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Mathematical Treasure: Hilbert and Bernays in Mathematischen Wissenschaften

Frank J. Swetz (The Pennsylvania State University)

The Grundlehren der mathematischen Wissenschaften (Foundations of Mathematical Knowledge) series was begun in 1920 by Richard Courant (1888-1972) and published by Springer. It was and is intended to present contemporary research findings in textbook form for the benefit of students of higher mathematics. The first 100 volumes were published in German; then, following the Second World War, the series appeared in English. The year 2013 saw the publication of Volume 347 of this series, a book on Poisson structures.

Volume 50 of Mathematischen Wissenschaften contained the second volume of Foundations of Mathematics (1939), by David Hilbert (1862-1943) and Paul Bernays (1888-1977). The first volume 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. Second order arithmetic was a formalization of the system of natural numbers that superseded that established by Giuseppe Peano (1858-1932) in Peano’s Axioms.

Hilbert’s and Bernays’ Table of Contents presented the list of topics covered within the first 375 pages of the book.

The Special Collections staff at the Linderman Library of Lehigh University in Bethlehem, Pennsylvania, is pleased to cooperate with the Mathematical Association of America to exhibit this and other items from the Library’s holdings in “Mathematical Treasures.” In particular, Convergence would like to thank Lois Fischer Black, Curator, Special Collections, and Ilhan Citak, Archives and Special Collections Librarian, for their kind assistance in helping to make this display possible. You may use these images in your classroom; all other uses require permission from the Special Collections staff, Linderman Library, Lehigh University.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Hilbert and Bernays in Mathematischen Wissenschaften," Convergence (August 2014)