Kupffer returned to Göttingen in mid-October to attend a Magnetic Congress at which Sabine90 of London, Lloyd91 of Dublin, and Steinheil92 of Munich were present. Mrs. Sabine, who had translated Gauss’ Allgemeine Theorie des Erdmagnetismus, accompanied her husband. The translation was made primarily for the use of army officers who were going on the Antarctic magnetic expedition.
In the last year of his life Gauss was annoyed several times by a religious crank, a Quedlinburg schoolteacher and doctor of theology named Carl Schöpffer. He delighted in attacking the Copernican system of astronomy and had delusions of persecution. On several occasions he reported miraculous escapes, claiming to have been in physical danger from his imagined foes. Schöpffer had received rather short shrift at the hands of Karl von Raumer, Encke, and Johann von Lamont.
Schöpffer went to Göttingen in the spring of 1854, having resolved to use the university library in his astronomical “research.” He founded a monthly magazine called Blätter der Wahrheit, which died after the ninth issue. Soon after his arrival in Göttingen Schöpffer got acquainted with Gauss, who treated him in a clever, yet friendly manner. Gauss gave him some books to read and told him to seek his advice whenever he believed he needed it. Alexander von Humboldt had also accorded him a friendly hearing.
Schöpffer recounted at great length the course of his previous rebuffs in opposing the Copernican system, at the same time mentioning as authority the names of several earlier astronomers and philosophers who had been on his side of the controversy. Gauss listened to the long harangue in silence, which Schöpffer fortunately interpreted as approval. Gauss was in poor health during his last year and did not feel able to argue with this fanatic who actually believed that Gauss had some doubts about the Copernican system. Humboldt had given him a shrewd answer by saying that if he could find some astronomer of repute to come out against the system, he (Humboldt) would immediately declare himself against it. When Gauss heard this alleged statement of his old friend, he merely answered: “If I were only twenty years younger!”
Schöpffer reported that he was subjected to arsenic poisoning in Göttingen and that one day on the street there he escaped injury from a nearby explosion.
The thirty-first annual convention of German scientists and physicians met in Göttingen September 18–23, 1854, Schöpffer attempted to get on the program in order to make another attack on the Copernican system. Three Göttingen professors, Baum, Listing, and Weber, were instrumental in keeping him off the program. Finally he planned to walk into the meeting and start speaking, mistakenly believing that he could count on the support of Gauss and Hausmann. On the way to the meeting he learned that Gauss was ill and could not attend and that Hausmann was out of the city on an unexpected journey. Thus Schöpffer had to drop his bold plan.
The entire episode ended when Schöpffer returned to Quedlinburg from Göttingen at Easter, 1855, soon after Gauss’ death.
XX
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The Doyen of German Science, 1832–1855
Heinrich Ewald married as his second wife on December 12, 1845, Auguste Schleiermacher (1822–1897), daughter of a prominent finance councilor and head librarian in Darmstadt.93 Gauss was quite pleased when his son-in-law wrote him of his engagement, and sent him a cordial letter of congratulation on October 30, in which he stated that he had long hoped Ewald would marry again, and realized how lonesome he must have been, for under similar circumstances he married in less than a year, whereas Ewald had been a widower five years. He reminded Ewald in the letter that he had corresponded with the bride’s uncle Ludwig Schleiermacher, author of a book on analytical optics, and had a high opinion of his scientific training.
In 1847 the King of Hanover restored the liberal constitution of 1833, and, at the earnest solicitation of the academic senate, an offer was made in 1848 to Ewald to return, on most generous terms, to the position from which he had been discharged ten years before. The offer was gladly accepted, for Ewald had never been quite happy in Tübingen, and he was a 100 per cent Hanoverian.
A daughter was born to Ewald on May 5, 1850, and she was given the name Caroline Therese Wilhelmine, Therese Gauss serving as godmother. At the christening Gauss, Ewald, Weber, and the others in the group played croquet on the lawn after they had drunk chocolate. Miss Ewald continued to live at her father’s old home in Göttingen until her death on May 5, 1917; she never married. She and her mother in later years often visited Joseph Gauss and family at his home on Wilhelmstrasse in Hanover. In July, 1859, Miss Ewald and her mother visited Therese Gauss at her home in Dresden. From 1848 to 1866 Ewald worked happily and assiduously at Göttingen, his death occurring there on May 4, 1875.
Gauss was again made happy in 1849 when Weber was called back to his professorship in Göttingen. But Gauss was too old to collaborate with him again on the brilliant research in which they had engaged more than a decade before. It cheered him to have his intimate friends visit him in the late afternoon and early evening hours. Just to have Ewald and Weber near meant much to him. At least two members of the Göttingen Seven had returned to the fold. Weber lived on to attain the ripe old age of eighty-seven, and died June 23, 1891. He was busy with his work in physics during most of his life, but so retired was his life in his last years that many scientists had forgotten he was still alive. Near the close of his life Weber’s memory failed. The guest book of the students’ mathematical club in Göttingen shows his name entered in January, 1891. Hermann Amandus Schwarz (1843–1921), who was professor of mathematics in Göttingen until 1892, had taken him to a meeting of the club. After his memory failed Weber used to express frequently the desire to return to Göttingen, and when he was told that he was actually in Göttingen there came the answer: “No, that is not the Göttingen of Gauss.”
Gauss was often sought out by young scientists recommended to him by Alexander von Humboldt. As he grew older he became more and more convinced that mathematics could be studied from books without a teacher. In his day many students were poorly prepared, and he complained repeatedly about this condition in his letters. He felt that his lectures must be worthy of himself and his science. This explains why he usually had only a handful of students at any time while several blocks away his colleague B. F. Thibaut (1775–1832) was lecturing to a hundred students on elementary mathematics. It was Gauss’ custom to announce the same courses year after year; there was very little variety. The result is that it is hardly possible to speak of a Gaussian School in mathematics. Distinguished mathematicians profited by his writings, but perhaps only one of them enjoyed the intimate relationship of pupil to teacher. That was Bernhard Riemann, and as a matter of fact he was already at the level of a master, probably one should include Eisenstein, who will be discussed shortly, and Dedekind on this list with Riemann.
On the other hand, it is correct to speak of a Gaussian School in astronomy, at least for a certain time. Schumacher led off in 1808, then in 1810, and soon thereafter came Encke, Gerling Möbius, and Nicolai, who sought and found theoretical and practical training at the Göttingen observatory.
Gauss always took a personal interest in his students. He was grieved that two of his gifted students died young. One of them, Johannes Friedrich Posselt, was born in 1794 as the son of a clergyman on the Danish island of Föhr. He served from 1819 until his death in 1823 as professor of mathematics at the University of Jena. Posselt was acquainted with Goethe through the latter’s official connections with the university.
Friedrich Ludwig Wachter was born in Cleve in 1792 as the son of a high school principal who was later transferred to Hamm in Westphalia. Wachter in his “vita” for the Göttingen faculty expressed thus his purpose in study: “not to burden the memory with many things, but to recognize the true reason of scholarship and to sharpen the intellect and to train judgment.” He specialized in astronomy under Gauss in 1810 and 1811 and even as a student published some astronomical calculations at the instigation of his teacher. For acquiring the doctor’s degree
in 1813 he Wanted to use a purely mathematical topic from the theory of curved surfaces. Meanwhile Wachter had been called to teach at the high school in Altenburg, on the basis of the splendid report of his examiners. Gauss and Thibaut were not among the examiners; the examination in mathematics was handled by Tobias Mayer, the physicist. Wachter had been admitted to the oral examination after he had promised to make up the dissertation. He had refused to defend theses because of inexperience in speaking Latin! The case of Gerling was mentioned as a precedent. This request was granted; it shows how progressive Göttingen was at that time in contrast to many other German universities, even in later decades. Wachter owed his job in Altenburg to Gauss, whose strong recommendation was enough to get it for him. His teaching in Altenburg was interrupted from November, 1813, to July, 1814, by army service.
Wachter’s dissertation, written after his return from the army, was on an astronomical subject; to it was attached a five-page note on the parallelogram of forces. The mysterious and tragic death of Wachter was discussed in Chapter XV.
Another pupil of Gauss, who name is still well known in mathematics for his work in synthetic geometry and the geometric interpretation of imaginary elements, was Karl Georg Christian von Staudt, who was born in 1798 in Rothenburg ob der Tauber and served as professor of mathematics at the University of Eriangen until his death there in 1867. A remark in a letter to Bessel on December 15, 1826, shows the high opinion Gauss had of von Staudt. During his stay of several years in Göttingen von Staudt felt that he was not only benefited by the master’s teaching, but also gladdened by his recognition and praise. Whenever von Staudt handed Gauss his solution of an assigned problem. Gauss would give the student his own solution, with the joking remark that he counted on mutual satisfaction.
In a letter on April 14, 1822, Bessel recommended to Gauss his pupil Heinrich Ferdinand Scherk, who was born in 1798 in Posen and went to Göttingen with financial support from the Prussian government. Gauss was highly pleased with Scherk and considered him one of the best pupils he ever had. Scherk’s later success justified Gauss’ praise. In 1826 he became professor of mathematics at the University of Halle, where he numbered among his students E. E. Kummer, who ranked as one of the leading mathematicians of the nineteenth century. In a sense, then, Gauss may be thought of as the mathematical grandfather of Kummer. Scherk was called in 1834 to Kiel, which was then Danish; his teaching there was highly successful, but he was too much of a German patriot and agitated for the founding of a German navy. In 1852 he lost his Kiel professorship through politics and took refuge in Bremen as a teacher in a public school, dying there in 1885.
H. B. Lübsen (1801–1864), a former Oldenburg petty officer, worked himself up by his own efforts and was very successful as a private teacher of mathematics in Hamburg. His textbooks for self-instruction in algebra and arithmetic went through many editions and were popular until recent times; they are said to have exerted great influence on young students. In the foreword to the first edition of a textbook94 on higher geometry, Lübsen wrote: “Theory, said my revered teacher Gauss, attracts practice as the magnet attracts iron.”
Another student of Gauss deserves mention, even though his name has almost been forgotten. Ludwig Christoph Schnürlein was born on April 14, 1792, in Ansbach as the son of an innkeeper. He was sickly from birth and could not be sent to school until the age of nine. After confirmation he thought of preparing for his father’s business. One Buzengeiger, who was then teaching at the high school in Ansbach and frequented the Schnürlein tavern, discovered the boy’s special talent for mathematics. He encouraged him to devote himself to this study, gave him private instruction and all manner of aid. On his recommendation Schnürlein was able to begin studies at the University of Tübingen at the age of twenty-seven (Easter, 1819), without having graduated from high school. In his fourth semester Schnürlein transferred to the University of Erlangen. Soon afterward he passed an examination in Munich with such brilliant success that he received from the Academy of Sciences for three years a stipend of five hundred florins, and was advised to study astronomy in Göttingen.
Schnürlein joyfully seized the opportunity and used it in the best possible manner. For him Gauss was a model of the teacher and the object of his highest reverence. In the Gauss Archive there is a letter from a high official to Gauss, in which Schnürlein is discussed and these words occur: Für Schnürlein sind Sie der liehe Gött. In the published Gauss correspondence occasional mention is made of Schnürlein’s comet calculations. In 1824 Schnürlein became assistant at the observatory in Bogenhausen. When this position was abolished after two years, he participated in Munich in a competitive examination for a teaching job in mathematics and physics; he got the grade of “excellent ability.” The same year he was appointed to the high school faculty in Erlangen, and in 1830 to the same job in Hof. There he was active for about twenty years and enjoyed great success, until his retirement, when he moved to Bamberg; his death occurred on November 7, 1859. In August, 1850, the University of Erlangen conferred the honorary doctorate on Schnürlein, at the instigation of von Staudt.
Schnürlein published an elementary calculation of the length of arc of the ellipse and hyperbola, relations among surfaces of the second order, extension and generalizations which are connected with Bernoulli’s numbers. He also published interpretations of Gauss’ methods for calculating the elements of the orbit of a comet.
One of Gauss’ prominent students was Justus Georg Westphal, who was born on March 18, 1824, in Colborn near Luchow in Hanover, studied in Göttingen, and was assistant at the observatory 1851–1855, having been appointed lecturer in 1854. His dissertation was Evolutio radicum aequationum algebraicarum e ternis terminis constantium in series infinitas (1850). He discovered the Comet 1852 III on July 24, observed solar and lunar eclipses, star occultations, comets, and asteroids. Westphal left Göttingen in the fall of 1855 and died on November 9, 1859, in Lüneburg.
No discussion of Gauss’ students would be complete without mention of Moritz A. Stern, who was born in Frankfurt am Main on June 28, 1807, took his doctorate in Göttingen in 1829, and served on the mathematics faculty there from 1829 until his retirement in 1884. Stern died on January 30, 1894, in Zurich. He published extensively both in mathematics and astronomy. His address at the Gauss centenary in 1877 contained much valuable information and was well received.
A name frequently connected with Gauss in the late nineteenth century was that of Ernst Christian Julius Schering, who was born on July 13, 1833, in Sandbergen, northeast of Lüneburg. In 1852 he went to Göttingen, where he studied under Gauss, Weber, and later Dirichlet. In 1857 he took his doctorate with the dissertation Zur mathematischen Theorie elektrischer Ströme and in 1858 was appointed lecturer with a paper Ueber die conforme Abbildung des Ellipsoids auf der Ebene. Schering married Maria Malmsten (1848–1920), daughter of a mathematician and diplomat in Stockholm. He edited the first six volumes of the Collected Works of Gauss, and made them models of perfection; he had the advantage of personal association as a young man with Gauss and was very versatile. His widow placed his papers at the disposal of his successors in the editorship of the Gauss Collected Works. Schering served on the Göttingen faculty from 1858 until his death on November 2, 1897. He published works in mathematics and astronomy, as well as two important monographs on Gauss.
The last of Gauss’ students who achieved fame in astronomy was Friedrich August Theodor Winnecke (1835–1897), who studied in Göttingen from 1853 to 1856. He served as director of the observatory in Strassburg from 1872 to 1886. Winnecke investigated the paths of double stars and comets and made determinations of the solar parallax. He published a splendid pamphlet on Gauss at the time of the centenary, in 1877, in which he gave many interesting glimpses of the master in his last years. The pamphlet was in the popular style.
Ernst Wilhelm Gustav von Quintus Icilius (1824–1885) studied Under Gauss and served from 1849 to 1853 on the Göttingen faculty. He then ser
ved as professor of physics at the Polytechnic Institute in Hanover. Gauss considered his dissertation Die Atomgewichte vom Palladium, Thallium, Chlor, Silber, Kohlenstoff, und Wasserstoff nach der Methode der Kleinsten Quadrate berechnet (1847) only an exercice de collège and forced him to cut out of it some material which was contrary to the method of least squares. The reader may wonder how the poor fellow got the name of Quintus Icilius. Guichard was originally the family name. Colonel Karl Gottlieb Guichard had dared to correct Frederick the Great when he once erroneously called the Roman centurion Icilius by the name “Ilicius.” Old Fritz forced the colonel to attach the two Latin names to his own.
Two other students of Gauss should be mentioned in passing, men who have not been entirely forgotten. The first was Theodor Wittstein,95 who later served on the faculty at the Polytechnic Institute in Hanover. The other was Alfred Enneper (1830–1885), who served on the Göttingen faculty from 1859 until his death. He was regarded as a capable mathematician and published extensively.
Among the mechanics who furnished instruments to Gauss was Moritz Meyerstein (1808–1882), who came from the neighboring town of Einbeck. He was the owner of a large mechanical workshop, and Göttingen conferred an honorary doctorate on him. His successor was August Becker, who was born October 23, 1838, in Göttingen.
Gauss’ own records show that he took in 2,267 thalers in student fees from 1808 to 1821. In 1845 they amounted to 422 thalers. During his last years of teaching, 1846–1853, Gauss had a total of 790 thalers; 67 paid promptly, 4 were free, and 15 paid some time later.
In his lectures Gauss frequently liked to have examples calculated, and assigned problems whose results he sometimes published. He had many calculations carried out by Gerling, Nicolai, Encke, and others, so that in a letter to Encke Nicolai once congratulated him on the completion of a little example in calculating (the preliminary calculation of the orbit of Pallas)—a problem which Gauss had assigned him as a problem.
Carl Friedrich Gauss, Titan of Science_A Study of His Life and Work Page 31