# Mathematical Digest

### Short Summaries of Articles about Mathematics

in the Popular Press

"Slaves to Logic": Reviews by John Naughton of *The Universal Computer:The Road from Leibniz to Turing* and *Computers Ltd: What They ReallyCan't Do.* *Nature,* 19 April 2001.

Naughton reviews * The Universal Computer: The Road from Leibniz toTuring,* by Martin Davis, and *Computers Ltd: What They Really Can'tDo,* by David Harel. The reviewer summarizes Davis's book as a tracing ofintellectual threads linking Leibniz to Turing, covering the work of GeorgeBoole, Gottlob Frege, Georg Cantor, David Hilbert, and Kurt Gödel. Thereviewer describes Harel's book as an antidote to any illusions that there areno limits to what one can achieve with computer hardware and software. Hestates that the latter book gives an overview of the nature of algorithms andtheir applications and limitations and is accessible to a general audience.

*--- Annette Emerson *