As a native of Brunswick I heard Gauss mentioned when I was young and was happy to believe in his greatness without understanding of what it consisted. It made a deeper impression on me when I first heard about his geometric representation of imaginary numbers or, as they were still called at that time, impossible quantities. By that time, as a student at the Collegium Carolineum (the present-day Institute of Technology), I had delved a little way into higher mathematics and, soon after, when Gauss celebrated the golden jubilee of his doctorate in 1849, he was sent congratulations by our faculty, which had been composed by the brilliant philologist Petri, in which the passage 'he has made possible the impossible' particularly attracted my attention. I went to Göttingen at Easter 1850 and there I gained a somewhat deeper understanding when I was introduced to the elements of number theory in the seminar by a short, but very interesting, course by Moritz Stern. On my way back and forward to the Observatory, where I took a course given by the excellent Professor Goldschmidt on popular astronomy, I occasionally met Gauss and was happy to observe his stately, awe-inspiring appearance, and very often I saw him close up at his usual place in the Literary Museum, which he regularly visited in order to read the newspapers.
At the start of the following winter semester I considered myself mature enough to attend his lectures on the method of least squares, and so, carrying the attendance book for the lectures, and with palpitating heart, I entered his living room where I found him sitting at his desk. He didn't seem very pleased at my announcement, but I had heard that he didn't like to give courses. After he had signed his name in my attendance book he said after a short silence, "Perhaps you've heard that it is always rather doubtful whether my lectures will materialise. Where do you live? At Vogel the barber? Well that's a piece of good luck since he is also my barber. I'll let you know through him.
A few days later Vogel, a character known throughout the city, quite puffed up with the importance of his mission, came to my room to let me know that several other students had signed up and that Privy Court Councillor Gauss would deliver his course.
There were nine of us students, and of these I slowly got better acquainted with August Ritter and Moritz Cantor. We were all regular attendees, seldom was one of us absent, despite the path to the Observatory being sometimes unpleasant during winter. [The course was held for three hours each week.] The lecture room, separated from Gauss' office by an anteroom, was quite small. We sat at a table which had room for three people comfortably at each side, but not for four. Gauss sat opposite the door at the top end, at a reasonable distance from the table, and when we were all present, the two who came in last had to sit quite close to him with their notebooks on their laps. Gauss wore a lightweight black cap, a rather long brown coat and grey trousers. He usually sat in a comfortable attitude, looking down, slightly stooped, with his hands folded above his lap. He spoke quite freely, very clearly, simply and plainly; but when he wanted to emphasise a new point of view, for which he used a particularly characteristic word, then he would raise his head, turn to one of those sitting beside him, and gazed at the student with his beautiful, penetrating blue eyes during his emphatic speech. That was unforgettable. He spoke using language which was almost without dialect, only occasionally one could hear traces of a Brunswick dialect. When counting, for example, he wasn't ashamed to use his fingers and, rather than saying 'eins', 'zwei', 'drei', it sounded like 'eine', 'zweie', 'dreie', and so on, like one can hear among those in the market place. If he proceeded from an explanation of principles to the development of mathematical formulas, then he got up, and in a stately very upright posture he wrote on a blackboard beside him in his peculiarly beautiful handwriting in which he always succeeded, through economy and deliberate arrangement, in making do with a rather small space. For numerical examples, on whose careful completion he placed special value, he brought along the requisite data on little slips of paper.
Gauss completed the presentation of the first part of his course on 24 January 1851. In this part he had made us familiar with the essence of the method of least squares. This had been followed by an extremely clear development of the fundamental concepts and principle theorems of the calculus of probabilities which he illustrated with original examples. This served as an introduction to the second and third way of establishing the method, which I must not explain here. I can only say that we followed, with ever increasing interest, this distinguished lecture course in which several examples from the theory of definite integrals were also treated. It seemed to us that Gauss himself, despite previously lacking interest in giving the course, was now getting joy from his teaching activities. The course ended on 13 March when Gauss stood up, as we all did, and he dismissed us with some friendly words of farewell, "It only remains for me to thank you for the great regularity and attention with which you have followed my lectures, probably thought of as rather dry." A half century has passed since then but this lecture course which he claimed to be dry is unforgettable in my memory and is one of the finest I have ever heard.