HILBERT, DAVID.

The Foundations of Geometry. Authorized translation by E.J. Townsend.

Chicago, Open Court, 1902. Small 8vo. Orig. full red cloth, gilt. A rather faint dampstain along first hinge on frontcover, otherwise fine. VII,143 pp.

First English edition of Hilbert's "Grundlagen der Geometrie" from 1899, one of the most influential publications in 2oth Century mathematics.

Throughout the 19th century geometry was developed far beyond our intuitive conception of space; hyperbolic geometry was discovered by Gauss, Bolyai, and Lobachevsky and elliptic geometry by Riemann. However, Euclidean and non-Euclidean geometry still involved an intuitive idea about the concepts 'point', 'line', 'lies on', 'between', etc. In his 'Grundlagen' Hilbert set out to give a strictly formal formulation of geometry were points, lines, planes are nothing more than abstract symbols and concepts as 'lies on' are simply algebraic relations between these symbols. Through his method Hilbert could analyse independence and completeness of the axioms for geometry and he presented a new smaller set of axioms for Euclidean geometry. It can not be said that the 'Grundlagen' contains new and surprising discoveries, its importance lies in the great influence which Hilbert's method had on all fields of mathematics, and even other sciences as physics, chemistry, and biology. The 'Grundlagen' initiated a whole new paradigm shift and eventually evolved mathematics, throughout the 20th century, into a network of axiomatic formal systems.

Order-nr.: 35061