THE WORK OF ALAN BAKER

The theory of transcendental numbers, initiated by Liouville in 1844, has been enriched greatly in recent years. Among the relevant profound contributions are those of A. Baker, W. M. Schmidt and V. A. Sprindzuk. Their work moves in important directions which contrast with the traditional concentration on the deep problem of finding significant classes of functions assuming transcendental values for all non-zero algebraic values of the independent variable. Among these, Baker's have had the heaviest impact on other problems of mathematics. Perhaps the most significant of these impacts has been the application to diophantine equations. This theory, carrying a history of more than thousand years, was, until the early years of this century, little more than a collection of isolated problems subjected to ingenious ad hoc methods…