XXI — Gathering Up the Threads: A Broad Horizon
XXII — Religio Scientiae : A Profession of Belief From the Philosopher and Lover of Truth
XXIII — Sunset and Eventide: Renunciation
XXIV — Epilogue
1. Apotheosis: Orations of Ewald and Sartorius
2. Valhalla: Posthumous Recognition and Honors
Appendixes, Bibliography and Index
Appendix A — Estimates of His Services
Appendix B — Honors, Diplomas, and Appointments of Gauss
Appendix C — The Will of Gauss
Appendix D — Children of Gauss
Appendix E — Genealogy
Appendix F — Chronology of the Life of Carl F. Gauss
Appendix G — Books Borrowed by Gauss From the University of Göttingen Library During His Student Years
Appendix H — Courses Taught by Gauss
Appendix I — Doctrines, Opinions, Theories, and Views
Bibliography
1. Publications of Gauss
2. About Gauss
An Introduction to Gauss’s Mathematical Diary by Jeremy Gray
Gauss’s Mathematical Diary
Commentary on Gauss’s Mathematical Diary by Jeremy Gray
Annotated Bibliography
List of Illustrations
Frontispiece:
Carl Friedrich Gauss: full-length portrait by R. Wimmer in the Deutsches Museum in Munich (1925)
At the end of Chapter X:
The birthplace of C. F. Gauss
The Gauss coat-of-arms
Silhouette of Gauss in his youth
Bust of Gauss by Friedrich Künkler (1810)
The Collegium Carolinum in Brunswick
The Schwarz portrait of Gauss (1803)
Minna Waldeck, second wife of Gauss
Portrait of Gauss by S. Bendixen (1828)
A sketch of Gauss by his pupil J. B. Listing
The observatory of the University of Göttingen
The courtyard of the Göttingen observatory as it appeared in Gauss’ time
Gauss’ personal laboratory in the observatory as he left it
The Gauss-Weber telegraph (Easter, 1833)
Gauss’ principal instrument, the Repsold meridian circle
Gauss and Weber
Biermiller’s copy (1887) of the Jensen portrait of Gauss (1840)
Ritmüller’s portrait of Gauss on the terrace of the observatory
Gauss in 1854
Gauss about 1850
Portrait of Wolfgang Bolyai by János Szabó
Johann Friedrich Pfaff
At the end of Chapter XXIII:
Heinrich Christian Schumacher
Heinrich Wilhelm Matthias Olbers
Friedrich Wilhelm Bessel
Alexander von Humboldt
Johann Franz Encke
Johann Benedikt Listing
The Philipp Petri daguerreotype of Gauss on his deathbed
The copper memorial tablet in Gauss’ death chamber, given by King George V of Hanover (1865)
The grave of Gauss in St. Albans Cemetery in Göttingen
The bust of Gauss by C. H. Hesemann (1855) in the University of Göttingen library
Joseph Gauss
Heinrich Ewald
Minna Gauss Ewald, a watercolor by L. Becker (1834)
Wilhelm Gauss
Eugene Gauss
Therese Gauss and her husband, Constantin Staufenau
Therese Gauss, a sketch by J. B. Listing
Schaper’s monument to Gauss in Brunswick (1880)
Bust of Gauss by W. Kindler (in the Dunnington Collection)
Bust of Gauss by Friedrich Küsthardt in Hildesheim
The Gauss-Weber monument in Göttingen, by Hartzer (1899)
The Gauss monument by Janensch, in Berlin
The Gauss Tower on Mount Hohenhagen, near Dransfeld, dedicated 1911
The Brehmer medal of Gauss (1877)
The Eberlein bust of Gauss in the Hohenhagen Tower
The bust of Gauss by F. Ratzenberger (1910), in the Dunnington Collection
Commemorative postage stamp issued for the Gauss Centennial, 1955
Introduction to Dunnington’s Gauss: Titan of Science
by Jeremy Gray
Dunnington’s biography of Gauss was first published almost 50 years ago, and remains unrivalled for its combined breadth, depth, and accuracy. It was the product of three decades of labour on substantially all the known sources, and it is regrettable that it has been so long out of print. Gauss continues to reward the attention of historians—there have been at least five other biographies since 1953 (those by Wussing [1976], Reich [1977], Bühler [1981], Hall [1970], and Worbs [1955]) as well as an extensive, thoroughly-researched essay by K.O. May [1972])—and some of their discoveries are noted in the text as we proceed, but Dunnington’s book remains the core of any attempt to understand Gauss and his work. Walter Kaufmann Bühler, one of these later biographers, rightly called Dunnington’s book ‘by far the most important’ of the major biographies of Gauss (Bühler [1981], p. 166).
Apart from its merits as a biography, to which I shall return, Dunnington’s study is notable for the wealth of information it contains in its numerous appendices. There is a useful chronology of his life and a good bibliography of his work. There is a list of the books Gauss read at university, which is very helpful in sorting out what he learned and when. There is a remarkable genealogy of his descendants reaching to 1953 (the family tree is currently maintained by Susan Chambless, herself a Gauss descendant, at http:homepages.rootsweb.com/~schmblss). There is a lengthy bibliography of writings about Gauss. The Gauss scholar may now also consult the extensive work by Uta Merzbach: Carl Friedrich Gauss: a Bibliography, published in 1994. This lists the full publication details of all Gauss’s works, locates all his surviving letters, and records such information as the names of everyone known to Gauss, whether a predecessor or a contemporary, and where their names were mentioned by him. It also brings up to date the list of works about Gauss. The simplest way to keep up with studies on Gauss may well be to navigate the Web, starting perhaps with the Web site of the British Society for the History of Mathematics (http://www.dcs.warwick.ac.uk/bshm.html) but one should also consult the Mitteilungen der Gauss-Gesellschaft, which carries many articles devoted to Gauss (their home page can be found at http://www.math.uni-hamburg.de/math/ign/gauss/gaussges.html). A select bibliography has been added to this book, but unlike those by Dunnington and Merzbach it does not aim to be complete but merely to point out some recent additions to the literature which the reader of this book may welcome.
Any account of someone’s life and work founders, in the last analysis, on our inability to grasp the creative process. Just as novelists leave behind works that are no simple record of the life and cannot be used to supplement the documentary record in any easy way (if at all) mathematicians and scientists do not simply respond to circumstances and turn them into theorems and discoveries. Much of the life Gauss lived could have been lived by anyone without there being so much to show for it. In many ways, Gauss led the life of a competent astronomer, no different from a number of his contemporaries. Nothing in his situation can account for his profound originality. Dunnington rightly establishes that the circumstances of Gauss’s life did dispose him to some topics rather than others. His astronomical work was part of an extensive German enterprise, often well-funded and with good new instruments. His survey of the State of Hanover in the 1820s likewise saw him securely placed in the world of useful work. Both activities were congenial to someone with Gauss’s remarkable ability as a calculator, not to mention his capacity for sheer hard work. But the circumstances cannot explain how Gauss came to invent the method of least squares and rediscover the lost asteroid Ceres, or discover the concept of intrinsic curvature and open a new field in the study of geometry. To his credit, Dunnington does not speculate
where the evidence is inevitably lacking.
Dunnington, instead, put a great deal of careful effort into his account of the German political and intellectual scene in Gauss’s day.1 Those who knew Gauss, who helped him on his way in his teens and as a young man, and who were his friends in later life, are described and located in their various milieus. The prosaic but essential side of Gauss’s activity is well described, from the details of equipment, its purchase and maintenance, to the conduct of the famous survey and the work on the electric telegraph. At the same time, every aspect of Gauss’s scientific and mathematical work is discussed in detail.
Nonetheless, Dunnington’s book has become dated in two significant ways. A modern reader is likely to feel that he became too close to his subject, and that he did not always explain the mathematics with sufficient clarity. It is hard not to be impressed, even over-impressed, with Gauss’s achievements, but while some have found his personality less attractive, Dunnington comes over as Gauss’s best friend, excusing and explaining away all the imperfections of his hero. As he endearingly admits in the opening words of the Foreword, he ‘must plead guilty to a bias in favor of Gauss.’ The entries in the index for aspects of Gauss’s personality are, in their entirety: sensitive, noble in bearing, thoroughly conservative, not a utilitarian, slow in passing judgement, dislike of travel, wise investor, aristocratic, thorough, despised pretence, religious in nature, practical in concept of religion, kind but austere, accepted misfortune. Some are undoubtedly correct—Gauss not only left his family a lot of money but rescued the university widows’ fund—but unless one would spurn the label ‘thoroughly conservative’ or holds different religious views, there is little here that one would not wish for oneself. Bühler, by contrast, noted that ‘Early in his adult life, Gauss severed most of the ‘meaningful’ social and emotional ties a man could have.’ (Bühler, p. 13), which is not such an attractive aspect, and May commented that ‘Those who admired Gauss most and knew him best found him cold and uncommunicative’ (Dictionary of Scientific Biography, p. 308). The result of Dunnington’s bias is a book which, although it was written in 1953, is oddly Victorian in tone. While the reader may easily make allowance for this, and no attempt has been made to mitigate the effect, he or she may also wonder what is missing. How reliable are the facts presented here, how fair, has a full picture been presented or a flattering half-view?
It has become inevitable that we doubt the anecdotes about the young Gauss. They were written down only late in life, they derive from the fond but perhaps inaccurate memories of Gauss and his mother. They exaggerate, but such were Gauss’s prodigious abilities that they came to be believed. Today, we find it easy to strike them down, instinctively reacting against stories that we see as pandering to the romantic ideal of the genius. Did Gauss really learn to read and to do elementary arithmetic with so little help? Bühler, in his biography of Gauss, wrote simply that ‘many of these anecdotes cannot be substantiated, nor are they of serious interest’ [1981, p. 5]. And perhaps they are fairy tales, even if they can be traced back to Gauss himself, as Bühler admitted in a footnote. May, on the other hand, found the famous stories convincing. But even if the evidence is not unimpeachable, even if it is at times unreliable, it is held in question today as much for the message it carries as for its lack of documentation.
The feeling that Dunnington is partisan lingers throughout the book. What sort of a colleague was he among the astronomers? When he surveyed Hanover? During the affair of the Göttingen Seven, when two of his close friends were dismissed from their jobs at the University of Göttingen for refusing to take an oath of allegiance to the reactionary Duke of Cumberland? There is no one, true view of a person. There are only multiple, often contradictory views, and Dunnington’s is partial and perhaps inevitably so; there is a general tendency for biographers to sympathise with their subjects. But in fact, most biographers concur that it was among astronomers that Gauss was most at home. He felt useful, they in turn were impressed by his observational, and still more by his computational, skills. But they were not over-awed. With Bessel, Olbers, Schumacher and others Gauss enjoyed a long correspondence and friendships that he was denied elsewhere. In the long survey of Hanover, Gauss climbed the mountains, endured the bad weather and the sleepless nights that every one else had to endure, and generally impressed everyone as a team player, albeit an important one. And in the miserable affair of the Göttingen Seven, Gauss was prudent, less reactionary than some of his circle, and in any case incapable of rescuing Weber, Ewald, and the others from the consequences of their actions. No one at the time seems to have expected him, or wanted him, to do much more than he did, or much differently. Dunnington’s hero is no one’s villain.
The problem is that the same haze diffuses over the scientific achievements. Was there no one doing comparable work at the time? Had Abel really only come one-third of the way that Gauss had managed in creating a theory of elliptic functions? What, precisely, did Gauss know about non-Euclidean geometry? Is Gauss the chief architect of the theory and method of least squares in statistics? Dunnington is not given to outright exaggeration, but contemporary mathematicians and scientists are kept in the shade unless they are also close friends or colleagues of Gauss, and mentioned as often for their personal views as the qualities of their work. This not only misses an opportunity to make Gauss’s work stand out more clearly by comparison with the best of what else was being done at the time, it hinders the readers’ chances of assessing Gauss’s influence. This may be why much of the subsequent literature on Gauss omits reference to Dunnington’s book, not only in cases where they have little to add, but on the more interesting occasions when they disagree.
By keeping to himself rather than putting himself out socially, by his carefully honed writing style, which Crelle compared to ‘gruel’, Gauss minimised his influence on his contemporaries. He could be generous, as with his praise of Eisenstein and Sophie Germain (no prejudice against women in this instance at least) but he could be withholding too, as he surely was with the discoverers of non-Euclidean geometry. Part of Dirichlet’s lasting legacy is undoubtedly that he made Gauss’s number theory comprehensible to the small but important audience of German research mathematicians. As a result, number theory became a major concern of the major mathematical nation of the nineteenth century, but to whom is the credit due, Gauss or Dirichlet? The question is barely tackled here. One has the impression that nonetheless German mathematicians gravitated around Gauss, or perhaps his published work, but that French mathematicians did not, but the biographer would have had to have shifted focus considerably to bring such matters into discussion.
It was pointed out by May that Gauss’s motto ‘Pauca, sed matura’ (Few, but ripe) tends to obscure the fact that Gauss wrote a very great deal. There are two substantial books and 12 volumes in his Werke, and even if one allows for the generous commentaries, and the fact that quite a bit of it was written for the desk drawer, that is a lot of pages. The bulk of it is made up of astronomical work, much of it about asteroids, surveying, and error analysis. This has given rise to a controversy about whether Gauss should be regarded as primarily a mathematician, and if so a pure or an applied mathematician, or as a scientist. The controversy is at once enjoyable and fruitless. The sciences and mathematics advance in different ways and even at different speeds. Gauss was acclaimed in his day for his work on the orbits of asteroids, an exciting topic then but one of less interest today, so much so that some recent commentators have seen fit to explain why Gauss bothered. His work on the electric telegraph was pioneering in its day, but—as Dunnington described—it did not lead to a great technological advance. He won a prize for his work on theoretical cartography, which laid down the theory that has guided work in the subject ever since, but which was by no means the deepest part of his work on differential geometry. Rightly or wrongly, it seems that one cannot win fame as a ‘geodesist’. The mathematics, on the other hand, that Gauss did, not all of which is desc
ribed here, is a secure part of modern mathematics in a number of different areas, and it was appreciated by the best of his younger contemporaries.
It is therefore to be regretted that Dunnington’s account of Gauss’s mathematics has become, and perhaps always was, a little indistinct. There is, of course, an admirable account by Felix Klein in his Entwickelung der Mathematik, and the lengthy essays on different aspect of Gauss’s mathematics that adorn volume X.2 of the Werke are classics of German historical scholarship. Guided by these, and in the belief that accounts of anything can be given which are clear at least to those with the right sort of background knowledge, I have written an Appendix on Gauss’s mathematical work, concentrating on those topics that Dunnington himself discussed. I have also appended a translation, with commentary, of Gauss’s mathematical diary, an interesting document in itself and which I hope will interest a wider readership than it had on its original publication.
Throughout the book there are occasions when the reader will wish Dunnington had done things differently. I have resisted the temptation to rewrite the book. It is Dunnington’s Gauss that is worth reprinting. Were it not to pass that test one would be driven to contemplate co-authorship across the tomb, and while there are successful examples of such collaboration I did not wish to attempt one. It is better to have in print the considered view of someone who spent nearly thirty years on the task, I believe, than to tinker nervously with it, even when accuracy and the highest of current standards may be on one’s side. There are remarkably few footnotes, for example. This makes it difficult, if not impossible, to determine the sources of Dunnington’s information. Short of spending a year doing someone else’s research, or hiring a fact checker from the New York Times, there is nothing to be done. But there are occasions when later writers have brought up information that changes the picture Dunnington presented in significant ways. I have taken up these matters in the annotated bibliographical essay which will be found at the end of the book, and added footnotes, where I note a number of recent and valuable accounts of the mathematical and scientific work have appeared.2
Carl Friedrich Gauss, Titan of Science_A Study of His Life and Work Page 2