By W.S. Anglin
This publication is completely valueless in each achievable approach. it's a secret to me why Springer have introduced shame upon themselves through publishing this inept drivel. an entire account of Anglin's incompetence will require a overview as thick because the ebook itself, yet expectantly a number of deterring examples will suffice.
First, there are numerous blatant authentic error, e.g.:
"There have been 5 planets (or so Kepler inspiration) and 5 commonplace 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 known as fake in view that they're such ludicrous nonsense, e.g.:
"Just as many of us prior to Lobachevsky notion that Euclid's parallel postulate was once one of those sacred fact, such a lot of humans sooner than Hamilton proposal that the legislation of commutativity for multiplication was once ineluctable. For us it's a common that this legislations don't need to carry, in view that we now have a prepared instance of noncommutativity in matrix multiplication." (p. 195)
The inspiration that there's a few kind of "law" in the market approximately commutativity of multiplication which can or would possibly not carry is a truly infantile false impression. even 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 which means whatever except as a completely inconsequential declare approximately naming conventions. Anglin's stupidity is very nerve-racking in mild of his conceited description of his personal e-book as providing "a deep penetration into the major mathematical and philosophical points of the heritage of mathematics", "giving the coed a chance to return to an entire and constant wisdom" (p. viii).
Let us provide 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 make sure that the video games of arithmetic are consistent." Now, most likely so one can "give the coed a chance to return to a whole and constant knowledge," Anglin professes to supply the opposite facet of the coin: "the formalist can answer [that] even if a number of the video games of arithmetic are certainly inconsistent, and for this reason 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 publication is filled with unsubstantiated revisionist heritage influenced via unabashed Christian propaganda ("God" is the access within the index with the main references by means of a long way; extra, in reality, than Euclid, Archimedes, Newton and Riemann combined), e.g.:
"Most of the mathematicians on the Academy and the Museum rejected the hot truths [sic] of Christ's revelation. this is often unlucky simply because ... if the mathematicians had joined the Christians, the darkish a long time may were brightened by means of a discussion among cause and religion. because it used to be, this discussion was once postponed to the later heart a while, while thinkers like Thomas Aquinas (1225-1275) complex philosophies that have been inspired as a lot by way of the weather as via the Bible." (p. 111)
What a loss for arithmetic that we needed to wait such a lot of centuries for the good geometer Aquinas!