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Grundlagen der Mathematik (foundations of mathematics) is a 2-volume work by David Hilbert and Paul Bernays describing Hilbert's approach to the foundations of mathematics. It introduced second order arithmetic. Publication history 1934-1939 First German edition 1944 Reprint of first edition 1968-1970 Second German edition 1979 Russian translation 2001 French translation The Hilbert Bernays project starts to produce an English translation. References Sieg, Wilfried; Ravaglia, Mark (2005), "Chapter 77. David Hilbert and Paul Bernays, Grundlagen der Mathematik", in Grattan-Guinness, Ivor, Landmark writings in western mathematics 1640--1940, Elsevier B. V., Amsterdam, pp. 981–99, doi:10.1016/B978-044450871-3/50158-3, ISBN 978-0-444-50871-3, MR2169816, http://www.hss.cmu.edu/philosophy/techreports/154_Sieg.pdf  Hilbert, David; Bernays, Paul (1934), Grundlagen der Mathematik. I, Die Grundlehren der mathematischen Wissenschaften, 40, Berlin, New York: Springer-Verlag, ISBN 978-3-540-04134-4, JFM 60.0017.02, MR0237246, http://www.ags.uni-sb.de/~cp/p/hilbertbernays/goal.htm  Hilbert, David; Bernays, Paul (1939), Grundlagen der Mathematik. II, Die Grundlehren der mathematischen Wissenschaften, 50, Berlin, New York: Springer-Verlag, ISBN 978-3-540-05110-7, JFM 65.0021.02, MR0272596, http://www.ags.uni-sb.de/~cp/p/hilbertbernays/goal.htm  Hilbert, David; Bernays, Paul (1968) [1934], Grundlagen der Mathematik. I, Die Grundlehren der mathematischen Wissenschaften, 40 (2nd ed.), Berlin, New York: Springer-Verlag, MR0237246  Hilbert, David; Bernays, Paul (1970) [1939] (in German), Grundlagen der Mathematik. II, Die Grundlehren der mathematischen Wissenschaften, 50 (2nd ed.), Berlin, New York: Springer-Verlag, ISBN 978-3-540-05110-7, MR0272596  External links Hilbert Bernays Project which aims to produce an English translation of Grundlagen der Mathematik.