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Mathematical Digest

Short Summaries of Articles about Mathematics
in the Popular Press

"The Sheer Logic of IT": Review of The Universal Computer: The Road fromLeibniz to Turing, by Martin Davis. Reviewed by Christos Papadimitriou. AmericanScientist, March-April 2001, pages 168-171.

This book traces the origins of modern computers back to Gottfried WilhelmLeibniz, who is best known for his development of the calculus (simultaneouslywith Isaac Newton). Leibniz, the reviewer writes, ``dreamed about reducinghuman reasoning to a purely mechanical and symbolic task.'' The book arguesthat what paved the road to computers, starting with this 17th century dreamand leading to the ``universal Turing machine,'' was the development of themathematical field of logic. The reviewer does not quite agree that logicplayed such a big role, arguing that two of the key developers, Alan Turing andJohn von Neumann, were not logicians. Nevertheless, this admiring and positivereview states that this subject ``could not have found a more eloquent andworthy chronicler.''

--- Allyn Jackson

American Mathematical Society