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The Proof and Paradox of Kurt Gödel

A-IncompletenessIn 1932 the Austrian-born logician Kurt Gödel (1906-1978) articulated one of modernity’s greatest concepts: that no formal mathematical system could prove every mathematical truth. Simply put, some things you just can’t prove, even if you know they’re true. In this biography of a man and a theory, MacArthur Fellow, philosopher, and novelist Goldstein places Gödel’s famous incompleteness theorem within the context of his life: Vienna between the wars, the positivists and postmodernists of the 1940s, his days at Princeton and friendship with Albert Einstein, his never-ending search for logic, and his paranoid delusions. Despite his tortured end, Gödel’s elegant proof profoundly influenced modern thought.
Norton. 296 pages. $22.95. ISBN: 0393051692

NY Times Book Review 4 of 5 Stars
"Gödel’s Platonism inspired him to deeds as daring as any knight’s: he proved his famous incompleteness theorem for its sake. … A biography with two focuses—a man and an idea—Incompleteness unfolds its surprisingly accessible story with dignity, tenderness and awe." Polly Shulman

New Yorker 4 of 5 Stars
"… enthralling intellectual biography. … Gödel’s strategy—one of ‘heart-stopping beauty,’ as Goldstein justly observes—was to use logic against itself." Jim Holt

Boston Globe 3.5 of 5 Stars
"The irony here is that Gödel’s celebrated theorems were and continue to be hijacked by the very thinkers to whom he was diametrically opposed. Thus the Austrian exile from Nazi Germany was doubly exiled, and his isolation and ultimate descent into delusion become more poignant." Anthony Doerr 3.5 of 5 Stars
"Goldstein’s Incompleteness is both an eminently lucid explanation of Gödel’s theorem and its implications, and a full-blooded defense of it from those who would claim it for the cause of PoMo relativism. … It’s a challenging book, nevertheless, because of its focus on abstract concepts, but it doesn’t require specialized knowledge and it’s never gratuitously murky." Laura Miller

San Francisco Chronicle 3.5 of 5 Stars
"Out of this unpromising but irresistible material, the philosophical novelist Rebecca Goldstein has fashioned a deeply confounding book—brainbustingly hard in some stretches, beguilingly empathic in others. … To Goldstein’s enduring credit, and despite what she aptly calls her subject’s ‘opacity,’ we come away from Incompleteness with a sense of Gödel both at his most brilliant and, later, at his most neurotic." David Kipen

Critical Summary

Gödel, according to Goldstein (who met him once at a garden party at Princeton), fit the paradox of the title, from his personality to his philosophy. In this volume of Norton’s new Great Discoveries series, Goldstein rethinks Gödel’s theories. She claims that he drew on Plato’s idea of a transcendent mathematical reality outside the realm of human logic and argued, contrary to the Postmodernists, that an objective certainty underlies everything outside human thought. Critics agree that Goldstein tells her subject’s story in clear, empathic prose, though she’s better at describing than explaining Gödel’s theorem to the lay reader. Nevertheless, her rich contextual history will engage readers interested in this important subject—especially those who think they can prove anything.

Supplemental Reading

Gödel, Escher, Bach An Eternal Golden Braid | Douglas R. Hofstadter (1979): Award Star Pulitzer Prize. Hofstadter explores the music of Bach, artwork of Escher, and mathematics of Gödel as fodder for a philosophical meditation on human creativity, consciousness, AI, self, and reality.