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The Incomplete Gödel Gregory H. Moore Incompleteness: The Proof and Paradox of Kurt Gödel. Rebecca Goldstein. 296 pp. W. W. Norton, 2005. $22.95.A World Without Time: The Forgotten Legacy of Gödel and Einstein. Palle Yourgrau. x + 210 pp. Basic Books, 2005. $24.Such eminent 20th-century physicists as Albert Einstein, Niels Bohr and Werner Heisenberg are well known to almost all scientists, whether or not they happen to be physicists. Yet most scientists are unfamiliar with eminent mathematicians from the same period, such as David Hilbert (Germany) and Oswald Veblen (United States). A rare exception is John von Neumann (Hungary...

GÖDEL AND THE NATURE OF MATHEMATICAL TRUTH II [7.27.05]A Talk with Verena Huber-Dyson I doubt that pure philosophical discourse can get us anywhere. Maybe phenomenological narrative backed by psychological and anthropological investigations can shed some light on the nature of Mathematical Truth. As to Beauty in mathematics and the sciences, here speaks Sophocles' eyewitness in Antigone: "..... Why should I make it soft for you with tales to prove myself a liar? Truth is Right." Princeton, 1950sEinstein & Gödel Photo by Oskar Morgenstern, Institute of Advanced Study Archives A true Realist, a true Platonist will not stoop to choose...

Gödel mistrusted our ability to communicate. Natural language, he thought, was imprecise, and we usually don't understand each other. Gödel wanted to prove a mathematical theorem that would have all the precision of mathematics—the only language with any claims to precision—but with the sweep of philosophy. He wanted a mathematical theorem that would speak to the issues of meta-mathematics. And two extraordinary things happened. One is that he actually did produce such a theorem. The other is that it was interpreted by the jazzier parts of the intellectual culture as saying, philosophically exactly the opposite of what he had...

February 14, 2005CONNECTIONSTruth, Incompleteness and the Gödelian Way By EDWARD ROTHSTEIN John Patrick NaughtonRebecca Goldstein's new book is about the mathematician Kurt Gödel. elativity. Incompleteness. Uncertainty. Is there a more powerful modern Trinity? These reigning deities proclaim humanity's inability to thoroughly explain the world. They have been the touchstones of modernity, their presence an unwelcome burden at first, and later, in the name of postmodernism, welcome company.Their rule has also been affirmed by their once-sworn enemy: science. Three major discoveries in the 20th century even took on their names. Albert Einstein's famous Theory (Relativity), Kurt Gödel's famous Theorem (Incompleteness)...