In the English edition, the chapter on the Geometry of Numbers has been enlarged to include the important findings of H. Lenstraj furthermore, tried and tested examples and exercises have been included. The translator, Prof. Charles Thomas, has solved the difficult problem of the German text into English in an admirable way. He deserves transferring our 'Unreserved praise and special thailks. Finally, we would like to express our gratitude to Springer-Verlag, for their commitment to the publication of this English edition, and for the special care taken in its production. Vienna, March 1991...

"Few mathematical structures have undergone as many revlSlons or have been presented in as many guises as the real numbers. Every generation re-examines the reals in the light of its values and mathematical objectives." This citation is said to be due to Gian-Carlo Rota, and in this book its correctness again is affirmed. Here I propose to investigate the structure of the mathematical continuum by undertaking a rather unconventional access to the real numbers: the intuitionistic one. The traces can be tracked back at least to L.E.J. Brouwer and to H. Weyl. Largely unknown photographies of...

In einem informativen und anregenden Streifzug von Pythagoras uber Bach zu Bohr zeigt der Autor den Einfluss der Zahlen in der Welt des Wissens und unserer Kultur. In einer lebendigen und personlich gefarbten Sprache, unterstutzt durch eine Fulle bestechend schoner Abbildungen, wird der weit gespannte Themenbereich einem breiten Leserkreis verstandlich dargestellt.
Dass nach einem Jahr nach Erscheinen bereits die dritte Auflage erfolgte, belegt die These, dass viele Menschen Mathematik vor allem als wesentlichen Bestandteil unserer Kultur empfinden und daruber mehr erfahren wollen. In der...