Gauss’ maternal grandfather, Christoph Benze, was a stonemason in the small village Velpke, near Brunswick. As a consequence of working on sandstone, he suffered from the customary pulmonary consumption, from which he died at the age of thirty. He was survived by a daughter, Dorothea, and a younger son, Johann Friedrich. The son took up weaving, in which he soon attained artistic damask-weaving, without further guidance, and as a whole revealed an extraordinarily intelligent, shrewd mind. Gauss as a small boy thought a great deal of him, and later this feeling increased as he guided him in conversation on stimulating matters and thereby recognized his unusual talents and capacities. He always bewailed the uncle’s untimely death December 2, 1809, with the declaration: “A born genius was lost in him.”
The daughter, Dorothea, moved about 1769 from Velpke to Brunswick and married Gebhard Dietrich Gauss in 1776. She was a woman of natural, clever understanding, of unpretentious, happy spirit and a strong character. Her great son was her only child, her pride! She clung to him with the deepest love just as he did to her up to her last hour. Possessed of sound health, although in the last four years totally blind, she reached the unusually advanced age of ninety-seven and died at her son’s home in the observatory, where she had lived for twenty-two years, on April 19, 1839.
The founder of the Benze line, Andreas Benze, was a contemporary of the elder Hinrich Gooss. Of his twin sons born on February 4, 1687, one, also christened Andreas, was survived by two daughters and two sons, the eldest of whom, Christoph Benze, married Katharina Marie Krone; he died on September 1, 1748, in the seventh year of his marriage.
Dorothea served as a maid for seven years before she married Gebhard Dietrich. From the son we learn that this marriage was not a very happy one, “chiefly because of external circumstances and because the two characters were not compatible.” He boasts of his mother as “a very good, excellent woman.” Of his father: “in many respects worthy of esteem and really esteemed, but in his home was quite domineering, uncouth, and unrefined”; also “he never possessed his complete confidence.” This is indication enough of the fact that this child belonged more to the mother than the father in mental affinity. Dorothea had a younger brother, Christoph Andreas, born on June 11, 1748, several months before the father’s death; of him we know very little.
II
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The Enchanted Boyhood
Up to the end of his life Gauss loved to recall numerous episodes of his early childhood. These anecdotes reveal unmistakably occasional sparks of genius. He remembered them correctly and knew how to lend them rare charm by his lively, happy way of narrating; never did the slightest deviation occur in the retelling of them.
His memory went back to very earliest childhood, when he had once been near death. The previously mentioned Wendengraben (now Wilhelmstrasse) on which his parents were living, although later walled over, was once an open canal connected with the Ocker, abundantly filled with water in the spring. The little boy, unguarded, was playing on it and fell in, but was rescued just before drowning, as though destined by Providence for high scientific accomplishment.
Even in his earliest years Gauss gave extraordinary proofs of his mental ability. After he had asked various members of the household about the pronunciation of letters of the alphabet, he learned to read by himself, we are told, even before he went to school, and showed such remarkable comprehension of number relationships and such an incredible facility and correctness in mental arithmetic that he soon attracted the attention of his parents and the interest of intimate friends.
Gauss’ father carried on in the summer what we would call today a bricklayer’s trade. On Saturdays he was accustomed to give out the payroll for the men working under him. Whenever a man worked overtime he was, of course, paid proportionately more. Once, after the “boss” had finished his calculations for each man and was about to give out the money, the three-year-old boy got up and cried in childish voice: “Father, the calculation is wrong,” and he named a certain number as the true result. He had been following his father’s actions unnoticed, but the figuring was carefully repeated and to the astonishment of all present was found to be exactly as the little boy had said. Later Gauss used to joke and say that he could figure before he could talk.
Gauss entered the St. Katharine’s Volksschule in 1784, after he had reached his seventh year. Here elementary instruction was offered, and the school was under the direction of a man named J. G. Büttner. The schoolroom was musty and low, with an uneven floor. From the room one could look on one side toward the two tall, narrow Gothic spires of St. Katharine’s Church, on the other toward stables and the rear of slums. Here Büttner, the whip in his hand, would go back and forth among about two hundred pupils. The whip was recognized by great and small of the day as the ultima ratio of educational method, and Büttner felt himself justified in making unsparing use of it according to caprice and need. In this school, which seems to have had the cut and style of the Middle Ages, young Gauss remained for two years without any incident worth recording.
Eventually he entered the arithmetic class, in which most pupils remained until their confirmation, that is, until about their fifteenth year. Here an event occurred which is worthy of notice because it was of some influence on Gauss’ later life, and he often told it in old age with great joy and animation.
Büttner once gave the class the exercise of writing down all the numbers from 1 to 100 and adding them. The pupil who finished an exercise first always laid his tablet in the middle of a big table; the second laid his on top of this, and so forth. The problem had scarcely been given when Gauss threw his tablet on the table and said in Brunswick low dialect: “Ligget se” (There ’tis). While the other pupils were figuring, multiplying, and adding, Büttner went back and forth, conscious of his dignity; he cast a sarcastic glance at his quick pupil and showed a little scorn. In the end, however, he found on Gauss’ tablet only one number, the answer, and it was correct. But the young boy was in a position to explain to the teacher how he arrived at this result. He said: “100+1=101; 99+2=101, 98+3=101, etc, and so we have as many ‘pairs’ as there are in 100. Thus the answer is 50×101, or 5,050.” Gauss sat quietly, firmly convinced that his problem had been correctly solved, just as he later did in the case of any completed piece of work. Many of the other answers were wrong and were at once “rectified” by the whip.
Büttner now considered that the proper thing to do was to order a better arithmetic book6 from Hamburg, in order to give it to the boy whose accomplishments astonished him and soon brought him face to face with the fact that there was nothing more for him to teach the boy.
The Velpke relatives shook their heads, and of course an early death was prophesied for him, according to the old popular belief that heaven’s favorites must perish young. The Brunswick neighbors, the father’s customers, and others were impressed. His talent had already been shown in his fourth year. In the living room, in which he stayed a great deal with his mother, was hanging an old-fashioned calendar, and soon the little boy could read all the numbers on it. But when the relatives were called together to witness this feat, he got along very poorly, not because he could not read the numbers, but because of the nearsightedness with which he was troubled.
Either Büttner or Bartels7 even called the boy’s father in to talk about the boy’s education. His questions as to how to get means for continued study were met with the rejoinder that assistance of patrons in high position would be won. Thus the rather stubborn father agreed that the boy would no longer have to spin a certain amount of flax every evening. It is said that the elder Gauss, when he arrived home after the conversation, carried the spinning wheel into the back yard and later chopped it up for kindling wood in the kitchen.
Mathematical books now took the place of the spinning wheel in the evening hours; this was attended to by Johann Christian Martin Bartels (1769–1836), the son of Heinrich Elias Friedrich Bartels, a pewterer, living on the Wendengraben. He a
ssisted Büttner, the duties of this office being to cut pens for the smaller boys and to help them in their writing by erasing all the flourishes. A close relationship soon grew up between Bartels, who was himself interested in mathematics, and this remarkable neighbor’s child. Teacher and pupil became intimate friends; they studied mathematics together, with such zeal that Bartels himself decided to devote his life to this branch. Thus Gauss in his eleventh year came into independent possession of the binomial theorem in its complete generality and became acquainted with the theory of infinite series, which opened for him the way to higher analysis.
We owe much to Bartels for the service which he performed in informing several persons of high rank in Brunswick about the ability of young Gauss, particularly E. A. W. Zimmermann.8
One day Zimmermann ordered Bartels to bring the young boy to him. News of unusual talent had already reached his ears; schoolmates had set the report in circulation. Professor Hellwig, the new mathematics teacher at the Katharineum, had handed back Gauss’ first written work with the remark that it was superfluous that such a mathematician should continue to appear in his classes.
According to Gauss’ own statement it was almost against his father’s will that he left Büttner’s school. With the aid of “older” friends, among whom were Bartels and doubtless also the philologist Johann Heinrich Jakob Meyerhoff (1770–1812), whom we shall meet later, he had mastered by private study the elements of the ancient languages. In every other respect he was far in advance of persons of his age. Two years later the Katharineum began to take on new life under the direction of Conrad Heusinger.
The Duchess once found young Gauss in the yard of the palace, absorbed in a book. At first skeptical, she soon found in the course of her conversation with him that the little boy understood what he was reading. Very much astonished, she told the Duke to have the boy summoned. When the lackey reached the Gauss home, he was first sent to the older brother, Georg, with his message; but Georg, weeping, strove against the lackey’s entrance. After being corrected, he rejoined that it concerned his brother, the “good-for-nothing” who always “stuck his nose in a book.” After Carl became a world-famous man and the industrious brother an ordinary laborer, Georg is alleged to have said: “Yes, if I had known that, then I would be a professor now; it was offered to me first, but I didn’t want to go to the castle.” Georg Gauss was by no means as silly as he is here pictured. Shortly after the incident with the lackey, he went on his period of “wandering.” On winter nights Gebhard Dietrich would make the boys go to bed early to save light and heat. In his attic room Carl Friedrich would take a turnip, hollow it out, and roll a wick of rough cotton for it; some fat furnished the fuel, and by the dim light thus obtained he studied half the night until cold and exhaustion forced him to seek his bed.
The surroundings of the Duke delighted the modest, somewhat bashful fourteen-year-old boy, and the tactful Duke, conscious of the fact that he had a very unusual individual before him, knew how to win his love and how to use the means which were necessary for his further education. Young Gauss appeared a bit awkward, but the chief thing of importance was that the Duke quickly and clearly recognized his ability. Gauss departed, enriched in several ways. He received his first logarithmic tables from Geheimrat Feronçe von Rotenkreuz, the minister of state.9 Assisted by the Duke, he entered the Collegium Carolinum in 1792.
“Five thalers to Councilor Zimmermann for a mathematical [instrument] case bought from the mechanic Harborth for a young man named Gauss.” This expenditure, by an order of June 28, 1791, from the special account of the ducal chamber, reveals the first actual trace of the Duke’s interest in Gauss. From the chamberlain’s accounts it seems that on July 20 ten thalers were to be furnished him yearly, and Zimmermann was to be paid for further expense. On June 12, 1792, came the clause: “These payments are to continue as long as he shall attend the Carolineum.” The designation “tuition” cannot be taken in its genuine sense (these are entered under that heading) because Gauss had a “free place” and according to the monthly attendance lists was an “extra free-pupil.” There is no doubt that the Duke gave him many other funds and considerable support from his own private means.
The friendship between Gauss and Zimmermann lasted until the death of the latter on July 1, 1815. The son wrote thus about his father’s death, under date of March 16, 1816: “My father died last year at the moment when the body of his majesty the Duke was being interred,10 so much was he overpowered by feelings of melancholy (as is disclosed in a letter half completed by him) that he suffered a stroke. Unfortunately I was just then absent and neither physician nor surgeon to be had. When help came to him after two hours, alas it was too late.”11
When Gauss entered the Collegium Carolinum in 1792, it was at the zenith of its fame. Hänselmann states that there were two viewpoints which were important in the plan on which Duke Karl had founded the institution in 1745. At that time there were no institutions of higher learning for those who wished to study subjects not taught in the four faculties of a university. This new creation was to fill a gap between Gymnasium and university. Future officers, architects, engineers, mechanics, merchants, and farmers were to find the opportunity to equip themselves with an education grown universal to meet the higher demands of life, and at the same time with the elements of their own fields of specialization. Ancient and modern languages; Christian dogma and morals; philosophy; universal, ecclesiastical, and literary history; statistics; civil and canon law; mathematics, physics, and natural history; anatomy; German poetry and oratory; the theory of the beautiful in painting and sculpture; exercises in drawing and painting, in music, dancing, fencing, and riding, in turning and glass polishing—all this and more were embraced in the curriculum. But what gave the Carolineum its really attractive standing was the spirit in which they were presented. Not at the purely practical demands of life alone was the scheme of this course directed; the pupils were taught to regard themselves as carriers of the new culture, of the freer and nobler education of the taste and the heart. Zachariä, Gärtner, Ebert, K. A. Schmidt, and a group of colleagues were dedicating their best powers to the Carolineum. The day of this newer culture was just then dawning in Germany. In spite of occasional disappointments, such as could not have been avoided in so high an undertaking, these men might have said that that goal was not an idle one; the course started was the true one.
Distinguished and useful men of various positions in life, both native and foreign, were proud of what they had taken away from Brunswick. Academic teachers like Gellert, Ernesti, Kästner, and Heyne avowed that the youths prepared there were distinguished by thorough knowledge, diligence, and worthy morals. Whenever and wherever the new culture of bon-sens and good taste was pursued, the Carolineum was recognized as one of its worthiest nurseries. In the last decade of the eighteenth century there went forth from this institution a number of graduates who were to gain a certain amount of fame; besides Gauss and Bartels there were Ide, Illiger, and Dräseke, the well-known pulpit orator. (We shall return to Ide and Illiger later.) All were born in Germany, and all the children of poor parents, with the exception of Illiger, whose father was a merchant.
When Gauss entered, most of the famous teachers had passed away. Only the last one, Ebert, died on March 15, 1795, not long before Gauss left there. But excellent successors worked in their place. Johann Joachim Eschenburg (1743–1820) took Zachariä’s place in 1777 as professor of philosophy and belles-lettres; Johann Ferdinand Friedrich Emperius was professor of Greek, Latin, and English and after Schmidt’s death also professor of religious instruction; after 1787 August Ferdinand Lueder was professor of history and statistics in the position vacated by Remer, who was called to Helmstedt. In 1810 he became A. L. von Schlözer’s successor in Göttingen. Except for Zimmermann these were the more important of those who saw Gauss sitting in their classes at that time.
On February 18, 1792, Gauss signed himself in the register of the Carolineum 462 Johann
Friedrich Carl Gauss, of Brunswick. Later he never used this name Johann; on all his writings one finds Carl Friedrich Gauss. While in this institution he completed his knowledge of the ancient languages and learned the modern languages. During the four years he remained there he was occupied with abstruse mathematical investigations and studies. The essential foundations of his fund of knowledge were deepened and broadened before he left Brunswick.
He seems to have studied carefully at that time the works of Newton, Euler, and Lagrange. Especially did he feel himself attracted by the great spirit of Newton, whom he revered and whose method he fully mastered. During the last year in his native city Gauss discovered the “method of least squares,” that method of bringing observations into a calculation so that the unavoidable observational errors affect the result as little as possible, and so that the deviations of the value finally obtained from the observational results are a minimum in any single case and as a whole. Daniel Huber in Basel seems to have arrived at the same method. Adrien-Marie Legendre (1752–1833) also discovered it and published it in 1805 in his Nouvelles méthodes pour la determination des orbites, while the Gaussian deduction did not appear in print until 1809. Thus according to the custom then in vogue Legendre gained the right of priority; the date of publication of a discovery passed for the date of discovery itself. Adrain, in the United States, is also said to have deduced the method in 1808, an article on the law of probability of error appearing in The Analyst, a periodical published by him at Philadelphia.
About the year 1750 certain indirect observations in astronomy led to observation equations, and the question as to the proper manner of their solution arose. Boscovich in Italy, Mayer and Lambert in Germany, Laplace in France, Euler in Russia, and Simpson in England proposed different methods for the solution of such cases, discussed the reasons for the arithmetical mean, and endeavored to determine the law of facility of error. Simpson, in 1757, was the first to state that positive and negative errors are equally probable; and Laplace, in 1774, was the first to apply the principles of probability to the discussion of errors of observation. Laplace’s method for finding the values of q unknown quantities from n observation equations consisted in imposing the conditions that the algebraic sum of the residuals should be zero, and that their sum, all taken with the positive signs, should be a minimum. By introducing these conditions, he was able to reduce the n equations to q, from which the q unknowns were determined. This method he applied to the deduction of the shape of the earth from measurements of arcs of meridians, and also from pendulum observations.
Carl Friedrich Gauss, Titan of Science_A Study of His Life and Work Page 4