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155th out of 282 books
—
106 voters
On Formally Undecidable Propositions of Principia Mathematica and Related Systems
First English translation of revolutionary paper (1931) that established that even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will not give rise to contradictions. Introduction by R. B. Braithwaite.
Paperback, 80 pages
Published
April 1st 1992
by Dover Publications
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The greatest achievement in human thought to date, IMHO. Every family ought have a copy on their coffee table. I read this the summer after high school, and have gone back a few times. In less than one hundred pages, that silent madman Gödel will shatter your mind, put it back together with turing tape, and leave you changed forever. Minimal mathematical background is required.
This is the hardest text that I have ever read in my life. The result is revolutionary, and it is worth all the effort. Because of the conceptual density of the book, I needed to read it many times to get acquainted with the notation and to realize indeed how beautiful the proof is: all concepts introduced are so cleverly used that the proof is minimalistic and inevitable and its main result is compelling in its force and implications.
Godel gives one of the most interesting proofs I have seen. The proof itself is hard to read and understand, to say the least. However, the consequences of his proof are incredible.
I totally understood this book and I am not lying at all.
Although the proof suffers from old and somewhat clunky notation, the beauty of Godel's numbering still manages to shine through. A work of massive historical value, and well introduced as well.
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