Hilbert, Göttingen and the Development of Modern Mathematics

David Hilbert is one of the outstanding mathematicians of the twentieth century and probably the most influential. This book highlights Hilbert’s contributions to mathematics, putting them in their historical, social and cultural context. With this aim, particular attention is paid to Hilbert’s axiomatic method and his proposal for the foundations of mathematics, the so-called Hilbert’s program; the development of algebraic number theory, the theory of integral equations, modern algebra and the structural image of mathematics; the axiomatization of Euclidean Geometry in his magnum opus Grundlagen der Geometrie; the famous list of Mathematical Problems presented in Paris in 1900; the mathematical tradition of the University of Göttingen, which became the world’s mathematical centre under the leadership of Felix Klein and Hilbert; the great debate on the foundations of mathematics in the twenties between formalists and intuitionists; and finally, Hilbert’s work on the theory of relativity and the foundations of quantum mechanics.

The target audience of this book is mainly academic, although the use of complex mathematical formulas and abstract mathematical concepts have been avoided as far as possible so that it is understandable to general-interest science readers.