Editing Carl Friedrich Gauss (section)

==== 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" />