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Mathematics: A Concise History and Philosophy (Undergraduate Texts in Mathematics), by W.S. Anglin
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This is a concise introductory textbook for a one-semester (40-class) course in the history and philosophy of mathematics. It is written for mathemat ics majors, philosophy students, history of science students, and (future) secondary school mathematics teachers. The only prerequisite is a solid command of precalculus mathematics. On the one hand, this book is designed to help mathematics majors ac quire a philosophical and cultural understanding of their subject by means of doing actual mathematical problems from different eras. On the other hand, it is designed to help philosophy, history, and education students come to a deeper understanding of the mathematical side of culture by means of writing short essays. The way I myself teach the material, stu dents are given a choice between mathematical assignments, and more his torical or philosophical assignments. (Some sample assignments and tests are found in an appendix to this book. ) This book differs from standard textbooks in several ways. First, it is shorter, and thus more accessible to students who have trouble coping with vast amounts of reading. Second, there are many detailed explanations of the important mathematical procedures actually used by famous mathe maticians, giving more mathematically talented students a greater oppor tunity to learn the history and philosophy by way of problem solving.
- Sales Rank: #2539008 in Books
- Published on: 1996-04-04
- Original language: English
- Number of items: 1
- Dimensions: 9.21" h x .75" w x 6.14" l, 1.19 pounds
- Binding: Hardcover
- 261 pages
Review
"...The book is well written and will help those who look for a deeper understanding of mathematical culture." -- MATHEMATICAL REVIEWS
Most helpful customer reviews
9 of 12 people found the following review helpful.
disappointing
By A Customer
Unfortunately, the text is liberally sprinkled
with personal conjecture which makes it difficult
to tell where opinion ends and history begins.
Additionally, the abbreviated format often leads
to shallow treatment of historically importatnt
topics (e.g. Zeno's paradoxes).
10 of 11 people found the following review helpful.
Worthless
By Viktor Blasjo
This book is utterly worthless in every conceivable way. It is a mystery to me why Springer have brought disgrace upon themselves by publishing this inept drivel. A complete account of Anglin's incompetence would require a review as thick as the book itself, but hopefully a few deterring examples will suffice.
First, there are many blatant factual errors, e.g.:
"There were five planets (or so Kepler thought) and five regular polyhedra. This could not be an accident!" (p. 158)
Since Kepler's work on Mars, Jupiter and Saturn are mentioned on the same page, one wonders whether it is Mercury, Venus or the Earth that Anglin imagines Kepler to have been ignorant of.
Other statements cannot even be called false since they are such ludicrous nonsense, e.g.:
"Just as many people before Lobachevsky thought that Euclid's parallel postulate was a kind of sacred truth, so many people before Hamilton thought that the law of commutativity for multiplication was ineluctable. For us it is a commonplace that this law need not hold, since we have a ready example of noncommutativity in matrix multiplication." (p. 195)
The notion that there is some sort of "law" out there about commutativity of multiplication that may or may not hold is a very childish misconception. Whether we call certain operations with matrices and quaternions "multiplication" or not is purely a matter of convention. Thus the alleged "law" that "many people" allegedly held for "ineluctable" has no meaning whatsoever other than as a thoroughly inconsequential claim about naming conventions. Anglin's stupidity is particularly disturbing in light of his immodest description of his own book as offering "a deep penetration into the key mathematical and philosophical aspects of the history of mathematics", "giving the student an opportunity to come to a full and consistent knowledge" (p. viii).
Let us give another example of what Anglin considers to be "a deep penetration" into philosophical issues. We read that "there are various objections to formalism," e.g. that "formalism offers no guarantee that the games of mathematics are consistent." Now, presumably in order to "give the student an opportunity to come to a full and consistent knowledge," Anglin professes to offer the other side of the coin: "the formalist can reply [that] although some of the games of mathematics are indeed inconsistent, and hence trivial, others are not" (pp. 218-219). It is not clear in what sense Anglin fancies the assertion that mathematics is consistent to be a "reply" to the challenge to prove as much.
Finally, the book is full of unsubstantiated revisionist history motivated by unabashed Christian propaganda ("God" is the entry in the index with the most references by far; more, in fact, than Euclid, Archimedes, Newton and Riemann combined), e.g.:
"Most of the mathematicians at the Academy and the Museum rejected the new truths [sic] of Christ's revelation. This is unfortunate because ... if the mathematicians had joined the Christians, the Dark Ages would have been brightened by a dialogue between reason and faith. As it was, this dialogue was postponed to the later Middle Ages, when thinkers like Thomas Aquinas (1225-1275) advanced philosophies that were influenced as much by the Elements as by the Bible." (p. 111)
What a loss for mathematics that we had to wait so many centuries for the great geometer Aquinas!
8 of 9 people found the following review helpful.
Trite; filled with unnecessary religious hot air
By Democritus
This is a simplistic and shallow book. Proof if any is needed that relgious dogma (and the authors desire to spread it ... even in a maths book!) poisons the mind. The authors frequent attempts to bring god into the picture are unsubtle, (mostly) irrelevant and unbelievably crass. I am disappointed in Springer; how on earth did they allow this to be published?
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