# Mathematical Digest

### Short Summaries of Articles about Mathematicsin 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