Grundlagen der Mathematik

Short description: Two-volume work by David Hilbert and Paul Bernays

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", 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, 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, archived from the original on 2011-05-17, https://web.archive.org/web/20110517092213/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, archived from the original on 2011-05-17, https://web.archive.org/web/20110517092213/http://www.ags.uni-sb.de/~cp/p/hilbertbernays/goal.htm 
• Hilbert, David; Bernays, Paul (1968), Grundlagen der Mathematik. I, Die Grundlehren der mathematischen Wissenschaften, 40 (2nd ed.), Berlin, New York: Springer-Verlag, ISBN 978-3642868955 
• Grundlagen der Mathematik. II, Die Grundlehren der mathematischen Wissenschaften, 50 (2 ed.), Berlin-New York: Springer-Verlag, 1970, ISBN 978-3642868979 
• Hilbert, David; Bernays, Paul (2011) (in German, English), Grundlagen der Mathematik I — Foundations of Mathematics I, Part A: Prefaces and §§ 1–2 (1st ed.), London: College Publications, ISBN 978-1-84890-033-2, http://www.collegepublications.co.uk/other/?00022 
• Hilbert, David; Bernays, Paul (2013) (in German, English), Grundlagen der Mathematik I — Foundations of Mathematics I, Part B: §§ 3–5 and Deleted Part I of the 1st Edn. (1st ed.), London: College Publications, ISBN 978-1-84890-075-2, http://www.collegepublications.co.uk/other/?00025 

External links

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