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From the Introduction.In 1931 there appeared in a German scientific periodical a relatively short paper with the forbidding title "Uber formal unentscheidbare Satze der Principia Mathematica und verwandter Systeme" ("On Formally Undecidable propositions of Principia Mathematica and Related Systems"). Its author was Kurt Godel, then a young mathematician of 25 at the University of Vienna and since 1938 a permanent member of the Institute for Ad...

Nel 1931 un giovane viennese, Kurt Gödel, diede alle stampe una breve memoria sulle "proposizioni formalmente indecidibili dei Principia mathematica e sistemi affini". Increduli, logici e matematici assistettero al crollo del luminoso edificio hilbertiano, tutto basato sull'onnipotenza del metodo assiomatico. In quelle pagine, infatti, si dimostrava l'incompletezza di un'ampia classe di teorie formali, tra cui l'aritmetica, nonché l'impossibil...

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In 1931, Kurt Godel published his fundamental paper that challenged certain basic assumptions underlying much research in mathematics and logic. Nagel and Newman provide a readable and accessible explanation of the main ideas and broad implications of Godel's discovery.

In 1931 Kurt Godel disrupted some of the fundamental assumptions underlying mathematics and logic with the publication of his revolutionary paper, "On Formally Undecidable Propositions of Principia Mathematica and Related Systems". Ironically, few mathematicians of the time were able to understand the young scholar's complex proof, and the full importance of this work was largely overlooked for many years. Godel was at last recognized by his p...