Leipzig: Akademische verlagsgesellschaft, 1931. 8vo. pages: -174-198. FIRST EDITION. Original printed back wrapper; front wrapper in facsimile (from the copy owned by Princeton University, with Überreicht vom Verfasser printed on top); small stain (from tape?) on bottom corner of first page. Preserved in a full morocco clamshell case. Item #12852
First edition of the first printing of Gödel's Proof, the single most celebrated result in mathematical logic. This paper, On Formally Undecidable Propositions (Incompleteness Theorem) is of legendary rarity. We were only able to locate one copy at Princeton University. Famed mathematician Kurt Gödel proved two extraordinary theorems. His paper showed that arithmetic was incomplete. In any consistent formal system able to describe simple arithmetic, there are propositions that can be neither proved nor disproved on the basis of the system. Thus a larger system may have to be used to prove consistency, and its consistency assumed; all pretty unsatisfactory.
Accepted by all mathematicians, these propositions have revolutionized mathematics, showing that mathematical truth is more than logic and computation. It helped tear down the notion that there was anything certain about the universe.. According to philosophy professor Rebecca Goldstein, Gödel was an intellectual heir to Plato, whose sense of alienation from the positivists and post-modernists of the 1940's was only ameliorated by his friendship with Einstein. As Goldstein writes, "That his work, like Einstein's, has been interpreted as not only consistent with the revolt against objectivity but also as among its most compelling driving forces is . . . more than a little ironic."
Gödel (1906-1978), an Austrian born philosopher and mathematician, studied at Vienna. He saw much of the development of the positivist school of philosophy and was apparently unconvinced. He investigated the larger logical system put forward by Russell and Whitehead in their Principia mathematica and his resulting paper (above) may well be the most significant event in 20th century mathematics.