Keith Douglas' Web Page

About me Find out who I am and what I do.
My resumé A copy of my resumé and other documentation about my education and work experience for employers and the curious.
Reviews, theses, articles, presentations A collection of papers from my work, categorized and annotated.
Current research projects What I am currently working on, including some non-research material.
Interesting people People professionally "connected" to me in some way.
Interesting organizations Organizations I am "connected" to. (Some rather loosely.)
Intellectual/professional influences Influences on my work, including an organization chart. Here you can also buy many good books on philosophy and other subjects via amazon.com. I have included brief reviews of hundreds of books.
Professional resources Research sources, amazon.com associates programs, etc.
What is the philosophy of computing? A brief introduction to my primary professional interest.
My intellectual heroes A partial list of important people. Limited to the dead.
My educational philosophy As a sometime teacher I've developed one. Includes book resources.

Book Influences - History of Mathematics

Title
Author
Purchase / Enjoy Cover
Comment
A History of Mathematics Boyer, revised by Merzbach As much history of math as one could reasonably get covering the entire history of the field from Egypt all the way to some 20th century developments (including along the way India, China, the Americas - to a little extent - and Islam). Astonishing, and one learns how many theorems are misnamed, if proper credit were due. One is equally amazed at the progress beginning c. 1500. For all that time negative numbers had barely been considered, if at all. About 350 years after we almost have have quaternions! My only complaints about this encyclopedic, though readable, tome are: (1) that it is almost too breezy and requires familiarity with a lot of recent developments to understand older topics. I am not one who opposes "presentism", but sometimes a presentist understanding does make for a more terse presentation. (Amazing how terse and breezy aren't incompatible!) (2) There seem to be a few more typoes than usual, however none seem too crucial.
e: the Story of a Number Maor e is often overshadowed by π, another important mathematical constant. This little book attempts to remedy that with a popular history of this number which does seem to crop up more than one would think. This volume unfortunately requires some varying levels of mathematical sophistication to appreciate fully; some chapters seem to presuppose no more than high school algebra - others it would do to have some knowledge of partial derivatives and other topics from third (or further) semesters of calculus. Nevertheless if one is patient, all is explained in some (but not complete) detail and the genius of Napier and Euler, the two biggest figures in this history, is evident.
Engines of Logic: Mathematicians and the Origin of the Computer Davis A readable (though some mathematical courage is needed) history of logic as pertains to the eventual development of the computer as we know it. Ends more or less with Turing, though as the author points out, there has been further work and connections made. Davis seems to have missed, however, where von Neumann himself cites Turing on the "stored program" concept (which is buried somewhere in his collected works). Other than this omission, this is a good, popular introduction to this somewhat underappreciated history. Davis points out that many computer histories are histories of machines and engineers; his little book is a history of concepts and work which stemmed from ultimately philosophical and foundational questions. This leaves, perhaps, the two other factors in the computing revolution which have yet to be fully told: the role of management and organization of behaviour sorts (Simon, etc.) and, finally, the art and design aspects which culminated (at least in some respects) in 1984.
Journey Through Genius: the great theorems of mathematics Dunham A neat little history of math book, rich with both the math and stories about the mathematicians.
Li, Qi and Shu: An Introduction to Science and Civilization in China Yoke A short introduction to Chinese protoscientific thought. Includes discussions of astronomical instruments, cosmological hypotheses, alchemical treatises, algebra manuals, etc. Also contains some discussion about the influences on traditional China on these subjects from Arabic, Persian and Indian origins. A slight oversight is found in the section on algebra - there is no mention that the Chinese could not have solved the general 10th degree polynominal equation, as the author comes close to implying.
Mathematical Experience Davis A curious book, though packed with interesting stuff. A collection of articles and essays more than a sustained argument. I seem to remember that Dana Scott (at his farewell lecture) didn't like it very much, so be warned.
Numerical Notation: A Comparative History Chrisomalis What it says on the tin, as the saying goes. However, somehow the world seems to have invented numerical notation more than general writing (!) so there are a lot of different systems to talk about. Not only does the author go through what looks like most of the world's systems, but also analyzes the historical development of same, postulates laws of the statics and dynamics of such systems and occaisonally speculates as to the cognitive systems, ideas and functions involved. Particularly interesting in the latter case are large valued Chinese numerals (up to 104096!) and the origin of the zero. The latter might be especially interesting to philosophers, especially if done comparitively: did metaphysics impede or strengthen the acceptance of zero in various places? Chrisomalis does not answer, but encourages careful investigation of the question. While the book is sometimes dry, it is still a fascinating read in the big picture and for some striking details.
The Annotated Turing: A Guided Tour through Alan Turing's Historic Paper on Computability and the Turing Machine Petzold The subtitle of this generally lucid book adequately describes its contents. There are a few overzealous remarks, and as with many popularizations (and this is only a semi- as the author does analyze every line of Turing's epochal, brilliant paper) the final chapters are more speculative than the rest. There is a lot of historical background in the analysis; this book in a way is a lot like my "influences on Turing" paper. (See my papers page.) However, a lot of said analysis is derivative: he makes a lot of use of The Honours Class, the Reid biography of Hilbert, the usual sources for Gödel, and of course Hodges' biography of Turing himself.
The Honors Class: Hilbert's problems and their solvers Yandell Very engaging book about the Hilbert problems and their solvers. I even recommended it to my (relatively mathematically illiterate) mother, because of its brief discussions of the early 20th century/late 19th century German university system.
The Works of Archimedes Heath (ed.) This book is a partial (some semiredundant proofs removed) collection of the mathematical and physical works of Archimedes. Heath adds many (~150 pages) notes, commentary and introduction. Unfortunately this "Rough Draft Printing" edition is pretty shoddy: markings in the original show up on the pages, etc. I know the work is public domain, but really, that ought not to be an excuse.
Why Beauty is Truth: A History of Symmetry Stewart While this book was disappointing in one respect (very little on Emmy Noether) it succeeds in almost every other way. It consists of a history of the mathematics of symmetry (with some move into physics) from the Babylonian solving of quadratic equations to octonions and beyond. It does repeat a few common errors (space is not curved in GR: spacetime is; atom[os] does not mean indivisible, it means "not to be cut") but these are minor compared to the engaging writing style and detail present. (Lagrange was Italian? I never knew ...)

 

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