| Thirty Five Years of Automating Mathematics 2003 Edition Contributor(s): Kamareddine, F. D. (Editor) |
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ISBN: 1402016565 ISBN-13: 9781402016561 Publisher: Springer OUR PRICE: $104.49 Product Type: Hardcover - Other Formats Published: November 2003 Annotation: N.G. de Bruijn was a well established mathematician before deciding in 1967 at the age of 49 to work on a new direction related to Automating Mathematics. In the 1960s he became fascinated by the new computer technology and decided to start the Automath project where he could check, with the help of the computer, the correctness of books on mathematics. Through his work on Automath de Bruijn started a revolution in using the computer for verification, and since, we have seen more and more proof-checking and theorem-proving systems. Automath was written in Algol 60 and implemented on the primitive computers of the sixties. Thirty years on, both technology and theory have evolved a lot leading to impressive new directions in using the computer for manipulating and checking mathematics. This volume is a collection of papers with a personal flavour. It consists of 11 articles which propose interesting variations to or examples of mechanising mathematics and illustrate differ developments in symbolic computation in the past 35 years. The first paper is by de Bruijn himself where he uses his experience of automating mathematics to reason about the human mind. After that a number of intriguing articles have been contributed by amongst others Henk Barendregt, who proposes a mathematical proof language between informal and formalised mathematics which helps make proof assistants more user friendly, and Robert Constable, explaining how Automath's telescopes, books and definitions compare to recent developments in computational type theory made by his Nuprl group. The volume further includes a strong argumentation by Arnon Avron that for automated reasoning, there is an interesting logic, somewhere strictly between first and second order logic, determined essentially by an analysis of transitive closure, yielding induction; and Murdoch Gabbay presenting an interesting generalisation of Fraenkel-Mostowski (FM) set theory within higher-order logic, and applying it to model Milner's p-calculus. |
| Additional Information |
| BISAC Categories: - Mathematics | Logic - Computers | Data Processing - Mathematics | Applied |
| Dewey: 004.015 |
| LCCN: 2003062874 |
| Series: Applied Logic |
| Physical Information: 0.85" H x 6.5" W x 9.7" (1.43 lbs) 320 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: THIRTY FIVE YEARS OF AUTOMATING MATHEMATICS: DEDICATED TO 35 YEARS OF DE BRUIJN'S AUTOMATH N. G. de Bruijn was a well established mathematician before deciding in 1967 at the age of 49 to work on a new direction related to Automating Mathematics. By then, his contributions in mathematics were numerous and extremely influential. His book on advanced asymptotic methods, North- Holland 1958, was a classic and was subsequently turned into a book in the well known Dover book series. His work on combinatorics yielded influential notions and theorems of which we mention the de Bruijn-sequences of 1946 and the de Bruijn-Erdos theorem of 1948. De Bruijn's contributions to mathematics also included his work on generalized function theory, analytic number theory, optimal control, quasicrystals, the mathematical analysis of games and much more. In the 1960s de Bruijn became fascinated by the new computer technology and as a result, decided to start the new AUTOMATH project where he could check, with the help of the computer, the correctness of books of mathematics. In each area that de Bruijn approached, he shed a new light and was known for his originality and for making deep intellectual contributions. And when it came to automating mathematics, he again did it his way and introduced the highly influential AUTOMATH. In the past decade he has also been working on theories of the human brain. |