Gödel's Proof
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Average rating4.2
15
Ratings5
Average rating4.2
In 1931 Kurt Gödel published his fundamental paper, "On Formally Undecidable Propositions of Principia Mathematica and Related Systems." This revolutionary paper challenged certain basic assumptions underlying much research in mathematics and logic. Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences—perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times." However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject. New York University Press is proud to publish this special edition of one of its bestselling books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.
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A very nice introduction and summary to Gödel's famous Incompleteness Theorem in which he proved any sufficiently complex formal system that can be represented within an arithmetic system has to be in some way incomplete. In short, he demonstrated that within a formal system there are statements that it will be capable of generating that must remain undecidable, as well as the existence of theorems which are true but which cannot be derived from the axiomatic statements of the formal system.
I highly recommend this if you are curious about Gödel's Theorem and have a basic understanding of set theory and formal logic. I think it does a great job taking you through the steps of the theorem and explaining things along the way, as well as explaining why it is important, as it points to the limits of formal systems and to the nature of their meta-statements, which cuts to the quick of mathematics; limiting certain notions about provability in maths all the way down to basic number theory and arithmetic.
