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
Carl Friedrich Gauss, Titan of Science_A Study of His Life and Work Page 1