Grundlagen der Mathematik (English: Foundations of Mathematics) is a two-volume work by David Hilbert and Paul Bernays. Originally published in 1934 and 1939, it presents fundamental mathematical ideas and introduced second-order arithmetic.

Publication history

• 1934/1939 (Vol. I, II) First German edition, Springer
• 1944 Reprint of first edition by J. W. Edwards, Ann Arbor, Michigan.
• 1968/1970 (Vol. I, II) Second revised German edition, Springer
• 1979/1982 (Vol. I, II) Russian translation of 1968/1970, Nauka Publ., Moscow
• 2001/2003 (Vol. I, II) French translation, L’Harmattan, Paris
• 2011/2013 (Parts A and B of Vol. I, prefaces and sections 1-5) English translation of 1968 and 1934, bilingual with German facsimile on the left-hand sides.
• The Hilbert Bernays Project is producing an English translation.

See also

• Hilbert–Bernays paradox

References

• Sieg, Wilfried; Ravaglia, Mark (2005), "Chapter 77. David Hilbert and Paul Bernays, Grundlagen der Mathematik" (PDF), in Grattan-Guinness, Ivor (ed.), 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, MR 2169816
• Hilbert, David; Bernays, Paul (1934), Grundlagen der Mathematik. I, Die Grundlehren der mathematischen Wissenschaften, vol. 40, Berlin, New York: Springer-Verlag, ISBN 978-3-540-04134-4, JFM 60.0017.02, MR 0237246, archived from the original on 2011-05-17
• Hilbert, David; Bernays, Paul (1939), Grundlagen der Mathematik. II, Die Grundlehren der mathematischen Wissenschaften, vol. 50, Berlin, New York: Springer-Verlag, ISBN 978-3-540-05110-7, JFM 65.0021.02, MR 0272596, archived from the original on 2011-05-17
• Hilbert, David; Bernays, Paul (1968) [1934], Grundlagen der Mathematik. I, Die Grundlehren der mathematischen Wissenschaften, vol. 40 (2nd ed.), Berlin, New York: Springer-Verlag, ISBN 978-3642868955, MR 0237246
• Hilbert, D.; Bernays, Paul (1970), Grundlagen der Mathematik. II, Die Grundlehren der mathematischen Wissenschaften, vol. 50 (2 ed.), Berlin-New York: Springer-Verlag, ISBN 978-3642868979, MR 0272596
• Hilbert, David; Bernays, Paul (2011) [1934/68], Grundlagen der Mathematik I — Foundations of Mathematics I, Part A: Prefaces and §§ 1–2 (in German and English) (1st ed.), London: College Publications, ISBN 978-1-84890-033-2, MR 3027390
• Hilbert, David; Bernays, Paul (2013) [1934/68], Grundlagen der Mathematik I — Foundations of Mathematics I, Part B: §§ 3–5 and Deleted Part I of the 1st Edn. (in German and English) (1st ed.), London: College Publications, ISBN 978-1-84890-075-2

External links

• Hilbert Bernays Project which aims to produce an English translation of Grundlagen der Mathematik.