By W.S. Anglin

ISBN-10: 0387942807

ISBN-13: 9780387942803

This booklet is totally valueless in each achievable method. it's a secret to me why Springer have introduced shame upon themselves by means of publishing this inept drivel. a whole account of Anglin's incompetence will require a assessment as thick because the ebook itself, yet with a bit of luck a number of deterring examples will suffice.

First, there are lots of blatant authentic error, e.g.:

"There have been 5 planets (or so Kepler notion) and 5 standard polyhedra. this couldn't be an accident!" (p. 158)

Since Kepler's paintings on Mars, Jupiter and Saturn are pointed out at the comparable web page, one wonders if it is Mercury, Venus or the Earth that Anglin imagines Kepler to were ignorant of.

Other statements can't also be referred to as fake for the reason that they're such ludicrous nonsense, e.g.:

"Just as many of us earlier than Lobachevsky proposal that Euclid's parallel postulate was once a type of sacred fact, such a lot of humans earlier than Hamilton notion that the legislation of commutativity for multiplication was once ineluctable. For us it's a regular that this legislation don't need to carry, seeing that we've a prepared instance of noncommutativity in matrix multiplication." (p. 195)

The suggestion that there's a few type of "law" in the market approximately commutativity of multiplication which could or would possibly not carry is a really infantile false impression. no matter if we name convinced operations with matrices and quaternions "multiplication" or now not is solely a question of conference. therefore the alleged "law" that "many humans" allegedly held for "ineluctable" has no that means whatever except as a completely inconsequential declare approximately naming conventions. Anglin's stupidity is especially aggravating in gentle of his conceited description of his personal ebook as delivering "a deep penetration into the most important mathematical and philosophical facets of the background of mathematics", "giving the coed a chance to return to a whole and constant wisdom" (p. viii).

Let us supply one other instance of what Anglin considers to be "a deep penetration" into philosophical matters. We learn that "there are quite a few objections to formalism," e.g. that "formalism deals no be sure that the video games of arithmetic are consistent." Now, possibly which will "give the scholar a chance to return to an entire and constant knowledge," Anglin professes to provide the opposite aspect of the coin: "the formalist can answer [that] even if a few of the video games of arithmetic are certainly inconsistent, and therefore trivial, others are usually not" (pp. 218-219). it isn't transparent in what feel Anglin fancies the statement that arithmetic is constant to be a "reply" the the problem to turn out as much.

Finally, the e-book is filled with unsubstantiated revisionist background encouraged through unabashed Christian propaganda ("God" is the access within the index with the main references through a long way; extra, in truth, than Euclid, Archimedes, Newton and Riemann combined), e.g.:

"Most of the mathematicians on the Academy and the Museum rejected the recent truths [sic] of Christ's revelation. this can be unlucky simply because ... if the mathematicians had joined the Christians, the darkish a while might were brightened by means of a discussion among cause and religion. because it used to be, this discussion was once postponed to the later center a while, while thinkers like Thomas Aquinas (1225-1275) complex philosophies that have been prompted as a lot through the weather as by means of the Bible." (p. 111)

What a loss for arithmetic that we needed to wait such a lot of centuries for the good geometer Aquinas!