Solving Equations in Integers :
Diophantine Analysis and
Transcendence Theory
by
Professor Alan Baker, FRS, Fields Medallist
Fellow of Trinity College, Cambridge
Professor of Pure Mathematics, University of Cambridge
United Kingdom
29 April 1997
ABSTRACT
Mathematics, in large part, can be said to have originated from the study of
equations in integers. Numerous results have been obtained through the centuries
to resolve particular instances and many great mathematicians, following in the
illustrious footsteps of Fermat, Euler, Gauss and Hilbert, have contributed to the
field. It is only in recent times, however, that a general method, based on
transcendence theory, has been successfully developed in this context. In the
public lecture held on 29 April 1997, Professor Alan Baker, a leading
mathematician in Transcendental Number Theory, surveyed the current state of the
science.