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ESSAYS IN THE FOUNDATIONS OF MATHEMATICS

2ND ED.

An ambitious but overly abbreviated assemblage of arguments.

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

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DYLAN GOES ELECTRIC!

NEWPORT, SEEGER, DYLAN, AND THE NIGHT THAT SPLIT THE SIXTIES

An enjoyable slice of 20th-century music journalism almost certain to provide something for most readers, no matter one’s...

Music journalist and musician Wald (Talking 'Bout Your Mama: The Dozens, Snaps, and the Deep Roots of Rap, 2014, etc.) focuses on one evening in music history to explain the evolution of contemporary music, especially folk, blues, and rock.

The date of that evening is July 25, 1965, at the Newport Folk Festival, where there was an unbelievably unexpected occurrence: singer/songwriter Bob Dylan, already a living legend in his early 20s, overriding the acoustic music that made him famous in favor of electronically based music, causing reactions ranging from adoration to intense resentment among other musicians, DJs, and record buyers. Dylan has told his own stories (those stories vary because that’s Dylan’s character), and plenty of other music journalists have explored the Dylan phenomenon. What sets Wald's book apart is his laser focus on that one date. The detailed recounting of what did and did not occur on stage and in the audience that night contains contradictory evidence sorted skillfully by the author. He offers a wealth of context; in fact, his account of Dylan's stage appearance does not arrive until 250 pages in. The author cites dozens of sources, well-known and otherwise, but the key storylines, other than Dylan, involve acoustic folk music guru Pete Seeger and the rich history of the Newport festival, a history that had created expectations smashed by Dylan. Furthermore, the appearances on the pages by other musicians—e.g., Joan Baez, the Weaver, Peter, Paul, and Mary, Dave Van Ronk, and Gordon Lightfoot—give the book enough of an expansive feel. Wald's personal knowledge seems encyclopedic, and his endnotes show how he ranged far beyond personal knowledge to produce the book.

An enjoyable slice of 20th-century music journalism almost certain to provide something for most readers, no matter one’s personal feelings about Dylan's music or persona.

Pub Date: July 25, 2015

ISBN: 978-0-06-236668-9

Page Count: 368

Publisher: Dey Street/HarperCollins

Review Posted Online: May 15, 2015

Kirkus Reviews Issue: June 1, 2015

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NUTCRACKER

This is not the Nutcracker sweet, as passed on by Tchaikovsky and Marius Petipa. No, this is the original Hoffmann tale of 1816, in which the froth of Christmas revelry occasionally parts to let the dark underside of childhood fantasies and fears peek through. The boundaries between dream and reality fade, just as Godfather Drosselmeier, the Nutcracker's creator, is seen as alternately sinister and jolly. And Italian artist Roberto Innocenti gives an errily realistic air to Marie's dreams, in richly detailed illustrations touched by a mysterious light. A beautiful version of this classic tale, which will captivate adults and children alike. (Nutcracker; $35.00; Oct. 28, 1996; 136 pp.; 0-15-100227-4)

Pub Date: Oct. 28, 1996

ISBN: 0-15-100227-4

Page Count: 136

Publisher: Harcourt

Review Posted Online: May 19, 2010

Kirkus Reviews Issue: Aug. 15, 1996

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