Table of Contents

Leibniz's Dream. Boole Turns Logic into Algebra. Frege: From Breakthrough to Despair. Cantor: Detour through Infinity. Hilbert to the Rescue. Godel Upsets the Applecart. Turing Conceives of the All-Purpose Computer. Making the First Universal Computers. Beyond Leibniz’s Dream.

About the Author

A distinguished prize-winning logician, Martin Davis has had a long career of more than six decades devoted to the important interface between logic and computer science. Born in New York City, he received his Ph.D. from Princeton University in 1950. He spent thirty years at New York University, where he helped found the computer science department. His expertise, combined with his genuine love of the subject and excellent storytelling, make him the perfect person to tell this story. Professor Davis is currently Professor Emeritus at New York University and now lives with his wife of 66 years in Berkeley, California.

Reviews

"The first edition of this book was one of the first to offer a serious study of the historical connections between logic and modern computing. It situates the development of the first computers within a scientific rather than a technological history: it tells the story of the life and work of a number of well-known logicians and how these established, in retrospect, part of the theoretical foundations of the modern computer. This third edition contains extensions and corrections of the first and second editions, including the addition of an Appendix on Cantor and Kronecker, correcting a dominant historical narrative in which both actors are played out against each other; a discussion of the advances that have been made with so-called deep learning techniques and a further extension of the chapter on Gödel.The book is highly accessible and engaging. It explains several basic mathematical and logical notions in an exceptionally clear and comprehensive manner. These are developed throughout the different stories of the people behind those notions. Moreover, it is against the background of this history of logical ideas, that Martin Davis enters into a more philosophical discussion with respect to advances in AI and so-called deep learning in the final chapter of the book. This book is thus a must-read not just for anyone who is willing to gain a better understanding of some of the basic logical principles behind our contemporary computing devices but also for those scholars who want to engage more deeply with the basic question of the connection between the history of computer science and its relation to logic and foundations of mathematics."—Liesbeth De Mol, Université de Lille"This book about computers is like no other. It is now in a 2018 edition, after a first publication in 2000. The update reflects some recent developments, for example the recent success of champion-beating computer Go playing. But the main purpose of this book is to describe all possible developments — past, present and future. It is about the core property of the computer, that makes it possible for a single machine to switch between Go-playing, facial recognition, displaying webpages and searching for extra-terrestrial life — and infinitely more. This is the universal nature of the computer, which every application now takes for granted.Thought rooted far back in the scientific revolution, the book focuses on the extraordinary discoveries of the 1930s and 1940s, when the concept of the universal machine emerged. This discovery, arising out of the purest research in mathematics, might be compared with the elucidation of atomic fission and DNA structure — dependent on highly non-obvious detail yet transforming the world. The Universal Computer springs from one of the very few people who after a long life can speak first-hand of how this transforming concept arose, with an authoritative account of the essential features. Martin Davis was himself a major contributor to the mathematical theory of computing and in at the beginning of the first electronic computers. For the more specialist reader, this book offers a pugnacious assertion of a computational philosophy of mind, and makes a contribution to the history of science which asserts the primacy of mathematical and logical ideas over engineering implementation. The more general reader will find Martin Davis an expert story-teller. He conveys the magic of the pioneer period, and he places it within a broad picture of human history and of its individual contributors. Foremost is the fascinating figure of Alan Turing, who first defined the universal machine concept, but who also set out the prospects for Artificial Intelligence. As Martin Davis mentions, Turing’s discussion of the potential of computers for chess-playing began in 1941, and the deep questions about mind and machine, as are so often argued about today, were well aired from the start. Computers are now cheaper and faster than the pioneers could dream of. They are physically smaller, yet huger in storage capacity. But their underlying principle has not changed. Unlike other computer books, this one will not become out of date."—Dr Andrew Hodges, author of Alan Turing: The Enigma, Mathematical Institute, University of Oxford.Praise for the previous edition:"Next year, Martin Davis will turn 90 years old. A legendary figure in mathematical logic, he is best known for resolving Hilbert’s Tenth Problem, together with Yuri Matiyasevich, Hilary Putnam, and Julia Robinson. Davis also did some of the world’s first computer programming, working in the 1950s on the ORDVAC computer, which had a central memory consisting of 40 vacuum tubes. A master expositor, Davis received the AMS Steele Prize for Exposition as well as the Chauvenet and Ford Prizes of the Mathematical Association of America. His popular book The Universal Computer originally appeared to wide acclaim in 2000 and was re-issued in 2012, in a special edition to honor the centenary of Alan Turing. The tale of how computers developed has been told many times and in many forms—and often with heavy emphasis on the computer as an engineering feat. Davis takes a completely different tack by tracing the origin of computers in developments in logic, starting with the ideas of Leibniz, who, as Davis puts it, "dreamed of machines capable of carrying out calculations, freeing the mind for creative thought." After an opening chapter on "Leibniz’s Dream," Davis discusses the lives and work of Boole, Frege, Cantor, Hilbert, Gödel, and Turing. The book closes with a discussion of the first computers that were built as well as a look towards the future. "When a distinguished expert offers a popular exposition of his subject, we greet the effort with keen anticipation," wrote Brian Blank in a review that appeared in the May 2001 issue of the Notices. "That is all the more true when the writer is as skilled as Martin Davis. It is a pleasure to report that in this case our anticipation is richly rewarded."—Bookshelf, Notices of the American Mathematical Society, 2017"The stories masterfully told in this book underscore the power of ideas and the ‘futility of predicting in advance where they will lead.’ … the structure and presentation of the material make the book an outstanding achievement."—SIGACT News, 2014"In just over two hundred pages, noted logician Davis (emer., New York Univ.) weaves the story, starting with Leibniz, Boole, and Frege, that leads to the universal computer. … One should read this book from cover to cover, and take the time to read the chapter notes. Do not miss Aiken's (1956!) quote in the introduction, and spend time thinking about the brief summary in the epilogue. Libraries that do not own the original edition will definitely want to acquire this book. Summing Up: Highly recommended. All levels/libraries." — CHOICE Magazine, October 2012"Now in a revised edition with added insights concerning Konrad Zuse, the success of the IBM Watson on the game show Jeopardy!, and more, The Universal Computer: The Road from Leibniz to Turing is an extraordinary study of computational pioneers who ultimately transformed the modern world. … highly recommended especially for college library computer science shelves, and an exceptional pick for any reader who is curious about the lives and efforts of great thinkers."—Library Bookwatch, September 2012"I read and enjoyed the first edition. Upon reading the second, I was again impressed. The book remains fresh and compelling. … I recommend this book very highly. It is suitable for a high school or college library."—Richard Wilders, MAA Reviews, September 2012"Anyone who works with computers today, anyone who seeks to look into the electronic future, can profit greatly from reading Martin Davis’s fine ramble through the history of logic and the lives of its pioneers."—John McCarthy, Stanford University"At last, a book about the origin of the computer that goes to the heart of the story: the human struggle for logic and truth. Erudite, gripping, and humane, Martin Davis shows the extraordinary individuals through whom the groundwork of the computer came into being, and the culmination in Alan Turing, whose universal machine now dominates the world economy."—Andrew Hodges, author of Alan Turing: The Enigma"This updated and eminently readable account of the development of computers and computability theory is a well-wrought tribute to the pioneers in those fields, and in particular to Alan Turing on the occasion of the 100th anniversary of his birth."—John W. Dawson, author of Logical Dilemmas: The Life and Work of Kurt Gödel"The author and I are near the same age, and what amazing progress we have seen in more than half a century since our college days! The great pioneers, Alan Turing and John von Neumann, would be truly astonished to see how computers have evolved and how they have invaded nearly every aspect of modern life-for both good and evil. In this centenary of Turing's birth, let us pause to honor their vision and multiple accomplishments and to enjoy the lively, readable and insightful story the author weaves for us in this book."—Dana S. Scott, University Professor Emeritus, Carnegie Mellon University, and ACM Turing Award Winner, 1976

"The first edition of this book was one of the first to offer a serious study of the historical connections between logic and modern computing. It situates the development of the first computers within a scientific rather than a technological history: it tells the story of the life and work of a number of well-known logicians and how these established, in retrospect, part of the theoretical foundations of the modern computer. This third edition contains extensions and corrections of the first and second editions, including the addition of an Appendix on Cantor and Kronecker, correcting a dominant historical narrative in which both actors are played out against each other; a discussion of the advances that have been made with so-called deep learning techniques and a further extension of the chapter on Gödel.The book is highly accessible and engaging. It explains several basic mathematical and logical notions in an exceptionally clear and comprehensive manner. These are developed throughout the different stories of the people behind those notions. Moreover, it is against the background of this history of logical ideas, that Martin Davis enters into a more philosophical discussion with respect to advances in AI and so-called deep learning in the final chapter of the book. This book is thus a must-read not just for anyone who is willing to gain a better understanding of some of the basic logical principles behind our contemporary computing devices but also for those scholars who want to engage more deeply with the basic question of the connection between the history of computer science and its relation to logic and foundations of mathematics."—Liesbeth De Mol, Université de Lille"This book about computers is like no other. It is now in a 2018 edition, after a first publication in 2000. The update reflects some recent developments, for example the recent success of champion-beating computer Go playing. But the main purpose of this book is to describe all possible developments — past, present and future. It is about the core property of the computer, that makes it possible for a single machine to switch between Go-playing, facial recognition, displaying webpages and searching for extra-terrestrial life — and infinitely more. This is the universal nature of the computer, which every application now takes for granted.Thought rooted far back in the scientific revolution, the book focuses on the extraordinary discoveries of the 1930s and 1940s, when the concept of the universal machine emerged. This discovery, arising out of the purest research in mathematics, might be compared with the elucidation of atomic fission and DNA structure — dependent on highly non-obvious detail yet transforming the world. The Universal Computer springs from one of the very few people who after a long life can speak first-hand of how this transforming concept arose, with an authoritative account of the essential features. Martin Davis was himself a major contributor to the mathematical theory of computing and in at the beginning of the first electronic computers. For the more specialist reader, this book offers a pugnacious assertion of a computational philosophy of mind, and makes a contribution to the history of science which asserts the primacy of mathematical and logical ideas over engineering implementation. The more general reader will find Martin Davis an expert story-teller. He conveys the magic of the pioneer period, and he places it within a broad picture of human history and of its individual contributors. Foremost is the fascinating figure of Alan Turing, who first defined the universal machine concept, but who also set out the prospects for Artificial Intelligence. As Martin Davis mentions, Turing’s discussion of the potential of computers for chess-playing began in 1941, and the deep questions about mind and machine, as are so often argued about today, were well aired from the start. Computers are now cheaper and faster than the pioneers could dream of. They are physically smaller, yet huger in storage capacity. But their underlying principle has not changed. Unlike other computer books, this one will not become out of date."—Dr Andrew Hodges, author of Alan Turing: The Enigma, Mathematical Institute, University of Oxford.Praise for the previous edition:"Next year, Martin Davis will turn 90 years old. A legendary figure in mathematical logic, he is best known for resolving Hilbert’s Tenth Problem, together with Yuri Matiyasevich, Hilary Putnam, and Julia Robinson. Davis also did some of the world’s first computer programming, working in the 1950s on the ORDVAC computer, which had a central memory consisting of 40 vacuum tubes. A master expositor, Davis received the AMS Steele Prize for Exposition as well as the Chauvenet and Ford Prizes of the Mathematical Association of America. His popular book The Universal Computer originally appeared to wide acclaim in 2000 and was re-issued in 2012, in a special edition to honor the centenary of Alan Turing. The tale of how computers developed has been told many times and in many forms—and often with heavy emphasis on the computer as an engineering feat. Davis takes a completely different tack by tracing the origin of computers in developments in logic, starting with the ideas of Leibniz, who, as Davis puts it, "dreamed of machines capable of carrying out calculations, freeing the mind for creative thought." After an opening chapter on "Leibniz’s Dream," Davis discusses the lives and work of Boole, Frege, Cantor, Hilbert, Gödel, and Turing. The book closes with a discussion of the first computers that were built as well as a look towards the future. "When a distinguished expert offers a popular exposition of his subject, we greet the effort with keen anticipation," wrote Brian Blank in a review that appeared in the May 2001 issue of the Notices. "That is all the more true when the writer is as skilled as Martin Davis. It is a pleasure to report that in this case our anticipation is richly rewarded."—Bookshelf, Notices of the American Mathematical Society, 2017"The stories masterfully told in this book underscore the power of ideas and the ‘futility of predicting in advance where they will lead.’ … the structure and presentation of the material make the book an outstanding achievement."—SIGACT News, 2014"In just over two hundred pages, noted logician Davis (emer., New York Univ.) weaves the story, starting with Leibniz, Boole, and Frege, that leads to the universal computer. … One should read this book from cover to cover, and take the time to read the chapter notes. Do not miss Aiken's (1956!) quote in the introduction, and spend time thinking about the brief summary in the epilogue. Libraries that do not own the original edition will definitely want to acquire this book. Summing Up: Highly recommended. All levels/libraries." — CHOICE Magazine, October 2012"Now in a revised edition with added insights concerning Konrad Zuse, the success of the IBM Watson on the game show Jeopardy!, and more, The Universal Computer: The Road from Leibniz to Turing is an extraordinary study of computational pioneers who ultimately transformed the modern world. … highly recommended especially for college library computer science shelves, and an exceptional pick for any reader who is curious about the lives and efforts of great thinkers."—Library Bookwatch, September 2012"I read and enjoyed the first edition. Upon reading the second, I was again impressed. The book remains fresh and compelling. … I recommend this book very highly. It is suitable for a high school or college library."—Richard Wilders, MAA Reviews, September 2012"Anyone who works with computers today, anyone who seeks to look into the electronic future, can profit greatly from reading Martin Davis’s fine ramble through the history of logic and the lives of its pioneers."—John McCarthy, Stanford University"At last, a book about the origin of the computer that goes to the heart of the story: the human struggle for logic and truth. Erudite, gripping, and humane, Martin Davis shows the extraordinary individuals through whom the groundwork of the computer came into being, and the culmination in Alan Turing, whose universal machine now dominates the world economy."—Andrew Hodges, author of Alan Turing: The Enigma"This updated and eminently readable account of the development of computers and computability theory is a well-wrought tribute to the pioneers in those fields, and in particular to Alan Turing on the occasion of the 100th anniversary of his birth."—John W. Dawson, author of Logical Dilemmas: The Life and Work of Kurt Gödel"The author and I are near the same age, and what amazing progress we have seen in more than half a century since our college days! The great pioneers, Alan Turing and John von Neumann, would be truly astonished to see how computers have evolved and how they have invaded nearly every aspect of modern life-for both good and evil. In this centenary of Turing's birth, let us pause to honor their vision and multiple accomplishments and to enjoy the lively, readable and insightful story the author weaves for us in this book."—Dana S. Scott, University Professor Emeritus, Carnegie Mellon University, and ACM Turing Award Winner, 1976"This is an excellent book that deserves to be widely read."--Roman Kossak, The Mathematical Intelligencer