of numbers, irregularities of distribution, elementary methods for equations over finite fields, diophantine inequalities for forms of odd degree, linear recurrence sequences. His best known accomplishment is the Subspace Theorem. His awards include the Frank Nelson Cole Prize in Number Theory, Humboldt Research Award, and Austrian Decoration for Science and Art.