Chapters from Gel's Unfinished Book on Foundational Research in Mathematics (Hardcover) (ISBN-13: 9783030971335)

Viennese logician Kurt Gel (1906-1978) became world-famous overnight with his incompleteness theorems of 1931. The first one states the impossibility to represent all of mathematics in one closed system, the second that there is no ultimate guarantee that such systems could not lead to contradictions. Soon after the publication of Gel's sensational article, he was invited to write, together with Arend Heyting, a concise book about the status of foundational research in mathematics. With Gel prolonging the delivery of his part, Heyting lost patience and published his part in 1934. It has been generally believed that Gel had made little headway with his chapters. A search in the Gel papers showed the contrary to be the case: he had meticulously listed well over a hundred works to study and had practically finished two chapters in his Gabelsberger shorthand, and outlined a third.

Jan von Plato is professor of philosophy at the University of Helsinki. His books include Saved From the Cellar (Springer, 2017), Can Mathematics Be Proved Consistent? (Springer, 2020) and Kurt Gel: The Princeton Lectures on Intuitionism (Edited by Maria H舂een-Anttila and Jan von Plato, Springer 2021).