Editing Carl Friedrich Gauss (section)

=== Youth and education ===
[[File:Braunschweig Brunswick Geburtshaus CF Gauss (1914).jpg|thumb|upright|Birthplace in Brunswick (destroyed in World War II)]]
[[File:Goe.Kurze.Geismarstr.Gauss.Wohnhaus.JPG|thumb|upright|Gauss's home as student in Göttingen]]
Gauss was born on 30 April 1777 in [[Braunschweig|Brunswick]] in the [[Duchy of Brunswick-Wolfenbüttel]] (now in the German state of [[Lower Saxony]]). His family was of relatively low social status.<ref>{{cite book | last = Borch | first = Rudolf | title = Ahnentafel des Mathematikers Carl Friedrich Gauß | trans-title = Ancestors' Tabel of the mathematician Carl Friedrich Gauss | series = Ahnentafeln Berühmter Deutscher | volume = 1 | publisher = Zentralstelle für Deutsche Personen- und Familiengeschichte | date = 1929 | pages = 63–65 | language = de}}</ref> His father Gebhard Dietrich Gauss (1744–1808) worked variously as a butcher, bricklayer, gardener, and treasurer of a death-benefit fund. Gauss characterized his father as honourable and respected, but rough and dominating at home. He was experienced in writing and calculating, whereas his second wife Dorothea, Carl Friedrich's mother, was nearly illiterate.{{sfn|Dunnington|2004|p=8}} He had one elder brother from his father's first marriage.{{sfn|Dunnington|2004|pp=8–9}}

Gauss was a [[child prodigy]] in mathematics. When the elementary teachers noticed his intellectual abilities, they brought him to the attention of the [[Charles William Ferdinand, Duke of Brunswick|Duke of Brunswick]] who sent him to the local ''Collegium Carolinum'',{{efn|The ''Collegium Carolinum'' was a preceding institution of the [[Technical University of Braunschweig]], but at Gauss's time not equal to a university.{{sfn|Dunnington|2004|p=17}}
}} which he attended from 1792 to 1795 with [[Eberhard August Wilhelm von Zimmermann]] as one of his teachers.{{sfn|Schlesinger|1933|p=10}}{{sfn|Dunnington|2004|p=14}}<ref name="Ullrich">{{cite book | last1 = Ullrich | first1 = Peter | editor-last = Mittler | editor-first = Elmar | title = "Wie der Blitz einschlägt, hat sich das Räthsel gelöst" – Carl Friedrich Gauß in Göttingen | publisher = Niedersächsische Staats- und Universitätsbibliothek | date = 2005 | series = Göttinger Bibliotheksschriften 30 | pages = 17–29 | chapter = Herkunft, Schul- und Studienzeit von Carl Friedrich Gauß | isbn = 3-930457-72-5 | language = de | url = http://webdoc.sub.gwdg.de/ebook/e/2005/gausscd/html/Katalog.pdf}}</ref> Thereafter the Duke granted him the resources for studies of mathematics, sciences, and [[Classics|classical languages]] at the [[University of Göttingen]] until 1798.<ref name="scientificmonthly">{{cite journal |last1=Dunnington |first1=Waldo |year=1927 |title=The Sesquicentennial of the Birth of Gauss |url=http://www.mathsong.com/cfgauss/Dunnington/1927/ |journal=[[The Scientific Monthly]] |volume=24 |issue=5 |pages=402–414 |bibcode=1927SciMo..24..402D |jstor=7912 |archive-url=https://web.archive.org/web/20080226020629/http://www.mathsong.com/cfgauss/Dunnington/1927/ |archive-date=26 February 2008}}  Also available at {{cite web |title=The Sesquicentennial of the Birth of Gauss |url=http://gausschildren.org/genwiki/index.php?title=The_Sesquicentennial_of_the_Birth_of_Gauss}} Retrieved 23 February 2014. Comprehensive biographical article.</ref> His professor in mathematics was [[Abraham Gotthelf Kästner]], whom Gauss called "the leading mathematician among poets, and the leading poet among mathematicians" because of his [[epigram]]s.{{sfn|Dunnington|2004|p=24}}{{efn|Once Gauss drew a lecture scene with professor Kästner producing errors in a simple calculation.<ref name="Ullrich" />}} Astronomy was taught by [[Karl Felix Seyffer]], with whom Gauss stayed in correspondence after graduation;{{sfn|Dunnington|2004|p=26}} [[Heinrich Wilhelm Matthias Olbers|Olbers]] and Gauss mocked him in their correspondence.<ref>{{cite book | last = Wattenberg | first = Diedrich | author-link = Diedrich Wattenberg | title = Wilhelm Olbers im Briefwechsel mit Astronomen seiner Zeit | publisher = GNT – Verlag für Geschichte der Naturwissenschaften und der Technik | date = 1994 | place = Stuttgart | page = 41 | isbn = 3-928186-19-1 | language = de}}</ref> On the other hand, he thought highly of [[Georg Christoph Lichtenberg]], his teacher of physics, and of [[Christian Gottlob Heyne]], whose lectures in classics Gauss attended with pleasure.{{sfn|Dunnington|2004|p=26}} Fellow students of this time were [[Johann Friedrich Benzenberg]], [[Farkas Bolyai]], and [[Heinrich Wilhelm Brandes]].{{sfn|Dunnington|2004|p=26}}

He was likely a self-taught student in mathematics since he independently rediscovered several theorems.<ref name="Ullrich" /> He solved a geometrical problem that had occupied mathematicians since the [[Ancient Greece|Ancient Greeks]] when he determined in 1796 which regular [[polygon]]s can be constructed by [[Compass and straightedge constructions|compass and straightedge]]. This discovery ultimately led Gauss to choose mathematics instead of [[philology]] as a career.{{sfn|Dunnington|2004|p=28}} Gauss's mathematical diary, a collection of short remarks about his results from the years 1796 until 1814, shows that many ideas for his mathematical magnum opus [[Disquisitiones Arithmeticae]] (1801) date from this time.{{sfn|Dunnington|2004|p=37}}

As an elementary student, Gauss and his class were tasked by their teacher, J.G. Büttner, to sum the numbers from 1 to 100. Much to Büttner's surprise, Gauss replied with the correct answer of 5050 in a vastly faster time than expected.<ref>{{Cite web |date=2017-02-06 |title=Gauss's Day of Reckoning |url=https://www.americanscientist.org/article/gausss-day-of-reckoning |access-date=2025-03-27 |website=American Scientist |language=en}}</ref> Gauss had realised that the sum could be rearranged as 50 pairs of 101 (1+100=101, 2+99=101, etc.). Thus, he simply multiplied 50 by 101.<ref>{{Cite book |last=Posamentier |first=Alfred S. |title=Math Makers: The Lives and Works of 50 Famous Mathematicians|pages=242–243|publisher=Prometheus Books|year=2019}}</ref> Other accounts state that he computed the sum as 100 sets of 101 and divided by 2.<ref>{{Cite web |title=The Story of Gauss - National Council of Teachers of Mathematics |url=https://www.nctm.org/Publications/TCM-blog/Blog/The-Story-of-Gauss/ |access-date=2025-03-27 |website=www.nctm.org}}</ref>