New Advances in Transcendence Theory

by Alan Baker

This is an account of the proceedings of a very successful symposium of Transcendental Number Theory held in Durham in 1986. Most of the leading international specialists were present and the lectures reflected the great advances that have taken place in this area. Indeed, the evolution of transcendence into a fertile theory with numerous and widespread applications has been one of the most exciting developments of modern mathematics. The papers cover all the main branches of the subject, and include not only definitive research but valuable survey articles. The work as a whole is an important contribution to mathematics and will be of considerable influence in the further direction of transcendence theory as well as an authoritative account of its current state.

448 pages, Hardcover

First published October 28, 1988

About the author

Alan Baker was an English mathematician, known for his work on effective methods in Number theory, in particular those arising from transcendence theory. He was awarded the Fields Medal in 1970, at age 31. His academic career started as a student of Harold Davenport, at University College London and later at Cambridge. He was a visiting scholar at the Institute for Advanced Study in the fall of 1970. He is a fellow of Trinity College, Cambridge. His interests were in number theory, transcendence, logarithmic form, effective methods, Diophantine geometry and Diophantine analysis. In 2012 he became a fellow of the American Mathematical Society.

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Reviews

[Mike · Rating 4 out of 5]

This is the proceedings from a symposium on the topic of transcendence theory that was held in 1986 and thus contains a robust and diverse selection of essays on the topic. I see little need in going into great detail on the topic itself, because if you're at all interested in this book, you already understand the general layout of transcendence theory and its import to math. Cantor's cardinality argument and the concepts it spawned and counter-concepts as well as various problems in the global view of transcendence in number theory are explored and overall, it's a very useful volume.