Carl Friedrich Gauss

“ I therefore wish and hope sincerely that all the beautiful virtues which you praise in your future life companion and which well balance the absence of material endowments for a sensible man who feels that he stands firmly on his own feet, - will always prove themselves genuine, but also that you will always prove yourself worthy of the possession of such a treasure and that in this way the union will result in the true happiness of both of you. ”

“ Under the impossibility to form an opinion in regard to conditions and persons from my own knowledge, I willingly submit to the confidence that your age and your experience will protect you against such disappointment as indeed thoughtless and inexperienced youths fall prey to. ”

“ That your business is prospering gives me pleasure, but in a letter which your grandmother received lately there is a somewhat unintelligible intimation that you intend to give it up, to go into the country and there to carry on a wholesale business. ”

“ He became one of the most prominent business men in St. Louis and when he died, left a very considerable estate. He was highly esteemed as a man of ability and the strictest business and personal integrity. There was a very warm attachment between him and his father, as may be seen by the letters which they exchanged. My uncle had eight children, one of whom died in infancy and two of them after reaching maturity. His oldest son, named Carl Friedrich, is now living in the city of St. Louis, Missouri, where he is a leading and exceptionally wealthy business man. ”

“ Theresa married after her father's death. After her death her husband married again and it is worthy of note that his second wife in her will had the fairness to return to the Gauss family the property or a portion of it that had come from that source, a fairness not always shown. ”

“ That I now have also in the new world a grand-child on your side is very gratifying to me. In the old world my name will probably become extinct, since Joseph's marriage has remained childless for some years. In all probability Joseph will be placed in different circumstances in the near future, more pleasing to himself than a lieutenantcy in time of peace ”

“ With the sincerest wishes for the enduring happiness of your union, Your affectionate father, C. F. Gauss
Goettingen, February 15, 1844.
P. S. Letters via Liverpool travel neither more securely nor more quickly than via Havre, but always cost an enormous postage here, about three times as much as via Havre. Therefore in future send no letters via England, but always via Havre. ”

“ Joseph Gauss, son of C. F. Gauss' first marriage, who remained in Germany, later had a son, his only child, named Carl, who is still living (1926) in Hameln, Germany.
Ewald, mentioned above, was the German Orientalist, who first married Minna, C. F. Gauss' daughter by his first marriage. Minna is said to have had a good deal of her father's mentality, but died a few years after her marriage to Ewald. Ewald married again, as stated in above letter.
C. F. Gauss' second wife was also named Minna, and her daughter was named Theresa. Her sons were Eugene and William, who both came to America. ”

“ By chance at the same time we had received a jar of butter aus dem Altenlande from Joseph's wife, -- so there was nothing wanting for an omelette from my children in foreign countries but the eggs from William's chicken coop.
We were very much pleased with the Daguerre picture which your dear wife sent Theresa. The workmanship is better than I have ever seen in any Daguerre picture made in Europe. theresa reciprocates with two copies of her picture, which Mr. Angelroth will bring, one for you and one for William. ”

“ How did the world-renowned mathematician of Gottingen behave toward the young and unknown Hungarian? Students of scientific history know that on questions of priority of discovery many a bitter battle has been fought. Scientific men are only human, and they frequently fail to see the full merits of rival claimants. But Gauss showed himself as generous as a man as he was great as a scientist. ”

“ The opinion of leading mathematicians at this time seems to have been crystallizing very rapidly. Unconsciously the men of this formative period were adducing evidence which would give form and tendence to the developments in the field of mathesis at a later date. They appear to have been reaching out for that which, ignis fatuus-like, was always within easy reach, but not quite apprehensible.
A bolder student than Gauss was Ferdinand Carl Schweikart (1780-1857) who also has been credited with the founding of the non-Euclidean geometry. ”

“ I do not think he ever studied calculus and did not use logarithms. Aside from the fact that he used shortened methods of his own, this calculation does not prove great mathematical ability so much as it does his wonderful memory. He had my brother write down the long lines of figures for fear he might forget them, but he had to carry them in his mind in making the computations.
Another instance shows his memory of what he read - and I may say here that he was a great reader. He was a deeply pious man and had been a member of the Presbyterian Church for forty years previous to his death. ”

“ Einstein has elaborated them for his particular purposes (in his essay "Concerning the formal foundations of the general theory of relativity" [12] ) ; Gauss invented the calculus of absolute differentials in order to study those properties of a surface (in the theory of surfaces) which are not affected by the position of the surface in space nor by inelastic continuous deformations of the surface (deformations without tearing) , so that the value of the line-element does not alter at any point of the surface. ”

“ 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, so long as we read them in the submissive spirit in which an intelligent school-boy 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. ”

“ We have in German a term which very happily expresses the faculty, possessed by the most eminent of scientific geniuses, of discovering the important phases of ordinary phenomena: such men are said to have "Blick." Have we not an instance of a higher visual faculty, exalted not only by genius, but also by comprehensive knowledge, when a Gauss was led by the glistening of the windows of a church-tower which he was observing with his telescope to the idea of his heliotrope—an instrument without which no accurate triangulation is nowadays ever thought of ”

“ We may summarise these statements by saying that “reality” for the scientist reduces to the simplest co-ordination of experimental facts and that in view of the various possible types of spaces suggested by non-Euclidean geometry, physical measurements constitute our only means of determining which is the simplest, hence which is the real solution. This explains why Gauss (who as far back as 1804 had mastered in secret the essentials of non-Euclidean geometry) endeavoured to establish the geometry of space by means of light-ray triangulations. ”

“ It resulted in the discovery of one of the greatest mathematicians, perhaps the greatest, that Germany has ever produced—Gauss. He was then a young man of twenty-five, eking out a living by tuition. He had invented but not published several powerful mathematical methods (one of them now known as "the method of least squares") , and he applied them to Piazzi's observations. He was thus able to calculate an orbit, and to predict a place where, by the end of the year, the planet should be visible. ”

“ If we imagine constructions to be made with rigid rods in the surface (similar to that above with the marble slab) , we should find that different laws hold for these from those resulting on the basis of Euclidean plane geometry. The surface is not a Euclidean continuum with respect to the rods, and we cannot define Cartesian co-ordinates in the surface. Gauss indicated the principles according to which we can treat the geometrical relationships in the surface, and thus pointed out the way to the method of Riemann of treating multi-dimensional, non-Euclidean continua. ”

“ The battle of Austerlitz had brought the country into danger, and the Duke of Braunschweig was entrusted with a mission from Berlin to the Court of St. Petersburg. The fame of Gauss had travelled there, but the duke resisted all attempts to bring or entice him to the university of that place. On his return home, however, he raised the salary of Gauss. ”

“ Guasco was invited to dine with the King; praised for his excellent defence. Prisoners of War his Garrison and he; about 9,000 of them still on their feet; their entire loss had been 3,552 killed and wounded; that of the Prussians 3,033. Poor Guasco died, in Konigsberg, still prisoner, before the Peace came.
Of Austrian fighting in Silesia, this proved to be the last, in the present Controversy which has endured so long. No thought of fighting is in Daun; far the reverse. Daun is getting ill off for horse-forage in his Mountains; the weather is bad upon him ”

“ H. J. S. Smith, "it is probable that no mathematician of any age or country has ever surpassed Gauss in the combination of an abundant fertility in invention with an absolute rigorousness in demonstration which the ancient Greeks themselves might have envied." Wagener says, in the sketch of Gauss in the "Biographie Universelle," that 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. ”

“ Gauss' researches on the theory of numbers were the starting-point for a school of writers, among the earliest of whom was Jacobi. The latter contributed to Crelle's Journal an article on cubic residues, giving theorems without proofs. After the publication of Gauss' paper on biquadratic residues, giving the law of biquadratic reciprocity, and his treatment of complex numbers, Jacobi found a similar law for cubic residues. By the theory of elliptical functions, he was led to beautiful theorems on the representation of numbers by 2, 4, 6, and 8 squares. ”

“ Had Daun, at Olmutz, been as a Duke of Cumberland relieving Tournay, rushing into fight at Fontenoy, like a Hanover White-Horse, neck clothed with thunder, and head destitute of knowledge,—how lucky had it been for Friedrich! But Daun knows his trade better. Daun, though superior in strength, sits on his Magazine, clear not to fight. By no art of manoeuvring, had Friedrich much tried it, or hoped it, this time, could Daun have been brought to give battle. As Fabins Cunctator he is here in his right place; taking impregnable positions, no man with better skill in that branch of business ”

“ Mathematicians agree far better as to the form of the Law of Error than they do as to the manner in which it can be deduced and proved. They agree that among a number of discrepant results of observation, that mean quantity is probably the best approximation to the truth which makes the sum of the squares of the errors as small as possible. But there are three principal ways in which this law has been arrived at respectively by Gauss, by Laplace and Quetelet, and by Sir John Herschel. Gauss proceeds much upon assumption ”

“ It seems to me to be a more important matter whether a common measure can be found for Art and Discovery at all. Perhaps the test of how far a work can be replaced may be regarded as valid for each. When you say that Dostojewski gives you more than Gauss, this probably corresponds with the feeling that without Dostojewski you would have no 'Karamasoffs' and hence would lack a certain life-value that cannot be replaced. But if Gauss had failed to produce one of his fundamental theorems of Algebra, probably some other Gauss would have appeared, who would have achieved this result. ”

“ According to this, then, [Pg 185] our instinct increases the value of a work of art, as we feel that we are dependent on one being alone for its creation."
"But this is only to be admitted conditionally," said Einstein, "for the best that Gauss has given us was likewise an exclusive production. If he had not created his geometry of surfaces, which served Riemann as a basis, it is scarcely conceivable that anyone else would have discovered it. I do not hesitate to confess that to a certain extent a similar pleasure may be found by absorbing ourselves in questions of pure geometry." ”

“ Daun, in the last two days, had been felling even more trees than they are aware of,—thousands of trees in those Devil's wildernesses to Friedrich's right; and has secretly hewn himself roads, passable by night for men and ammunition-wagons there:—and in front of Friedrich, especially Hochkirch way, Daun seems busier than ever felling wood, this Friday night; numbers of people running about with axes, with lanterns over there, as if in the push of hurry, and making a great deal of noise. "Intending retreat for Zittau to-morrow!" ”

“ MAJOR QUINTUS ICILIUS. "Guichard is by birth a Magdeburger, age now thirty-four; a solid staid man, with a good deal of hard faculty in him, and of culture unusual for a soldier. A handy, sagacious, learned and intelligent man; whom Friedrich, in the course of a year's experience, has grown to see willingly about him. There is something of positive in Guichard, of stiff and, as it were, GRITTY, which might have offended a weaker taste; but Friedrich likes the rugged sense of the man ”