# Book Review: The Universal Computer by Martin Davis

I review this book that traces the history of the ideas behind the computer from Leibniz to Turing.

*The Universal Computer: The road from Leibniz to Turing* by Martin Davis is a fascinating look at the philosophy and logic that underlie all modern computers, such as the one I am typing this article on. It is also a joint biography of seven very smart men: Gottfried Wilhem Leibniz, George Boole, Gottlob Frege, Georg Cantor, David Hilbert, Kurt Gödel and Alan Turing.

Leibniz (1646 – 1716) was a German polymath: Lawyer, diplomat, philospher, mathematician etc. He conceived of the idea of a truly universal computer – one that would operate not just on numbers but on all of human knowledge. His dream was to code all concepts into numbers and then design a computer that would operate on those numbers, so that all human reasoning would be calculation. Clearly, this dream has not been realized. It may never be (my opinion is that it won’t).

George Boole (1815 – 1864) was an English mathematician and logician. He is best known for publishing a book with the modest title “The laws of thought”. This book radically revised and expanded logic, which had been more-or-less locked into being just what Aristotle had thought it should be.

Gottlob Frege (1848 – 1925) was a German mathematician, logician and philosopher. He made major advances in the axiomitization of mathematics, but had the very unpleasant experience of having his major work undermined just as it was going to press, when he received a letter from Bertrand Russell pointing out major flaws in his system.

Georg Cantor (1845 – 1918) was a German mathematician. He invented set theory and was the first person to come up with a sensible way of dealing with the mathematics of infinite numbers.

David Hilbert (1862 – 1943) was another German mathematician. He did fundamental work in many areas of math, but for this book’s purposes is most known for his statement “we must know, we shall know”, expressing his belief that all of mathematics can be known, and for his support of Cantor.

Kurt Gödel (1906 – 1978) was an Austrian (for a change!) mathematician. He proved that Hilbert’s statement was wrong, at least about some mathematical statements. More specifically, he showed that there is no formal mathematical system that is both complete and consistent.

and

Alan Turing (1912 – 1954) was an English logician and mathematician. As the book points out, it is not possible to say that any one person invented the computer. But if you had to pick one person, Turing would probably be the one. In particular, he invented the idea of what became known as a Turing machine, and proved that a simple but infininte tape of paper, with a single head for reading and writing and erasing, could be programmed to do all sorts of things.

What a fascinating group! And Martin Davis does a very good job of summarizing their thoughts and expressing them clearly. I warmly recommend this book to anyone interested in computers and logic.

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