Hilbert, Göttingen and the Development of Modern Mathematics

Description

David Hilbert is one of the outstanding mathematicians of the twentieth century and probably the most influential. This book highlights Hilberts contributions to mathematics, putting them in their historical, social and cultural context. With this aim, particular attention is paid to Hilberts axiomatic method and his proposal for the foundations of mathematics, the so-called Hilberts 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 worlds 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, Hilberts 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. Table of Contents List of Illustrations Introduction Chapter One Chapter Two Chapter Three Chapter Four Chapter Five Chapter Six Chapter Seven Chapter Eight Chapter Nine Chapter Ten Chapter Eleven Chapter Twelve Chapter Thirteen Chapter Fourteen Chapter Fifteen Chapter Sixteen Chapter Seventeen Chapter Eighteen Chapter Nineteen Chapter Twenty Chapter Twenty-One Chapter Twenty-Two Chapter Twenty-Three Epilogue Appendix Reference List Author Index