Philosopher and math populizer Berlinski (The Devil’s Delusion: Atheism and Its Scientific Pretensions, 2008, etc.) takes on the challenge of explaining the logical foundation of the elementary operations of arithmetic.
It’s no easy task. Indeed, it was not until the late 19th century that mathematicians were inspired to develop the axioms (unproven assumptions) enabling the development of theorems to prove the legitimacy of all those rules of thumb you learned in high school—e.g., that the product of two negative numbers is positive, or to divide fractions you invert the divisor and multiply. Along the way, mathematicians developed set theory, which showed that the operations possible with numbers could be generalized to define arcane structures called rings or fields. Why bother, Berlinski writes in the introduction, noting that most people dislike math. However, he continues, the reason is because such work has the grandeur of the absolute, of something deep in the human imagination. So readers with an open mind to, say, Peano’s five axioms for the natural numbers, may be putty in the hands of Berlinski. The author examines the world of integers, embracing positive and negative numbers, and then fractions, and he introduces many of the hallowed names of 20th-century mathematicians and logicians with charming asides and literary references. The author also explains the various laws of associativity and commutativity that the numbers obey, as well as the value of proof by induction and how it derives from Peano’s fifth axiom. “New math” for adults this is not. Rather, Berlinski delivers a tour de force by a mathematician who wants the intellectually curious and logically minded student to understand the foundations and beauty of one of the major branches of mathematics.
Pub Date: May 12, 2011
ISBN: 978-0-375-42333-8
Page Count: 240
Publisher: Pantheon
Review Posted Online: March 2, 2011
Kirkus Reviews Issue: March 1, 2011
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
BOOK REVIEW
BOOK REVIEW
An extravaganza in Bemelmans' inimitable vein, but written almost dead pan, with sly, amusing, sometimes biting undertones, breaking through. For Bemelmans was "the man who came to cocktails". And his hostess was Lady Mendl (Elsie de Wolfe), arbiter of American decorating taste over a generation. Lady Mendl was an incredible person,- self-made in proper American tradition on the one hand, for she had been haunted by the poverty of her childhood, and the years of struggle up from its ugliness,- until she became synonymous with the exotic, exquisite, worshipper at beauty's whrine. Bemelmans draws a portrait in extremes, through apt descriptions, through hilarious anecdote, through surprisingly sympathetic and understanding bits of appreciation. The scene shifts from Hollywood to the home she loved the best in Versailles. One meets in passing a vast roster of famous figures of the international and artistic set. And always one feels Bemelmans, slightly offstage, observing, recording, commenting, illustrated.
Pub Date: Feb. 23, 1955
ISBN: 0670717797
Page Count: -
Publisher: Viking
Review Posted Online: Oct. 25, 2011
Kirkus Reviews Issue: Feb. 1, 1955
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