The Universal Computer: The Road from Leibniz to Turing

Martin Davis, a fluent interpreter of mathematics and philosophy, locates the source of this knowledge in the work of the remarkable German thinker G. W. Leibniz, who, among other accomplishments, was a distinguished jurist, mining engineer, and diplomat but found time to invent a contraption called the "Leibniz wheel," a sort of calculator that could carry out the four basic operations of arithmetic. Leibniz subsequently developed a method of calculation called the calculus raciocinator, an innovation his successor George Boole extended by, in Davis's words, "turning logic into algebra." (Boole emerges as a deeply sympathetic character in Davis's pages, rather than as the dry-as-dust figure of other histories. He explained, Davis reports, that he had turned to mathematics because he had so little money as a student to buy books, and mathematics books provided more value for the money because they took so long to work through.) Davis traces the development of this logic, essential to the advent of "thinking machines," through the workshops and studies of such thinkers as Georg Cantor, Kurt Goedel, and Alan Turing, each of whom puzzled out just a little bit more of the workings of the world--and who, in the bargain, made the present possible. --Gregory McNamee

Product Description
One of the world's pioneers in the development of computer science offers a mesmerizing history of computers. Computers are everywhere today--at work, in the bank, in artist's studios, sometimes even in our pockets--yet they remain to many of us objects of irreducible mystery. How can today's computers perform such a bewildering variety of tasks if computing is just glorified arithmetic? The answer, as Martin Davis lucidly illustrates, lies in the fact that computers are essentially engines of logic. Their hardware and software embody concepts developed over centuries by logicians such as Leibniz, Boole, and Godel, culminating in the amazing insights of Alan Turing. The Universal Computer traces the development of these concepts by exploring with captivating detail the lives and work of the geniuses who first formulated them. Readers will come away with a revelatory understanding of how and why computers work and how the algorithms within them came to be.

* He is a brilliant researcher, who made fundamental contributions to areas such as computability (the Davis-Putnam- Robinson theorem, related to Hilbert's 10th problem) and algorithms (the Davis-Putnam algorithm for solving satisfiability problems).

* He is a master expositor (his 1958 book "Computability and Unsolvability" was one of the very first textbooks in its area, yet it is still widely read today despite the many other books written on this subject over the past 42 years).

* He has spent the last twenty years studying the history of logic and computation.

Davis's book is all one would hope for given his qualifications. It is insightful and engaging, and full of fascinating information that is hard to find elsewhere. I cannot imagine a better book on this subject.


What a compelling book!   January 25, 2001
Josh Fisher (Miami, FL)
13 out of 13 found this review helpful

This popular treatment of the development of computing turned out to be a book that I simply couldn't put down. Martin Davis interlaces the lives of the people who laid the groundwork for computing (and what interesting lives they led!) with a very understandable treatment of the technical side of the underpinnings of computing. I've heartily recommended this to my friends--technical minded and not--as book I think they really want to read.


The best popular history of the computer as logic engine   March 19, 2003
Charles Ashbacher (Marion, Iowa United States(cashbacher@yahoo.com))
10 out of 10 found this review helpful

While most of us consider computers to be some special silicon in a white box, they are in fact machines that execute rules in applied logic. For this reason, the history of computing has two tracks. The first is the hardware track, which generally starts with Charles Babbage and progresses through the recent advances in integrated circuits. One chapter of the book traces the historical development of computer hardware, starting with the Jacquard loom and moving up to the modern personal computer. The second is the history of logic that can be mechanically applied, which is the primary focus of this book.
Once again, the mathematics largely predates the applications. It is amazing how mathematicians develop mathematical structures that initially have no applications and then after some time, something appears that requires that form of mathematics. To me, it is nothing sort of amazing that Alan Turing invented an abstract universal computer long before any of the physical counterparts existed. No one has ever been able to substantially improve on his Turing machines and it is widely believed that they cannot be improved. This theme permeates the book and Davis does a very good job in presenting all of the advances in a historical context.
The contributions of Leibniz, Boole, Frege, Cantor, Hilbert, Godel and Turing are all described in detail, and it is clear how one person's work was built using that done by their predecessors. Other people noted include Bertrand Russell, Leopold Kronecker, and Albert Einstein.
This is the best popular history of the development of the computer viewed as a logic engine. I strongly recommend it as a book for courses in the history of mathematics and computing.


Logical roots of computers   March 28, 2002
7 out of 7 found this review helpful

This book traces the contributions of mathematical logicians to the development of modern day computers. Its cast of characters begins with Gottfried Leibnitz in the 17th century, continues with George Boole in the 19th century, Gottlob Frege and David Hilbert straddling the 19th and 20th centuries, and ends with Kurt Goedel, Alan Turing and John von Neumann in the 20th century. The author brings these great scientists to life by describing their works in the context of their lives and times. He shows that despite their exceptional intellects, they often had difficult obstacles to overcome, both in their own frailties as well as in their adversaries.

The book's main theme is that although modern computers were born out of the need to do heavy number crunching during WWII, their foundation is in logic, the very logic by which our own brains work. It tells a compelling story of how the quest for understanding of the very foundations of mathematics led to the development of the machines that we have come to depend on so heavily in our daily lives.

There are a few places where the reading becomes a bit difficult as the author outlines the work of Goedel and Turing in the early part of the 20th century. Nevertheless, this book is quite readable overall and very enjoyable (as soon as I finished reading it the first time, I immediately started reading it again). I recommend it to general reader who would like to know more about the theoretical underpinnings of computers.

The only comment I have is that all of the mathematicians covered were from Germany, England and the United States. I was left wondering if there might be contributors from other countries that were overlooked.


A Fun Read.   September 20, 2003
Jason T (Canada)
7 out of 7 found this review helpful

An entertaining book that will be enjoyed by anyone interested in mathematical logic or computation theory. Davis weaves history, anecdote, and mathematics into an exciting sketch of the major developments in mathematical logic and their role in the development of the computer. He does a commendable job in explaining the mathematics in an accessible fashion, without distorting it by over-simplification. A good book for people new to the field as well as those already familiar with these stories.