''Grundlagen der Mathematik'' (English: ''Foundations of Mathematics'') is a two-volume work by
David Hilbert
David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician, one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many a ...
and
Paul Bernays
Paul Isaac Bernays (17 October 1888 – 18 September 1977) was a Swiss mathematician who made significant contributions to mathematical logic, axiomatic set theory, and the philosophy of mathematics. He was an assistant and close collaborator of ...
. Originally published in 1934 and 1939, it presents
fundamental mathematical ideas and introduced
second-order arithmetic
In mathematical logic, second-order arithmetic is a collection of axiomatic systems that formalize the natural numbers and their subsets. It is an alternative to axiomatic set theory as a foundation for much, but not all, of mathematics.
A precurs ...
.
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.
*Th
Hilbert Bernays Projectis producing an English translation.
See also
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Hilbert–Bernays paradox
References
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External links
Hilbert Bernays Projectwhich aims to produce an English translation of ''Grundlagen der Mathematik''.
{{Authority control
1934 non-fiction books
1939 non-fiction books
Mathematical logic
Mathematics books
Logic books