G.J. Chaitin. *The Unknowable, *Springer-Verlag, Singapore,
July 1999. x + 122 pp. ISBN: 981-4021-72-5, US$29.00 hardcover.

This essential companion volume to Chaitin's highly successful ``The Limits of Mathematics,'' also published by Springer, gives a brilliant historical survey of the work this century on the foundations of mathematics, in which the author was a major participant. ``The Unknowable'' is a very readable and concrete introduction to Chaitin's ideas, and it includes a detailed explanation of the programming language used by Chaitin in both volumes. It will enable computer users to interact with the author's proofs and discover for themselves how they work. The software for ``The Unknowable'' can be downloaded from the author's Web site.

``Greg Chaitin's new book, `The Unknowable,' is a welcome addition to his oeuvre. In it he manages to bring his amazingly seminal insights to the attention of a much larger audience and to place them into historical context. His work has deserved such treatment for a long time.'' ---John Allen PAULOS, author of ``Once Upon a Number'' .

`'A `prequel' to `The Limits of Mathematics;' introduces metamathematical concepts from Cantor, Hilbert, Godel, Turing and the author's algorithmic information theory. Written in a very straight-forward manner, Chaitin's goal with `The Unknowable' is to describe the simple ideas at the core of undecidability. He does an admirable job.'' ---Michael D. SOFKA, Rensselaer Polytechnic Institute .

`` `The Limits of Mathematics' contains unconventional, new, and challenging reading at all levels, laymen and experts alike, the only prerequisite being the willingness to question and, if necessary, abandon long-held beliefs and prejudices.''---Karl SVOZIL, ``Complexity'' magazine.

``[`The Limits of Mathematics'] is a book that leaves the reader with the feeling of having witnessed one of those rare events: a good lecture.''---Vladimir TASIC, ACM SIGACT News.

NEW! The LISP interpreter for this book is now available as a Java applet! To try it, click here.

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