2. Valhalla: Posthumous Recognition and Honors
In a park of his native city of Brunswick, at the foot of a knoll now called the Gaussberg, is a splendid monument of Gauss by one of Germany’s greatest sculptors, Fritz Schaper (1841–1919). It was erected in 1877 for the centenary of the mathematician, and the granite base bears this inscription:
Dedicated by a grateful posterity on the centenary of his birthday in his native city Brunswick to the sublime thinker who unveiled the most recondite secrets of the science of numbers and of space, who fathomed the laws of terrestrial and celestial natural phenomena and made them serviceable to the welfare of humanity.
The house in which Gauss was born in Brunswick served as a museum until it was destroyed in an air raid on October 15, 1944. Fortunately the contents had been removed and are now kept in the municipal library, along with the Gauss manuscripts. A street, a bridge,133 and a school in Brunswick bear the name of Gauss, and a Gauss medal is conferred annually by the Scientific Society of Brunswick on some outstanding scientist. The Technical Institute of Brunswick has an oil painting and a bust of its most famous alumnus. The city of his birth has never been lax about honoring her greatest son. On several occasions publications about Gauss were subsidized by the city. In 1927 a special sesquicentennial celebration was held in Brunswick.134 A Gauss Memorial Room in the old City Hall of Brunswick, serving as a museum, was officially opened on February 23, 1955, the hundredth anniversary of his death.
In the Deutsches Museum at Munich one finds in the Hall of Honor a full-length oil portrait of Gauss in his academic robe, by R. Wimmer. Under it is the following inscription by the astronomer Professor Martin Brendel:
His mind penetrated into the deepest secrets of number, space, and nature;
He measured the course of the stars, the form and forces of the earth;
He carried within himself the evolution of mathematical sciences of a coming century.
The city and the University of Göttingen have not lagged behind Brunswick in honoring Gauss. On the campus of the university is a masterful monument of Gauss and Weber by Ferdinand Hartzer (1838–1906), erected in 1899. It represents the two scientists discussing their telegraph. Elaborate ceremonies were held for the unveiling. The only error in the monument lies in the fact that the two men appear to be almost of the same age, whereas actually Gauss was twenty-seven years older than Weber.
Perhaps the finest tribute ever paid Gauss was the publication of his Collected Works, which began in 1863 and extended to 1935. It was one of the most thorough jobs of editing ever done and was carried out by a considerable number of leading German scientists, each a specialist in his field. The publication was sponsored by the Royal Society of Sciences in Göttingen.
Banquets, lectures, and numerous other ceremonies celebrating the centenary and sesquicentennial of Gauss were held in Göttingen. A street in the city was named for him. The university set up the Gauss Archive to house his letters, manuscripts, and library. There are many mementos of him at the observatory and the department of geophysics. A bust is to be found in the main academic building. The heroic-sized white marble bust by Hesemann, generally considered the best, is housed in the university library. Special ceremonies were held in 1933 on the centenary of the telegraph, and a medal was issued. When the King ordered the Gauss medal soon after his death, he put on it this inscription: “George V, King of Hanover, to the Prince of Mathematicians,” and added these words: “Academiae suae Georgiae Augustae decori aeterno.”
Gauss was also honored in Berlin. On the Potsdam Bridge beside Helmholtz, Siemens, and Röntgen was a splendid monument of Gauss by Gerhard Janensch (1860–1933) showing him busy with the telegraph. On the facade of the Technical Institute at Charlottenburg beside Schinkel, Eytelwein, Redtenbacher, and Liebig is a fine sandstone bust of Gauss. The agricultural ministry has a bust of him by Janensch. Portraits of Gauss and Weber are to be found in the Reichspostmuseum.
The most imposing memorial is the Gauss Tower on Mt. Hohenhagen near the village of Dransfeld, a few miles from Göttingen. It is one vertex of the classical triangle, Brocken, Hohenhagen, Inselsberg, so important in the triangulation of the kingdom of Hanover. The tower is of basalt, topped by a red tile roof; it rises to a height of 120 feet, and from the observation platform the visitor has a splendid view of the rolling lands and forests of that region. It is a favorite spot for tourists. Nearby is a tavern, and also to be seen is a “Gauss stone” which he used in the survey. It was dedicated on July 29, 1911, before an audience of leading men of science and government. In the tower is a room containing relics, instruments, and a large marble bust of Gauss by Gustav Eberlein (1847–1926).
On the centenary of Gauss’ death in 1955 the government of Nether-Saxony established at the University of Göttingen and at the Institute of Technology in Brunswick a Gauss Fund of 15,000 marks each per year for visiting scholars or professors in his fields. At the Technology Institute in Hanover, a new building of the regional geodetic survey called the Gauss House is to be opened and dedicated September, 1955.
When the German expedition under Professor Erich von Drygalski of Munich was sent to the South Pole in 1903, its three-mast schooner was named the Gauss. This ship was in later years purchased by the United States government and put into service under another name, along the North Pacific coast from California to Alaska. A volcanic mountain discovered by the expedition was called the “Gaussberg.”
The name of Gauss occurs at so many places in mathematics and science that only a few instances where he has been honored will be mentioned.
The name “Gauss” was given to a unit used to measure the intensity of magnetic field,135 It is the intensity produced by a magnetic pole of unit strength (a “Weber”) at a distance of one centimeter. In 1932 the oersted was substituted for the gauss to represent the centimeter-gram-second unit of field intensity. The gauss is now the c.g.s. electromagnetic unit of induction. The term “gauss” may still be used if magnetic induction and magnetic field strength have the same dimensions.
In optics, the Gauss eyepiece is used in spectrometers and refractometers to set the axis of a telescope accurately at right angles to a plane polished surface. The Gauss eyepiece tube has an aperture in the side through which light is admitted to a piece of plane unsilvered glass at an angle of forty-five degrees to the axis of the telescope. The light is thus reflected past the cross wires and down the telescope tube to the plane polished surface. If the latter is exactly at right angles to the telescope axis, the light will be reflected back down the telescope and an image of the cross wires will be formed exactly coincident with the cross wires themselves. The observer must adjust the position of the telescope until this coincidence is obtained,
Gaussian logarithms are so arranged as to give the logarithm of the sum and difference of numbers whose logarithms are given. Gaussian logarithms are intended to facilitate the finding of the logarithms of the sum and difference of two numbers, the numbers themselves being unknown, but their logarithms being known, wherefore they are frequently called addition and subtraction logarithms.
The Gaussian method of approximate integration is one in which the values of the variable for which those of the function are given are supposed to be chosen at the most advantageous intervals.
A Gaussian period is a period of congruent roots in the division of the circle.
The hypergeometric series is also called the Gaussian series.
A Gaussian function is the hypergeometric function of the second order.
The Gaussian sum is a sum of terms the logarithm of which is the square of the ordinal number of the term multiplied by 2π√-1 times a rational constant, the same for all the terms.
In spherical trigonometry there are four important, frequently Used formulas commonly called Gauss’ analogies or Gaussian equations.
The name of Gauss is also frequently attached to a formula for approximate quadrature.
In geo
metry, Gauss’ theorem relates to the curvature of surfaces; the measure of curvature of surface depends only on the expression of the square of a linear element in terms of two parameters and their differential coefficients. There is a certain expression involving the equation of the surface and the coordinate of a point, called the “Gauss curvature,” which will be constant on the plane, the sphere, and certain other surfaces.
Gauss’ name is always attached to the rule for finding the date of Easter, a formula which he established.
Two magnetic measurements are called “Gauss’ A position” and “Gauss’ B position.”
During World War II the demagnetization of ships was called “degaussing.” Counteracting coils were placed about the ship’s compass so that it would respond normally to the earth’s field against magnetic mines. Officers in charge were called “degaussing officers,” and there were many so-called “degaussing stations.”
The law of quadratic reciprocity of Legendre is also known as the fundamental theorem of Gauss.
As these lines are being written, word comes of several special ceremonies in 1955 in Göttingen and elsewhere, marking the hundredth anniversary of the death of Gauss, The occasion is to be observed by the issuance of a special commemorative postage stamp bearing a profile picture of Gauss.
Appendixes, Bibliography and Index
Appendix A — Estimates of His Services
H. J. S. Smith (1826–1883), one of England’s leading mathematicians of the nineteenth century, gave the best appraisal of Gauss to be found:
If we except the great name of Newton (and the exception is one which Gauss himself would have been delighted to make) it is probable that no mathematician of any age or country has ever surpassed Gauss in the combination of an abundant fertility of invention with an absolute rigorousness in demonstration, which the ancient Greeks themselves might have envied. It may be admitted, without any disparagement to the eminence of such great mathematicians as Euler and Cauchy that they were so overwhelmed with the exuberant wealth of their own creations, and so fascinated by the interest attaching to the results at which they arrived, that they did not greatly care to expend their time in arranging their ideas in a strictly logical order, or even in establishing by irrefragable proof propositions which they instinctively felt, and could almost see to be true. With Gauss the case was otherwise. It may seem paradoxical, but it is probably nevertheless true that it is precisely the effort after a logical perfection of form which has rendered the writings of Gauss open to the charge of obscurity and unnecessary difficulty. The fact is that there is neither obscurity nor difficulty in his writings, as long as we read them in the submissive spirit in which an intelligent schoolboy is made to read his Euclid. Every assertion that is made is fully proved, and the assertions succeed one another in a perfectly just analogical order; there is nothing so far of which we can complain. But when we have finished the perusal, we soon begin to feel that our work is but begun, that we are still standing on the threshold of the temple, and that there is a secret which lies behind the veil and is as yet concealed from us . . . no vestige appears of the process by which the result Itself was obtained, perhaps not even a trace of the considerations which suggested the successive steps of the demonstration. Gauss says more than once that, for brevity, he gives only the synthesis, and suppresses the analysis of his propositions. Pauca sed matura were the words with which he delighted to describe the character which he endeavored to impress upon his mathematical writings. . . . If, on the other hand, we turn to a memoir of Euler’s, there is a sort of free and luxuriant gracefulness about the whole performance, which tells of the quiet pleasure which Euler must have taken in each step of his work; but we are conscious nevertheless that we are at an immense distance from the severe grandeur of design which is characteristic of all Gauss’ greater efforts. The preceding criticism, if just, ought not to appear wholly trivial; for though it is quite true that in any mathematical work the substance is immeasurably more important than the form, yet it cannot be doubted that many mathematical memoirs of our own time suffer greatly (if we may dare to say so) from a certain slovenliness in the mode of presentation; and that (whatever may be the value of their contents) they are stamped with a character of slightness and perishableness, which contrasts strongly with the adamantine solidity and clear hard modeling, which (we may be sure) will keep the writings of Gauss from being forgotten long after the chief results and methods contained in them have been incorporated in treatises more easily read, and have come to form a part of the common patrimony of all working mathematicians. And we must never forget that it is the business of mathematical science not only to discover new truths and new methods, but also to establish them, at whatever cost of time and labor, upon a basis of irrefragable reasoning.
The μαθημαθικòς πιθανολογω̑ν has no more right to be listened to now than he had in the days of Aristotle; but it must be owned that since the invention of the “royal roads” of analysis, defective modes of reasoning and of proof have had a chance of obtaining currency which they never had before. It is not the greatest, but it is perhaps not the least, of Gauss’ claims to the admiration of mathematicians, that, while fully penetrated with a sense of the vastness of the science, he exacted the utmost rigorousness in every part of it, never passed over a difficulty, as if it did not exist, and never accepted a theorem as true beyond the limits within which it could actually be demonstrated.136
In the Biographie universelle (Michaud, Paris, 1856) in a sketch of Gauss, Wagener wrote: “. . . each work of his is an event in the history of science, a revolution, which, overturning the old theories and methods, replaces them by new ones, and advances science to a height which no one had ever before dreamed of.”
M. Marie gave one of the clearest estimates of Gauss’ work which have come down to us:
The genius of Gauss is essentially original. If he treats a subject which has already claimed the attention of other scholars, it seems as if their works were wholly unknown to him. He has his own manner of approaching the problems, his own method, and his solutions are absolutely new. These solutions have the merit of being general, complete, and applicable to all the cases that can be included under the question. Unfortunately, the very originality of the methods, a particular mode of notation, and the exaggerated, perhaps affected, laconicism of his demonstrations, make the reading of Gauss’ works extremely laborious.137
An obituary notice of Gauss published by the Royal Astronomical Society contains these statements:
The Theoria motus will always be classed among those great works, the appearance of which forms an epoch in the history of the science to which they refer. The processes detailed in it are no less remarkable for originality and completeness, than for the concise and elegant form in which the author has exhibited them. Indeed it may be considered as the textbook from which have been chiefly derived those powerful and refined methods of investigation by which the German astronomy of the present century is especially characterized.138
Cayley, a leading British mathematician of the nineteenth century, wrote: “All that Gauss has written is first rate; the interesting thing would be to show the influence of his different memoirs in bringing to their present condition the subjects to which they relate, but this is to write a History of Mathematics from the year 1800.”
Isaac Todhunter, another important British mathematician of the period, had this to say: “Gauss’ writings are distinguished for the combination of mathematical ability with power of expression; in his hands Latin and German rival French itself for clearness and precision.”
Carl Friedrich Gauss, Titan of Science_A Study of His Life and Work Page 39