Carl Friedrich Gauss, Titan of Science_A Study of His Life and Work Read online

  Carl Friedrich Gauss

  Carl Friedrich Gauss

  Titan of Science

  by

  G. Waldo Dunnington, PhD

  with additional material

  by

  Jeremy Gray and Fritz-Egbert Dohse

  Published and Distributed by

  The Mathematical Association of America

  By G. Waldo Dunnington

  * * *

  Carl Friedrich Gauss: Inaugural Lecture on Astronomy

  and Papers on the Foundations of Mathematics

  Carl Friedrich Gauss: Titan of Science

  © 1955 by G. Waldo Dunnington

  Previously published by Hafner Publishing, New York

  Reprinted 2004 by

  The Mathematical Association of America (Incorporated)

  Additional material by Jeremy Gray (Introduction to

  Dunnington’s Gauss: Titan of Science, Introduction to Gauss’s

  Diary, Gauss’s Diary, and Commentary on Gauss’s Diary) and

  by Fritz-Egbert Dohse (biography of Guy Waldo Dunnington)

  ©2004 by

  The Mathematical Association of America (Incorporated)

  ISBN: 0–88385–547-X

  Library of Congress Catalog Card Number: 2003113540

  Current Printing (last digit):

  10 98765432

  MEMORIAE

  VIRI INCORRUPTISSIMI

  CAROLI FRIDERICI GAUSS

  ANIMAE AMOENISSIMAE

  ET

  INGENII FOECUNDISSIMI

  BIOGRAPHUS EJUS

  TOTO PECTORE

  HUNC LIBRUM

  DEDICAT

  Yet though thy purer spirit did not need

  The vulgar guerdon of a brief renown,

  Some little meed at least—some little meed

  Our age may yield to thy more lasting crown.

  For praise is his who builds for his own age;

  But he who builds for time must look to time for wage.

  — Grant Allen

  SPECTRUM SERIES

  Published by

  THE MATHEMATICAL ASSOCIATION OF AMERICA

  Committee on Publications

  Gerald L. Alexanderson, Chair

  Spectrum Editorial Board

  Gerald L. Alexanderson, Editor

  Robert Beezer

  Jeffrey L. Nunemacher

  William Dunham

  Jean Pedersen

  Michael Filaseta

  J. D. Phillips, Jr.

  Erica Flapan

  Marvin Schaefer

  Eleanor Lang Kendrick

  Harvey J. Schmidt, Jr.

  Ellen May cock

  Sanford Segal

  Russell L. Merris

  Franklin Sheehan

  John E. Wetzel

  The Spectrum Series of the Mathematical Association of America was so named to reflect its purpose: to publish a broad range of books including biographies, accessible expositions of old or new mathematical ideas, reprints and revisions of excellent out-of-print books, popular works, and other monographs of high interest that will appeal to a broad range of readers, including students and teachers of mathematics, mathematical amateurs, and researchers.

  777 Mathematical Conversation Starters, by John dePillis

  All the Math That’s Fit to Print, by Keith Devlin

  Carl Friedrich Gauss: Titan of Science, by G. Waldo Dunnington, with additional material by Jeremy Gray and Fritz-Egbert Dohse

  The Changing Space of Geometry, edited by Chris Pritchard

  Circles: A Mathematical View, by Dan Pedoe

  Complex Numbers and Geometry, by Liang-shin Hahn

  Cryptology, by Albrecht Beutelspacher

  Five Hundred Mathematical Challenges, Edward J. Barbeau, Murray S. Klamkin, and William O. J. Moser

  From Zero to Infinity, by Constance Reid

  The Golden Section, by Hans Walser. Translated from the original German by Peter Hilton, with the assistance of Jean Pedersen.

  I Want to Be a Mathematician, by Paul R. Halmos

  Journey into Geometries, by Marta Sved

  JULIA: a life in mathematics, by Constance Reid

  The Lighter Side of Mathematics: Proceedings of the Eugene Strens Memorial Conference on Recreational Mathematics & Its History, edited by Richard K. Guy and Robert E. Woodrow

  Lure of the Integers, by Joe Roberts

  Magic Tricks, Card Shuffling, and Dynamic Computer Memories: The Mathematics of the Perfect Shuffle, by S. Brent Morris

  The Math Chat Book, by Frank Morgan

  Mathematical Apocrypha, by Steven G. Krantz

  Mathematical Carnival, by Martin Gardner

  Mathematical Circles Vol I: In Mathematical Circles Quadrants I, II, III, IV, by Howard W. Eves

  Mathematical Circles Vol II: Mathematical Circles Revisited and Mathematical Circles Squared, by Howard W. Eves

  Mathematical Circles Vol III: Mathematical Circles Adieu and Return to Mathematical Circles, by Howard W. Eves

  Mathematical Circus, by Martin Gardner

  Mathematical Cranks, by Underwood Dudley

  Mathematical Evolutions, edited by Abe Shenitzer and John Stillwell

  Mathematical Fallacies, Flaws, and Flimflam, by Edward J. Barbeau

  Mathematical Magic Show, by Martin Gardner

  Mathematical Reminiscences, by Howard Eves

  Mathematical Treks: From Surreal Numbers to Magic Circles, by Ivars Peterson

  Mathematics: Queen and Servant of Science, by E.T. Bell

  Memorabilia Mathematica, by Robert Edouard Moritz

  New Mathematical Diversions, by Martin Gardner

  Non-Euclidean Geometry, by H. S. M. Coxeter

  Numerical Methods That Work, by Forman Acton

  Numerology or What Pythagoras Wrought, by Underwood Dudley

  Out of the Mouths of Mathematicians, by Rosemary Schmalz

  Penrose Tiles to Trapdoor Ciphers . . . and the Return of Dr. Matrix, by Martin Gardner

  Polyominoes, by George Martin

  Power Play, by Edward J. Barbeau

  The Random Walks of George Pólya, by Gerald L. Alexanderson

  Remarkable Mathematicians, from Euler to von Neumann, Ioan James

  The Search for E.T. Bell, also known as John Taine, by Constance Reid

  Shaping Space, edited by Marjorie Senechal and George Fleck

  Sherlock Holmes in Babylon and Other Tales of Mathematical History, edited by Marlow Anderson, Victor Katz, and Robin Wilson

  Student Research Projects in Calculus, by Marcus Cohen, Arthur Knoebel, Edward D. Gaughan, Douglas S. Kurtz, and David Pengelley

  Symmetry, by Hans Walser. Translated from the original German by Peter Hilton, with the assistance of Jean Pedersen

  The Trisectors, by Underwood Dudley

  Twenty Years Before the Blackboard, by Michael Stueben with Diane Sandford

  The Words of Mathematics, by Steven Schwartzman

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  Foreword

  It has been observed by many writers that there is no such thing as an impartial biography. If this be true, then the author must plead guilty of a bias in favor of Gauss. Yet Gauss is not a controversial figure, and hence decisions for or against him have been rare. In 1925 I was struc
k by the fact that there was no full-scale biography of Gauss. It seemed incredible that a man of his stature had never received detailed biographical treatment. Various scholars have commented on the fact. Several planned such a biography but never carried out their purpose. The reason is not hard to find, for it is difficult to make the life of a mathematician “readable.” I hope that I have at least partially succeeded, but it is with some trepidation that I lay this work before the public. Had I known in 1925 the magnitude of the task, I would probably never have started.

  Yet the search has been sweet and rewarding. I have “lived intimately” with Gauss for almost thirty years, and there have been many pleasant by-products of my research. I have found all that I sought except the death mask and three of the four Petri deathbed pictures. If it is acceptable to spend part of a lifetime in the study of Shakespeare or Bach, why should it be thought strange to do the same for the greatest mathematician of modern times, a man whose life exhibits so many charming facets?

  The present volume is derived almost entirely from contemporary sources, both manuscript and printed works. The letters and collected works of Gauss have been a rich mine of information. Reminiscences of his friends and students have been useful. His descendants have been very kind in allowing me to use letters, pictures, and other material. I have drawn freely from what I found. The nearest approximation to a biography of Gauss is the memorial monograph by his friend Sartorius (1856). Any biographer must use it. For some aspects of his life it is the only source. I have profited by the learning of those who have covered the ground before me.

  My purpose has been to set Gauss off against the times in which he lived, to show him as a man and scientist. It has been frequently observed that biography is more difficult to write than history. My aim has not been mere entertainment, but a full record of the life and achievements of Gauss.

  The most pleasant part of my searches occurred in the year I spent in his home at the Göttingen observatory, several weeks of which I spent at Brunswick amid the scenes of his boyhood. One cannot help enjoying the local flavor. Work in manuscripts and accumulated memorabilia conveys a vital spark which is lost in the printed work. It enables one to reconstruct the past.

  Probably all the evidence on Gauss is in; it is not likely that any new vital information will turn up, particularly since the great destruction of World War II. Year after year, the notes pile up, but I hope I have not yielded to vanity and exhibited too many of my diggings to the public. The chapters vary considerably in length, but that is inevitable in a biography; a novelist is not bothered by such a problem. There are certain natural dividing points in a human life, and the biographer cannot change them.

  It is hoped that the Appendixes will serve as a place of reference to primary sources. The reader will observe that Chapter XXIV and Appendix I are largely quotation, since it seems advisable to allow Gauss and certain authorities to speak for themselves. An effort has been made to keep footnotes to a minimum. In a work of this character it has not been deemed advisable to cite in footnotes bibliographical references to published letters. These are arranged chronologically in the published correspondence and can be easily found by anyone who is interested. The published correspondence is listed completely in the bibliography.

  The list of acknowledgments in a work of this kind, whose preparation has extended over a number of years, is necessarily a long one. I trust that I shall not omit any person whose name belongs here and I regret that a number of those named below have not lived to see the appearance of this biography in print.

  The Gauss family has been extremely helpful in the undertaking. First and foremost should be mentioned the late William T. Gauss of Colorado Springs, Colorado. For many years he eagerly collected all that he could find touching on the life and achievements of his grandfather; he very kindly allowed me to use as much of his collection as I desired. He displayed a more ardent interest in his ancestor than any other descendant. His daughter. Miss Helen W. Gauss, did not lag behind him in interest; she went over the early chapters with me and made many valuable suggestions. The late Miss Anne D. Gauss of St. Charles, Missouri, furnished much information through correspondence, and sent a number of pictures, as did the late Mrs. Ida H. Gauss of St. Louis, Missouri. Carl August Adolph Gauss of Hamlin, Germany, wrote me his childhood reminiscences of his grandfather and added many firsthand incidents which would have been otherwise very difficult (or impossible) to obtain; his son. Dr. Carl Joseph Gauss of Bad Kissingen, has kindly supplemented his father’s aid. The late Miss Virginia Gauss and her brother Eugene of Columbia, Missouri, were generous enough to give me their father’s set of Gauss’ collected works. Other descendants who have given aid are Mrs. J. Paul Annan of Shreveport, Louisiana, Professor Henry F. Gauss of the University of Idaho, Philip W Gauss of Port Arthur, Texas, and the late Matthew J. Gauss of St. Charles, Missouri.

  Special thanks are due Mrs. Carl Mirbt of Göttingen, who allowed me to use the manuscript record of her grandfather Wagner’s conversations with Gauss in his last days. The late Mrs. Elisabeth Stäckel of Heidelberg graciously placed at my disposal all of her husband’s Gauss notes. I am under great obligation to the late Mrs. Charlotte Hieb of Rübeland in the Harz, who gave me the original of the Petri daguerreotype showing Gauss on his deathbed, as well as other items; she was the widow of Georg Hieb, who was the founder of the Gauss Museum in Brunswick.

  Geheimrat Dr. Bruno Meyermann of the Göttingen observatory, and his wife, gave me innumerable leads and hints, thus expediting the work and making my year’s stay in their home (the Gauss apartment) a most pleasant and memorable one. I am also peculiarly indebted to a leading Gauss authority, the late Dr. Heinrich Mack, librarian of Brunswick, who displayed great enthusiasm for the work, gave me copies of his own publications, and guided me into the Gaussiana under his charge. The editors of Gauss’ Collected Works, Dr. Martin Brendel of Freiburg im Breisgau, and the late Dr. Ludwig Schlesinger of Giessen, as well as the latter’s widow, turned over to me a large quantity of valuable material.

  Others who gave special assistance of various sorts are Dr. A. Wietzke of Bremen, Rudolf Borch of Brunswick, Dr. Heinrich Schneider of Harvard University, the late Dr. G. A. Miller of the University of Illinois, the late Dr. Friedrich Hesemann of Göttingen, the late Dr. Karl R. Berger of Hamlin, and the late Dr. Harald Geppert of Giessen.

  The following list includes those to whom I am indebted for answering specific questions, giving me copies of their publications, or otherwise aiding me, though to a lesser extent than those mentioned above: Dr. Götz von Selle of Göttingen, Dr. Andreas Galle of Potsdam, Professor R. C. Archibald of Brown University, Miss Marthe Ahrens of Stettin, Dr. F. E. Brasch of the Library of Congress (Smithsonian Division), Dr. Wilhelm Lorey of Frankftirt am Main, Dr. Clemens Schaefer of the University of Cologne, Dr. Otto Spiess of Basel, Dr. Karl Metzner of Berlin, Rolf Erb and Mrs. Lucie Noack of Dresden, the late Dr. Erich Bessel-Hagen of Bonn, Dr. J. E. Hofmann of Tübingen, Mrs. Hildegard Leidig of Berlin, the late Baron August Sartorius von Waltershausen of Gauting (Bavaria), Dr. Harald Eisner von Gronow of Berlin, Dr. Günther Reichardt of Berlin, the late Dr. Alfred Stem of Zurich, Friedrich Sack of Brunswick, Dr. W. Jaeger of Berlin-Friedenau, Dr. H. Ludendorff of Potsdam, Professor Richard Courant of New York University, Dr. Eduard Berend of Geneva, the late Dr. Johannes Joachim of Göttingen, Major Fritz von Lindenau of Berlin-Schlachtensee, and, finally, a grandson of the mathematician A. F. Möbius (a pupil of Gauss), Dr. M. Möbius of Frankfurt am Main, as well as the three sons of Ernst Schering: Dr. Harald Schering of Hanover, Dr. Carl Schering of Darmstadt, and Dr. Walther M. Schering of Berlin.

  Grants from the Alexander von Humboldt Foundation and the Carl Schurz Memorial Foundation enabled me to spend a year in Göttingen and Brunswick on the research. A special grant from the Deutsche Forschungsgemeinschaft (Notgemeinschaft der Deutschen Wissenschaft) covered the cost of reproducing a number of pictures. More recently a special allowance from th
e Northwestern State College of Louisiana made it possible for me to spend a summer completing the writing of the work.

  Thanks of a unique nature must go to Miss Rosemary Johnston of Mansfield, Louisiana, who took on the onerous task of typing the entire manuscript, and to Irene Crawford Wagner, M.A, of Natchitoches, Louisiana, who compiled the index.

  G. WALDO DUNNINGTON

  Northwestern State College

  Natchitoches, Louisiana

  December 7, 1954

  Contents

  Foreword

  Introduction to Dunnington’s Gauss: Titan of Science by Jeremy Gray

  Guy Waldo Dunnington by Fritz-Egbert Dohse

  I — Introduction: Family Background

  II — The Enchanted Boyhood

  III — Student Days

  IV — The Young Man

  V — Astronomy and Matrimony

  VI — Further Activity

  VII — Back to Göttingen

  VIII — Labor and Sorrow

  IX — The Young Professor: A Decade of Discovery, 1812–1822

  X — Geodesy and Bereavement: The Transitional Decade, 1822−1832

  XI — Alliance With Weber: Strenuous Years

  XII — The Electromagnetic Telegraph

  XIII — Magnetism: Physics Dominant

  XIV — Surface Theory, Crystallography, and Optics

  XV — Germination: Non-Euclidean Geometry

  XVI — Trials and Triumphs: Experiencing Conflict

  XVII — Milestones on the Highways and Byways

  XVIII — Senex Mirabilis

  XIX — Monarch of Mathematics in Europe

  XX — The Doyen of German Science, 1832–1855