Mathematical Treasure: Grundlagen der Mathematik by Hilbert and Bernays

Author(s):

Frank J. Swetz (Pennsylvania State University)

David Hilbert (1862–1943) and Paul Bernays (1888–1977) were both involved in the 20th-century philosophical controversies concerning the foundations of mathematics. The first volume of their book, Grundlagen der Mathematik, was published in 1934. This work, a milestone in the development of modern logic and metamathematics, provided consistency proofs for several outstanding theorems and introduced the concept of second-order arithmetic.

Title page of Hilbert and Bernays's 1934 Grundlagen der Mathematik, volume 1.

The first two pages of the text:

First text page of Hilbert and Bernays's 1934 Grundlagen der Mathematik, volume 1.

Page 2 of Hilbert and Bernays's 1934 Grundlagen der Mathematik, volume 1.

Excerpts from David Hilbert’s earlier discussion of his ideas, “Die logischen Grundlagen der Mathematik,” Mathematische Annalen 88 (1922): 151–165.

Title page of the 1922 88th volume of Mathematische Annalen.

First page of Hilbert's 1922 article on the logical foundations of mathematics.

Later page of Hilbert's 1922 article on the logical foundations of mathematics.

The first three images were obtained from the Internet Archive’s digitization of the copy owned by the Digital Library of India. Mathematische Annalen may be found in HathiTrust.

Index to Mathematical Treasures

Frank J. Swetz (Pennsylvania State University), "Mathematical Treasure: Grundlagen der Mathematik by Hilbert and Bernays," Convergence (April 2021)

Convergence

Tags:

History of Mathematics