An ambitious but overly abbreviated assemblage of arguments.

ESSAYS IN THE FOUNDATIONS OF MATHEMATICS

2ND ED.

A collection of short proofs tackling fundamental problems and paradoxes in mathematics. 

Connor bombastically makes it clear that his quarry is the truth, however iconoclastic it might be, and that he has no reverence for the intellectual idols of academic mathematics: “Truth is an outrage; it does not defer to authority.” In that spirit, he challenges some fundamental conventions in modern math: He rejects imaginary numbers and provides what he claims is a disproof of Euler’s famous formula (and uses it to recalculate the speed of light), completes Fermat’s theorem, resolves Cantor’s paradox, and demonstrates the irrationality of pi—all in fewer than 50 pages of terse language and symbol-laden formulae. Obviously, this is a book that’s singularly intended for the mathematically sophisticated. There’s no overriding theme to the essays beyond the author’s ambition, which one can’t help but find impressive. Also, Connor’s command of the subject matter, including the pertinent scholarly literature, is beyond reproach. However, his arguments and proofs are developed so rapidly, and with so little explanation and commentary, that even the most mathematically astute readers will find them hard to parse and not entirely convincing. For example, in a discussion of Cantor’s paradox, the author contends that the notion of a set of all sets is logically impermissible. Not only is this position less than persuasive, given the brevity of its exposition, but he omits any treatment of the paradox’s extraordinary stakes, which, for Cantor, involved humanity’s basic (and errant) intuitions about infinity. Similarly, the author’s jarringly abridged treatment of Euler’s formula—about a page and a half of discussion—glosses over its centrality to complex number theory and trigonometry. In another chapter, Connor provides a solution to a problem that “bedeviled” the philosopher and mathematician Bertrand Russell in his youth, regarding the nature of propositions, but he neither provides a definition of propositions nor discusses why Russell considered it to be such an important problem. Overall, each section reads like an outline for a longer essay that’s yet to be completed. 

An ambitious but overly abbreviated assemblage of arguments. 

Pub Date: June 21, 2018

ISBN: 978-1-4809-2617-2

Page Count: 48

Publisher: Dorrance Publishing Co.

Review Posted Online: Dec. 27, 2018

Did you like this book?

No Comments Yet

Stricter than, say, Bergen Evans or W3 ("disinterested" means impartial — period), Strunk is in the last analysis...

THE ELEMENTS OF STYLE

50TH ANNIVERSARY EDITION

Privately published by Strunk of Cornell in 1918 and revised by his student E. B. White in 1959, that "little book" is back again with more White updatings.

Stricter than, say, Bergen Evans or W3 ("disinterested" means impartial — period), Strunk is in the last analysis (whoops — "A bankrupt expression") a unique guide (which means "without like or equal").

Pub Date: May 15, 1972

ISBN: 0205632645

Page Count: 105

Publisher: Macmillan

Review Posted Online: Oct. 28, 2011

Kirkus Reviews Issue: May 1, 1972

Did you like this book?

WHAT A WONDERFUL WORLD

A LIFETIME OF RECORDINGS

Noted jazz and pop record producer Thiele offers a chatty autobiography. Aided by record-business colleague Golden, Thiele traces his career from his start as a ``pubescent, novice jazz record producer'' in the 1940s through the '50s, when he headed Coral, Dot, and Roulette Records, and the '60s, when he worked for ABC and ran the famous Impulse! jazz label. At Coral, Thiele championed the work of ``hillbilly'' singer Buddy Holly, although the only sessions he produced with Holly were marred by saccharine strings. The producer specialized in more mainstream popsters like the irrepressibly perky Teresa Brewer (who later became his fourth wife) and the bubble-machine muzak-meister Lawrence Welk. At Dot, Thiele was instrumental in recording Jack Kerouac's famous beat- generation ramblings to jazz accompaniment (recordings that Dot's president found ``pornographic''), while also overseeing a steady stream of pop hits. He then moved to the Mafia-controlled Roulette label, where he observed the ``silk-suited, pinky-ringed'' entourage who frequented the label's offices. Incredibly, however, Thiele remembers the famously hard-nosed Morris Levy, who ran the label and was eventually convicted of extortion, as ``one of the kindest, most warm-hearted, and classiest music men I have ever known.'' At ABC/Impulse!, Thiele oversaw the classic recordings of John Coltrane, although he is the first to admit that Coltrane essentially produced his own sessions. Like many producers of the day, Thiele participated in the ownership of publishing rights to some of the songs he recorded; he makes no apology for this practice, which he calls ``entirely appropriate and without any ethical conflicts.'' A pleasant, if not exactly riveting, memoir that will be of most interest to those with a thirst for cocktail-hour stories of the record biz. (25 halftones, not seen)

Pub Date: May 1, 1995

ISBN: 0-19-508629-4

Page Count: 224

Publisher: Oxford Univ.

Review Posted Online: May 20, 2010

Kirkus Reviews Issue: March 1, 1995

Did you like this book?

more