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Gödel's incompleteness theorem--which showed that any robust mathematical system contains statements that are true yet unprovable within the system--is an anomaly in 20th-century mathematics. Its conclusions are as strange as they are profound, but, unlike other recent theorems of comparable importance, grasping the main steps of the proof requires little more than high school algebra and a bit of patience. Ernest Nagel and James Newman's original text was one of the first (and best) to bring Gödel's ideas to a mass audience. With brevity and clarity, the volume described the historical context that made Gödel's theorem so paradigm-shattering. Where the first edition fell down, however, was in the guts of the proof itself; the brevity that served so well in defining the problem made their rendering of Gödel's solution so dense as to be nearly indigestible.
This reissuance of Nagel and Newman's classic has been vastly improved by the deft editing of Douglas Hofstadter, a protégé of Nagel's and himself a popularizer of Gödel's work. In the second edition, Hofstadter reworks significant sections of the book, clarifying and correcting here, adding necessary detail there. In the few instances in which his writing diverges from the spirit of the original, it is to emphasize the interplay between formal mathematical deduction and meta-mathematical reasoning--a subject explored in greater depth in Hofstadter's other delightful writings. --Clark Williams-Derry
"A little masterpiece of exegesis. Nature An excellent non-technical account of the substance of Gdels celebrated paper. Bulletin of the American Mathematical SocietySee all Product Description
In 100 lucid and highly readable pages, presents the most important ideas of modern logic: axiomatisation (Euclid), formalization (Hilbert), metamathematical argumentation,... Read morePublished on May 18 2004 by Stavros Macrakis
The greatest merit of this book is its ability to take a rather arcaic and complicated proof and successfully present it, in a concise and understandable manner, to a broad... Read morePublished on Jan. 3 2004 by C. Goss
I read Godel's paper in grad school. I wish I had read this first, because it lays out the structure of the argument clearly. Read morePublished on May 1 2003 by Ken Braithwaite
This is a fantastic book that makes the important discoveries of Godel accessible to all interested readers. Read morePublished on Jan. 13 2003 by rationalist
The beauty of this book is that Godel's ideas and proof is explained with a minimum of symbolic strings. Read morePublished on Sept. 16 2002
The beauty of this book is that Godel's ideas and proof is explained with a minimum of symbolic strings. Read morePublished on Sept. 16 2002 by Mark Twain
Gödel's brilliant incompleteness theorem is astounding. He proves that every system, even that of the arithmetic integers, is inconsistent, and, essentially, he shows us that... Read morePublished on Sept. 5 2002 by Luc REYNAERT
As the reviewer below, I too am a medical student/mathematican. I consider myself the foremost amature number theorist since Fermat and can read and translate ANY mathematical or... Read morePublished on May 4 2002 by murino man