Editing Carl Friedrich Gauss (section)

=== Personality ===
==== Scholar ====
[[File:Carl Friedrich Gauß, Karikatur von Abraham Gotthelf Kästner, 1795.jpg|thumb|A student draws his professor of mathematics: Caricature of [[Abraham Gotthelf Kästner]] by Gauss (1795){{efn|Following Bolyai's handwritten Hungarian text at the bottom, Gauss intentionally characterized Kästner with the added the wrong addition.}}]]
[[File:Carl Friedrich Gauß, 003.jpg|thumb|upright|A student draws his professor of mathematics: Gauss sketched by his student [[Johann Benedict Listing]], 1830]]
In the first two decades of the 19th century, Gauss was the only important mathematician in Germany comparable to the leading French mathematicians.<ref name="Schubring">{{cite book | last1 = Schubring | first1 = Gert | editor-last1 = Fauvel | editor-first1 = John | editor-last2 = Flood | editor-first2 = Raymond | editor-last3 = Wilson | editor-first3 = Robin | editor-link1 = John Fauvel | editor-link2 = Raymond Flood (mathematician)| editor-link3 = Robin Wilson (mathematician) | title = Möbius and his band: Mathematics and Astronomy in Nineteenth-century Germany  | publisher = Oxford University Press | date = 1993 | pages = 21–33 | chapter = The German mathematical community}}</ref>  His ''Disquisitiones Arithmeticae'' was the first mathematical book from Germany to be translated into the French language.<ref>{{cite book | author-last = Schubring | author-first = Gert | title = Geschichte der Mathematik in ihren Kontexten | publisher = Birkhäuser| date = 2021 | pages = 133–134 | language = de}}</ref>

Gauss was "in front of the new development" with documented research since 1799, his wealth of new ideas, and his rigour of demonstration.{{sfn|Klein|1894|pp=100–101}} In contrast to previous mathematicians like [[Leonhard Euler]], who let their readers take part in their reasoning, including certain erroneous deviations from the correct path,{{sfn|Klein|1979|pp=5–6}} Gauss introduced a new style of direct and complete exposition that did not attempt to show the reader the author's train of thought.{{sfn|Dunnington|2004|p=217}}

{{blockquote|Gauss was the first to restore that ''rigor'' of demonstration which we admire in the ancients and which had been forced unduly into the background by the exclusive interest of the preceding period in ''new'' developments.|source={{harvnb|Klein|1894|p=101}} }}

But for himself, he propagated a quite different ideal, given in a letter to Farkas Bolyai as follows:<ref>{{Cite web|url=https://archive.org/details/briefwechselzwi00gausgoog/page/n124/mode/2up|title=Briefwechsel zwischen Carl Friedrich Gauss und Wolfgang Bolyai|first=Carl Friedrich Gauss|last=Farkas Bólyai|date=22 April 1899|publisher=B. G. Teubner|via=Internet Archive}}</ref>
{{blockquote|It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment. When I have clarified and exhausted a subject, then I turn away from it, in order to go into darkness again.|source={{harvnb|Dunnington|2004|p=416}} }}

His posthumous papers, his scientific [[Gauss's diary|diary]],<ref>{{cite journal | author-link1 = Felix Klein | editor-last = Klein | editor-first = Felix | title = Gauß' wissenschaftliches Tagebuch 1796–1814 | doi=10.1007/BF01449013 | year = 1903 | journal = [[Mathematische Annalen]] | volume = 57 | pages = 1–34 | s2cid = 119641638 | language = la, de | url = https://gdz.sub.uni-goettingen.de/id/PPN235181684_0057?tify=%7B%22pages%22%3A%5B8%2C9%5D%2C%22view%22%3A%22info%22%7D}} p. 2</ref> and short glosses in his own textbooks show that he empirically worked to a great extent.{{sfn|Bachmann|1922|pp=4–6}}{{sfn|Schlesinger|1933|p=18}} He was a lifelong busy and enthusiastic calculator, working extraordinarily quickly and checking his results through estimation. Nevertheless, his calculations were not always free from mistakes.{{sfn|Maennchen|1930|pp=64–65}} He coped with the enormous workload by using skillful tools.{{sfn|Maennchen|1930|pp=4–9}} Gauss used numerous [[mathematical table]]s, examined their exactness, and constructed new tables on various matters for personal use.<ref>{{cite book | last1 = Reich | first1 = Karin | editor-last = Mittler | editor-first = Elmar | title = "Wie der Blitz einschlägt, hat sich das Räthsel gelöst" – Carl Friedrich Gauß in Göttingen | publisher = Niedrsächsische Staats- und Universitätsbibliothek | date = 2005 | series = Göttinger Bibliotheksschriften 30 | pages = 73–86 | chapter = Logarithmentafeln – Gauß' "tägliches Arbeitsgeräth" | isbn = 3-930457-72-5 | language = de | url = http://webdoc.sub.gwdg.de/ebook/e/2005/gausscd/html/Katalog.pdf}}</ref> He developed new tools for effective calculation, for example the [[Gaussian elimination]].<ref>{{Citation | last1=Althoen | first1=Steven C. | last2=McLaughlin | first2=Renate | title=Gauss–Jordan reduction: a brief history | doi=10.2307/2322413 | year=1987 | journal=[[American Mathematical Monthly|The American Mathematical Monthly]] | issn=0002-9890 | volume=94 | issue=2 | pages=130–142 | jstor=2322413 | publisher=Mathematical Association of America}}</ref> Gauss's calculations and the tables he prepared were often more precise than practically necessary.{{sfn|Maennchen|1930|p=3}} Very likely, this method gave him additional material for his theoretical work.{{sfn|Maennchen|1930|pp=4–9}}{{sfn|Bachmann|1922|p=5}}

[[File:GaussSiegel1777-1855.png|thumb|upright|Gauss's [[Seal (emblem)|seal]] with his motto ''Pauca sed Matura'']]
Gauss was only willing to publish work when he considered it complete and above criticism. This [[perfectionism (psychology)|perfectionism]] was in keeping with the motto of his personal [[Seal (emblem)|seal]] {{lang|la|Pauca sed Matura}} ("Few, but Ripe"). Many colleagues encouraged him to publicize new ideas and sometimes rebuked him if he hesitated too long, in their opinion. Gauss defended himself by claiming that the initial discovery of ideas was easy, but preparing a presentable elaboration was a demanding matter for him, for either lack of time or "serenity of mind".<ref name="Biermann">{{Cite journal | last = Biermann | first = Kurt-R. | title = Über die Beziehungen zwischen C. F. Gauß und F. W. Bessel | journal = Mitteilungen der Gauß-Gesellschaft Göttingen | issue = 3 | pages = 7–20 | year = 1966 | language = de}}</ref> Nevertheless, he published many short communications of urgent content in various journals, but left a considerable literary estate, too.{{sfn|Klein|1979|p=29}}{{sfn|Dunnington|2004|pp=420–430}} Gauss referred to mathematics as "the queen of sciences" and arithmetics as "the queen of mathematics",{{sfn|Sartorius von Waltershausen|1856|p=79}} and supposedly once espoused a belief in the necessity of immediately understanding [[Euler's identity]] as a benchmark pursuant to becoming a first-class mathematician.<ref name="First-Class">{{cite book |last=Derbyshire |first=John |url=https://archive.org/details/primeobsessionbe00derb_0/page/202 |title=Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics |publisher=Joseph Henry Press |year=2003 |isbn=978-0-309-08549-6 |place=Washington, DC |page=202 |url-access=registration}}</ref>

On certain occasions, Gauss claimed that the ideas of another scholar had already been in his possession previously. Thus his concept of priority as "the first to discover, not the first to publish" differed from that of his scientific contemporaries.<ref name="Stigler">{{Cite journal | last = [[Stephen Stigler|Stigler]] | first = Stephen M. | title = Gauss and the Invention of Least Squares | journal = [[Annals of Statistics]] | volume = 9 | issue = 3 | pages = 465–474 | year = 1981| doi = 10.1214/aos/1176345451 | doi-access = free }}</ref> In contrast to his perfectionism in presenting mathematical ideas, his citations were criticized as negligent. He justified himself with an unusual view of correct citation practice: he would only give complete references, with respect to the previous authors of importance, which no one should ignore, but citing in this way would require knowledge of the history of science and more time than he wished to spend.<ref name="Biermann" />

==== Private man ====
Soon after Gauss's death, his friend Sartorius published the first biography (1856), written in a rather enthusiastic style. Sartorius saw him as a serene and forward-striving man with childlike modesty,{{sfn|Sartorius von Waltershausen|1856|p=102}} but also of "iron character"{{sfn|Sartorius von Waltershausen|1856|p=95}} with an unshakeable strength of mind.{{sfn|Sartorius von Waltershausen|1856|p=8}} Apart from his closer circle, others regarded him as reserved and unapproachable "like an [[Twelve Olympians|Olympian]] sitting enthroned on the summit of science".{{sfn|Wußing|1982|p=41}} His close contemporaries agreed that Gauss was a man of difficult character. He often refused to accept compliments. His visitors were occasionally irritated by his grumpy behaviour, but a short time later his mood could change, and he would become a charming, open-minded host.<ref name="Biermann" /> Gauss disliked polemic natures; together with his colleague [[Johann Friedrich Ludwig Hausmann|Hausmann]] he opposed to a call for [[Justus Liebig]] on a university chair in Göttingen, "because he was always involved in some polemic."{{sfn|Dunnington|2004|p=253}}

[[File:Göttingen, Kurze Straße 15, 001.jpg|thumb|Gauss's residence from 1808 to 1816 in the first floor]]
Gauss's life was overshadowed by severe problems in his family. When his first wife Johanna suddenly died shortly after the birth of their third child, he revealed the grief in a last letter to his dead wife in the style of an ancient [[threnody]], the most personal of his surviving documents.<ref>{{cite web | url = https://gauss.adw-goe.de/handle/gauss/2086 | title = Letter from Carl Friedrich Gauss to Johanna Gauss, 23. October 1809| website = Der komplette Briefwechsel von Carl Friedrich Gauss | date = 23 October 1809| publisher = Akademie der Wissenschaften zu Göttingen | access-date = 26 March 2023}}</ref>{{sfn| Dunnington|2004|pp=94–95}} His second wife and his two daughters suffered from [[tuberculosis]].{{sfn|Dunnington|2004|p=206, 374}} In a letter to [[Friedrich Wilhelm Bessel|Bessel]], dated December 1831, Gauss hinted at his distress, describing himself as "the victim of the worst domestic sufferings".<ref name="Biermann" />

Because of his wife's illness, both younger sons were educated for some years in [[Celle]], far from Göttingen. The military career of his elder son Joseph ended after more than two decades at the poorly paid rank of [[first lieutenant]], although he had acquired a considerable knowledge of geodesy. He needed financial support from his father even after he was married.<ref name="Gerardy" /> The second son Eugen shared a good measure of his father's talent in computation and languages but had a lively and sometimes rebellious character. He wanted to study philology, whereas Gauss wanted him to become a lawyer. Having run up debts and caused a scandal in public,<ref name="gausschildren">{{cite web | url = https://homepages.rootsweb.com/~schmblss/home/Letters/Gauss/1898-12-21.htm | title = Letter: Charles Henry Gauss to Florian Cajori – 21 December 1898 | access-date = 25 March 2023}}</ref> Eugen suddenly left Göttingen under dramatic circumstances in September 1830 and emigrated via Bremen to the United States. He wasted the little money he had taken to start, after which his father refused further financial support.<ref name="Gerardy" /> The youngest son Wilhelm wanted to qualify for agricultural administration, but had difficulties getting an appropriate education, and eventually emigrated as well. Only Gauss's youngest daughter Therese accompanied him in his last years of life.{{sfn|Dunnington|2004|p=374}}

In his later years Gauss habitually collected various types of useful or useless numerical data, such as the number of paths from his home to certain places in Göttingen or peoples' ages in days; he congratulated [[Alexander von Humboldt|Humboldt]] in December 1851 for having reached the same age as [[Isaac Newton]] at his death, calculated in days.{{sfn|Sartorius von Waltershausen|1856|p=71}}

Beyond his excellent knowledge of [[Latin]], he was also acquainted with modern languages. Gauss read both classical and modern literature, and English and French works in the original languages.{{sfn|Dunnington|2004|p=241}}{{efn|The first book he loaned from the university library in 1795 was the novel ''[[Clarissa; or, The History of a Young Lady|Clarissa]]'' from [[Samuel Richardson]].<ref>{{cite book | last1 = Reich | first1 = Karin | editor-last = Mittler | editor-first = Elmar | title = "Wie der Blitz einschlägt, hat sich das Räthsel gelöst" – Carl Friedrich Gauß in Göttingen | publisher = Niedrsächsische Staats- und Universitätsbibliothek | date = 2005 | series = Göttinger Bibliotheksschriften 30 | pages = 105–115 | chapter = Gauß' geistige Väter: nicht nur "summus Newton", sondern auch "summus Euler" | language = de | isbn = 3-930457-72-5 | url = http://webdoc.sub.gwdg.de/ebook/e/2005/gausscd/html/Katalog.pdf}}</ref>}} His favorite English author was [[Walter Scott]], his favorite German [[Jean Paul]]. At the age of 62, he began to teach himself [[Russian language|Russian]], very likely to understand scientific writings from Russia, among them those of [[Nikolai Lobachevsky|Lobachevsky]] on non-Euclidean geometry.<ref>{{cite book | last1 = Lehfeldt | first1 = Werner | author-link  = Werner Lehfeldt | editor-last = Mittler | editor-first = Elmar | title = "Wie der Blitz einschlägt, hat sich das Räthsel gelöst" – Carl Friedrich Gauß in Göttingen | publisher = Niedrsächsische Staats- und Universitätsbibliothek | date = 2005 | series = Göttinger Bibliotheksschriften 30 | pages = 302–310 | chapter = Carl Friedrich Gauß' Beschäftigung mit der russischen Sprache | language = de | isbn = 3-930457-72-5 | url = http://webdoc.sub.gwdg.de/ebook/e/2005/gausscd/html/Katalog.pdf}}</ref>{{sfn|Wußing|1982|p=80}} Gauss liked singing and went to concerts.{{sfn|Wußing|1982|p=81}} He was a busy newspaper reader; in his last years, he would visit an academic press salon of the university every noon.{{sfn|Sartorius von Waltershausen|1856|p=94}} Gauss did not care much for philosophy, and mocked the "splitting hairs of the so-called metaphysicians", by which he meant proponents of the contemporary school of ''[[Naturphilosophie]]''.{{sfn|Wußing|1982|p=79}}

Gauss had an "aristocratic and through and through conservative nature", with little respect for people's intelligence and morals, following the motto "[[Mundus vult decipi, ergo decipiatur|mundus vult decipi]]".{{sfn|Sartorius von Waltershausen|1856|p=94}} He disliked Napoleon and his system and was horrified by violence and revolution of all kinds. Thus he condemned the methods of the [[Revolutions of 1848]], though he agreed with some of their aims, such as that of a unified Germany.{{sfn|Sartorius von Waltershausen|1856|p=95}}{{efn|The political background was the confusing situation of the [[German Confederation]] with 39 nearly independent states, the sovereigns of three of them being Kings of other countries (Netherlands, Danmark, United Kingdom), whereas the [[Kingdom of Prussia]] and the [[Austrian Empire]] extended widely over the frontiers of the Confederation.}} He had a low estimation of the constitutional system and he criticized parliamentarians of his time for their perceived ignorance and logical errors.{{sfn|Sartorius von Waltershausen|1856|p=94}}

Some Gauss biographers have speculated on his religious beliefs. He sometimes said "God arithmetizes"{{sfn|Sartorius von Waltershausen|1856|p=97}} and "I succeeded – not on account of my hard efforts, but by the grace of the Lord."<ref>{{cite web | url = https://gauss.adw-goe.de/handle/gauss/731 | title = Letter from Carl Friedrich Gauss to Wilhelm Olbers, 3 September 1805| website = Der komplette Briefwechsel von Carl Friedrich Gauss | date = 23 October 1809| publisher = Akademie der Wissenschaften zu Göttingen | access-date = 26 March 2023}}</ref> Gauss was a member of the [[Lutheran church]], like most of the population in northern Germany, but it seems that he did not believe all Lutheran [[dogma]] or understand the Bible fully literally.{{sfn|Dunnington|2004|p=300}} According to Sartorius, Gauss' [[religious tolerance]],  "insatiable thirst for truth" and sense of justice were motivated by his religious convictions.{{sfn|Sartorius von Waltershausen|1856|p=100}}