View source for Carl Friedrich Gauss

{{Infobox_Scientist
| name =Johann Carl Friedrich Gauss
| box_width = 300px
| image = Carl Friedrich Gauss.jpg | caption = Carl Friedrich Gauss, painted by [[Christian Albrecht Jensen]]
| image_width = 230px
| birth_date = {{birth date|1777|4|30|df=y}}
| birth_place = [[Braunschweig]], [[Electorate of Brunswick-Lüneburg]], [[Holy Roman Empire]]
| death_date = {{death date and age|1855|2|23|1777|4|30|df=y}}
| death_place = [[Göttingen]], [[Kingdom of Hanover]]
| residence =  [[Image:Flag of Hanover 1837-1866.svg|20px|]] [[Kingdom of Hanover|Hanover]] 
| nationality = [[Germans|German]]
| field = [[Mathematics|Mathematician]] and [[Physics|physicist]]
| work_institutions = [[University of Göttingen]]
| alma_mater = [[University of Helmstedt]]
| doctoral_advisor = [[Johann Friedrich Pfaff]]
| doctoral_students =[[Friedrich Bessel]]<br>[[Christoph Gudermann]]<br>[[Christian Ludwig Gerling]]<br>[[Richard Dedekind]]<br>[[Johann Franz Encke|Johann Encke]]<br>[[Johann Benedict Listing|Johann Listing]]<br>[[Bernhard Riemann]]<br>[[Christian Heinrich Friedrich Peters]]
| known_for  = [[Number theory]]</br> [[List of topics named after Carl Friedrich Gauss|The Gaussian]]</br>[[Magnetism]] 
| prizes = [[Copley Medal]] (1838)
| religion = 
| footnotes = 
}}
'''Johann Carl Friedrich Gauss''' ({{IPAEng|ˈɡaʊs}}, {{audio|De-carlfriedrichgauss.ogg|Audio}}, {{lang-de|Gauß}}, {{lang-la|Carolus Fridericus Gauss}}) ([[30 April]] [[1777]] – [[23 February]] [[1855]]) was a [[Germans|German]] [[mathematician]] and [[scientist]] who contributed significantly to many fields, including [[number theory]], [[statistics]], [[mathematical analysis|analysis]], [[Differential geometry and topology|differential geometry]], [[geodesy]], [[electrostatics]], [[astronomy]], and [[optics]]. Sometimes known as the ''princeps mathematicorum''<ref>{{cite book
 | last = Zeidler
 | first = Eberhard
 | title = Oxford User's Guide to Mathematics
 | location = Oxford, UK
 | publisher = Oxford University Press
 | date = 2004
 | id = ISBN 0198507631
 | page = 1188
 }}</ref> ([[Latin]], usually translated as "the Prince of Mathematicians", although Latin ''princeps'' also can simply mean "the foremost") and "greatest mathematician since antiquity", Gauss had a remarkable influence in many fields of mathematics and science and is ranked as one of history's most influential mathematicians.<ref name="scientificmonthly">Dunnington, G. Waldo. (May, 1927). "[http://www.mathsong.com/cfgauss/Dunnington/1927/ The Sesquicentennial of the Birth of Gauss]". ''Scientific Monthly'' XXIV: 402–414. Retrieved on 29 June 2005. Comprehensive biographical article.</ref> 

Gauss was a [[child prodigy]], of whom there are many [[anecdote]]s pertaining to his astounding precocity while a mere toddler, and made his first ground-breaking mathematical discoveries while still a teenager. He completed ''[[Disquisitiones Arithmeticae]]'', his [[magnum opus]], in 1798 at the age of 21, though it would not be published until 1801. This work was fundamental in consolidating number theory as a discipline and has shaped the field to the present day.

== Early years (1777&ndash;1798) ==

[[Image:Statue-of-Gauss-in-Braunschweig.jpg|left|thumb|Statue of Gauss in his birthplace of Braunschweig]]

Gauss was born in [[Braunschweig]], in the [[Electorate of Brunswick-Lüneburg]], now part of [[Lower Saxony]], [[Germany]], as the only son of poor working-class parents.<ref>{{cite web |url= http://www.math.wichita.edu/history/men/gauss.html|title= Carl Friedrich Gauss|accessmonthday= |accessyear= |last= |first= |date= |work= |publisher=Wichita State University }}</ref> There are several stories of his early genius, all of them open to doubt; according to one, his gifts became very apparent at the age of three when he corrected, in his head, an error his father had made on paper while calculating finances. 

Another famous story, and one that has evolved in the telling, has it that in [[primary school]] his teacher, J.G. Büttner, tried to occupy pupils by making them add a list of [[integer]]s. The young Gauss reputedly produced the correct answer within seconds, to the astonishment of his teacher and his assistant [[Johann Christian Martin Bartels|Martin Bartels]]. Gauss' presumed method, which supposes the list of numbers was from 1 to 100, was to realise that pairwise addition of terms from opposite ends of the list yielded identical intermediate sums: 1 + 100 = 101, 2 + 99 = 101, 3 + 98 = 101, and so on, for a total sum of 50 × 101 = 5050 (''see [[Arithmetic progression|arithmetic series]] and [[summation]]'').<ref>http://www.americanscientist.org/template/AssetDetail/assetid/50686?&print=yes for discussion of original [[Wolfgang Sartorius von Waltershausen]] source.</ref> However whilst the method works, the incident itself is probably [[apocryphal]]; some, such as Joseph Rotman in his book ''A first course in Abstract Algebra'', question whether it ever happened.

His father had wanted him to follow in his footsteps and become a [[Freemasonry|mason]]. He was not supportive of Gauss's schooling in mathematics and science. Gauss was primarily supported by his mother in this effort and by the [[Charles William Ferdinand, Duke of Brunswick|Duke of Braunschweig]],<ref name="scientificmonthly"/> who awarded Gauss a fellowship to the Collegium Carolinum (now [[Technical University at Brunswick|Technische Universität Braunschweig]]), which he attended from 1792 to 1795, from where he moved to the [[Georg-August University of Göttingen|University of Göttingen]] from 1795 to 1798. While in university, Gauss independently rediscovered several important theorems;{{fact|date=July 2007}} his breakthrough occurred in 1796 when he was able to show that any regular [[polygon]] with a number of sides which is a [[Fermat number|Fermat prime]] (and, consequently, those polygons with any number of sides which is the product of distinct Fermat primes and a [[exponentiation|power]] of 2) can be constructed by [[Compass and straightedge constructions|compass and straightedge]]. This was a major discovery in an important field of mathematics; construction problems had occupied mathematicians since the days of the [[Ancient Greece|Ancient Greeks]], and the discovery ultimately led Gauss to choose mathematics instead of [[philology]] as a career. Gauss was so pleased by this result that he requested that a regular [[heptadecagon]] be inscribed on his [[Headstone|tombstone]]. The [[stonemasonry|stonemason]] declined, stating that the difficult construction would essentially look like a circle.

The year 1796 was most productive for both Gauss and number theory. He discovered a construction of the [[heptadecagon]] on March 30.<ref>'''Carl Friedrich Gauss''' §§365-366 in [[Disquisitiones Arithmeticae]]. Leipzig, Germany, 1801. New Haven, CT: Yale University Press, 1965.</ref> He invented [[modular arithmetic]], greatly simplifying manipulations in number theory. He became the first to prove the [[quadratic reciprocity]] law on [[April 8]]. This remarkably general law allows mathematicians to determine the solvability of any quadratic equation in modular arithmetic. The [[prime number theorem]], conjectured on [[May 31]], gives a good understanding of how the [[prime number]]s are distributed among the integers. Gauss also discovered that every positive integer is representable as a sum of at most three [[triangular number]]s on [[July 10]] and then jotted down in his diary the famous words, "[[Eureka (word)|Heureka]]! num = <math>\Delta+\Delta+\Delta</math>." On [[October 1]] he published a result on the number of solutions of polynomials with coefficients in [[finite field]]s, which ultimately led to the [[Weil conjectures]] 150 years later.

== Middle years (1799&ndash;1830) ==

In his 1799 doctorate ''in absentia'', ''A new proof of the theorem that every integral rational algebraic function of one variable can be resolved into real factors of the first or second degree'', Gauss proved the [[fundamental theorem of algebra]] which states that every non-constant single-variable [[polynomial]] over the [[complex number]]s has at least one [[root (mathematics)|root]]. Mathematicians including [[Jean le Rond d'Alembert]] had produced false proofs before him, and Gauss's dissertation contains a critique of d'Alembert's work. Ironically, by today's standard, Gauss's own attempt is not acceptable, owing to implicit use of the [[Jordan curve theorem]]. However, he subsequently produced three other proofs, the last one in 1849 being generally considered rigorous. His attempts clarified the concept of complex numbers considerably along the way.

Gauss also made important contributions to [[number theory]] with his 1801 book ''[[Disquisitiones Arithmeticae]]'' ([[Latin]], Arithmetical Investigations), which contained a clean presentation of [[modular arithmetic]] and the first proof of the law of [[quadratic reciprocity]]. In that same year, [[Italy|Italian]] astronomer [[Giuseppe Piazzi]] discovered the [[dwarf planet]] [[Ceres (dwarf planet)|Ceres]], but could only watch it for a few days. [[Image:Disqvisitiones-800.jpg|thumb|Title page of Gauss's ''Disquisitiones Arithmeticae'']]Gauss predicted correctly the position at which it could be found again, and it was rediscovered by [[Franz Xaver von Zach]] on [[December 31]], [[1801]] in [[Gotha (town)|Gotha]], and one day later by [[Heinrich Wilhelm Matthäus Olbers|Heinrich Olbers]] in [[Bremen]]. Zach noted that "without the intelligent work and calculations of Doctor Gauss we might not have found Ceres again." Though Gauss had been up to that point supported by the stipend from the Duke, he doubted the security of this arrangement, and also did not believe pure mathematics to be important enough to deserve support. Thus he sought a position in astronomy, and in 1807 was appointed Professor of Astronomy and Director of the astronomical observatory in [[Göttingen]], a post he held for the remainder of his life.

The discovery of Ceres by Piazzi on [[January 1]], [[1801]] led Gauss to his work on a theory of the motion of planetoids disturbed by large planets, eventually published in 1809 under the name ''Theoria motus corporum coelestium in sectionibus conicis solem ambientum'' (theory of motion of the celestial bodies moving in conic sections around the sun). Piazzi had only been able to track Ceres for a couple of months, following it for three degrees across the night sky. Then it disappeared temporarily behind the glare of the Sun. Several months later, when Ceres should have reappeared, Piazzi could not locate it: the mathematical tools of the time were not able to extrapolate a position from such a scant amount of data—three degrees represent less than 1% of the total orbit.

Gauss, who was 23 at the time, heard about the problem and tackled it. After three months of intense work, he predicted a position for Ceres in December 1801—- just about a year after its first sighting—and this turned out to be accurate within a half-degree. In the process, he so streamlined the cumbersome mathematics of 18th century orbital prediction that his work—- published a few years later as ''Theory of Celestial Movement''—- remains a cornerstone of astronomical computation.{{fact|date=July 2007}} It introduced the [[Gaussian gravitational constant]], and contained an influential treatment of the [[Least squares|method of least squares]], a procedure used in all sciences to this day to minimize the impact of [[Observational error|measurement error]]. Gauss was able to prove the method in 1809 under the assumption of [[normal distribution|normally distributed]] errors (see [[Gauss–Markov theorem]]; see also [[List of topics named after Carl Friedrich Gauss|Gaussian]]). The method had been described earlier by [[Adrien-Marie Legendre]] in 1805, but Gauss claimed that he had been using it since 1795.{{fact|date=July 2007}}
[[Image:Bendixen - Carl Friedrich Gauß, 1828.jpg|thumb|Gauss' portrait published in ''Astronomische Nachrichten'' 1828]]

Gauss was a prodigious [[mental calculator]]. Reputedly, when asked how he had been able to predict the trajectory of Ceres with such accuracy he replied, "I used [[logarithm]]s." The questioner then wanted to know how he had been able to look up so many numbers from the tables so quickly. "Look them up?" Gauss responded. "Who needs to look them up? I just calculate them in my head!"

In 1818 Gauss, putting his calculation skills to practical use, carried out a [[surveying|geodesic survey]] of the state of [[Kingdom of Hanover|Hanover]], linking up with previous [[Denmark|Danish]] surveys. To aid in the survey, Gauss invented the [[heliotrope (instrument)|heliotrope]], an instrument that uses a mirror to reflect sunlight over great distances, to measure positions.

Gauss also claimed to have discovered the possibility of [[non-Euclidean geometry|non-Euclidean geometries]] but never published it. This discovery was a major paradigm shift in mathematics, as it freed mathematicians from the mistaken belief that Euclid's axioms were the only way to make geometry consistent and non-contradictory. Research on these geometries led to, among other things, [[Albert Einstein|Einstein]]'s theory of general relativity, which describes the universe as non-Euclidean. His friend [[Farkas Bolyai|Farkas Wolfgang Bolyai]] with whom Gauss had sworn "brotherhood and the banner of truth" as a student had tried in vain for many years to prove the parallel postulate from Euclid's other axioms of geometry. Bolyai's son, [[János Bolyai]], discovered non-Euclidean geometry in 1829; his work was published in 1832. After seeing it, Gauss wrote to Farkas Bolyai: ''"To praise it would amount to praising myself. For the entire content of the work... coincides almost exactly with my own meditations which have occupied my mind for the past thirty or thirty-five years."'' This unproved statement put a strain on his relationship with János Bolyai (who thought that Gauss was "stealing" his idea), but it is now generally taken at face value.{{fact|date=July 2007}} Letters by Gauss years before 1829 reveal him obscurely discussing the problem of parallel lines. [[G. Waldo Dunnington|Waldo Dunnington]], a life-long student of Gauss, successfully proves in ''Gauss, Titan of Science'' that Gauss was in fact in full possession of non-Euclidian geometry long before it was published by János, but that he refused to publish any of it because of his fear of controversy.

[[Image:Normal distribution pdf.png|thumb|240px|left|Four [[normal distribution|Gaussian distributions]] in [[statistics]]]]

The survey of Hanover fueled Gauss's interest in [[Differential geometry and topology|differential geometry]], a field of mathematics dealing with [[curve]]s and [[surface]]s. This led in 1828 to an important theorem, the [[Theorema Egregium]] (''remarkable theorem'' in [[Latin]]), establishing an important property of the notion of [[curvature]]. Informally, the theorem says that the curvature of a surface can be determined entirely by measuring [[angle]]s and [[distance]]s on the surface. That is, curvature does not depend on how the surface might be [[embedding|embedded]] in 3-dimensional space.

== Later years and death (1831&ndash;1855) ==

[[Image:Göttingen-Grave.of.Gauß.06.jpg|thumb|right|Grave of Gauss at [[Albanifriedhof]]]]

In 1831 Gauss developed a fruitful collaboration with the physics professor [[Wilhelm Eduard Weber|Wilhelm Weber]], leading to new knowledge in [[magnetism]] (including finding a representation for the unit of magnetism in terms of mass, length and time) and the discovery of [[Kirchhoff's circuit laws]] in electricity. They constructed the first [[Electrical telegraph|electromagnetic telegraph]] in 1833, which connected the observatory with the institute for physics in Göttingen. Gauss ordered a magnetic [[observatory]] to be built in the garden of the observatory, and with Weber founded the [[magnetischer Verein]] (''magnetic club'' in [[German language|German]]), which supported measurements of earth's magnetic field in many regions of the world. He developed a method of measuring the horizontal intensity of the magnetic field which has been in use well into the second half of the 20th century and worked out the mathematical theory for separating the inner ([[planetary core|core]] and [[Crust (geology)|crust]]) and outer ([[magnetosphere|magnetospheric]]) sources of Earth's magnetic field.

Gauss died in Göttingen, [[Kingdom of Hanover|Hanover]] (now part of [[Lower Saxony]], Germany) in 1855 and is interred in the cemetery [[Albanifriedhof]] there. Two individuals gave eulogies at his funeral, Gauss's son-in-law [[Heinrich Ewald]] and [[Wolfgang Sartorius von Waltershausen]], who was Gauss's close friend and biographer. His brain was preserved and was studied by [[Rudolf Wagner]] who found its weight to be 1,492 grams and the cerebral area equal to 219,588 square centimeters (236.363 square feet). Highly developed convolutions were also found, which in the early 20th century was suggested as the explanation of his genius.<ref>Dunnington, 1927</ref>

==Family==
Gauss's personal life was overshadowed by the early death of his first wife, Johanna Osthoff, in 1809, soon followed by the death of one child, Louis. Gauss plunged into a [[Clinical depression|depression]] from which he never fully recovered. He married again, to Johanna's best friend named Friederica Wilhelmine Waldeck but commonly known as Minna. This second marriage does not seem to have been very happy as it was plagued by Minna's continuous illness.{{fact|date=July 2007}} When his second wife died in 1831 after a long illness,<ref>[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Gauss.html Gauss biography<!-- Bot generated title -->]</ref> one of his daughters, Therese, took over the household and cared for Gauss until the end of his life. His mother lived in his house from 1817 until her death in 1839.<ref name="scientificmonthly"/>

Gauss had six children. With Johanna (1780–1809), his children were Joseph (1806–1873), Wilhelmina (1808–1846) and Louis (1809–1810). Of all of Gauss's children, Wilhelmina was said to have come closest to his talent, but she died young. With Minna Waldeck he also had three children: Eugene (1811–1896), Wilhelm (1813–1879) and Therese (1816–1864). Eugene emigrated to the [[United States]] about 1832 after a falling out with his father, eventually settling in [[Saint Charles, Missouri|St. Charles]], [[Missouri]], where he became a well-respected member of the community.{{fact|date=July 2007}} Wilhelm also settled in Missouri, starting as a [[farmer]] and later becoming wealthy in the shoe business in [[St. Louis, Missouri|St. Louis]]. Therese kept house for Gauss until his death, after which she married.

Gauss eventually had conflicts with his sons, two of whom migrated to the United States. He did not want any of his sons to enter mathematics or science for "fear of sullying the family name". His conflict with Eugene was particularly bitter.{{fact|date=July 2007}} Gauss wanted Eugene to become a [[lawyer]], but Eugene wanted to study languages. They had an argument over a party Eugene held, which Gauss refused to pay for. The son left in anger and emigrated to the United States, where he was quite successful. It took many years for Eugene's success to counteract his reputation among Gauss's friends and colleagues. See also [[s:Robert Gauss to Felix Klein - September 3, 1912|the letter from Robert Gauss to Felix Klein]] on [[September 3]], [[1912]].

==Personality==
Gauss was an ardent [[perfectionism (psychology)|perfectionist]] and a hard worker. According to [[Isaac Asimov]], Gauss was once interrupted in the middle of a problem and told that his wife was dying. He is purported to have said, "Tell her to wait a moment till I'm done."<ref>{{cite book
 | last = Asimov | first = I.
 | title = Biographical Encyclopedia of Science and Technology; the Lives and Achievements of 1195 Great Scientists from Ancient Times to the Present, Chronologically Arranged.
 | location = New York
 | publisher = Doubleday
 | date = 1972
 }}</ref> This anecdote is briefly discussed in Waldo Dunnington's ''Gauss, Titan of Science'' where it is suggested that it is an apocryphal story. 

He was never a prolific writer, refusing to publish works which he did not consider complete and above criticism. This was in keeping with his personal motto ''pauca sed matura'' (few, but ripe). A study of his personal diaries reveals that he had in fact discovered several important mathematical concepts years or decades before they were published by his contemporaries.  Mathematical historian [[Eric Temple Bell]] estimated that had Gauss made known all of his discoveries, mathematics would have been advanced by 50 years.<ref>{{cite book
 | last = Bell | first = E. T.
 | chapter = Ch. 14: The Prince of Mathematicians: Gauss
 | title = Men of Mathematics: The Lives and Achievements of the Great Mathematicians from Zeno to Poincaré
 | location = New York
 | publisher = Simon and Schuster
 | pages = pp. 218–269
 | date = 1986
 | id = ISBN 0-671-46400-0
 }}</ref>

A criticism of Gauss is that he did not support the younger mathematicians who followed him. He rarely, if ever, collaborated with other mathematicians and was considered aloof and austere by many.{{fact|date=July 2007}} Though he did take in a few students, Gauss was known to dislike teaching. It is said that he attended only a single scientific conference, which was in [[Berlin]] in 1828. However, several of his students became influential mathematicians, among them [[Richard Dedekind]], [[Bernhard Riemann]], and [[Friedrich Bessel]]. Before she died, [[Sophie Germain]] was recommended by Gauss to receive her honorary degree.

Gauss usually declined to present the intuition behind his often very elegant proofs—-he preferred them to appear "out of thin air" and erased all traces of how he discovered them.{{fact|date=July 2007}} This is fully, however briefly, explained by Gauss himself in his "Disquisitiones Arithmeticae", where he states that all analysis (i.e. the paths one travelled to reach the solution of a problem) must be suppressed for sake of brevity.

Gauss was deeply religious and conservative.{{fact|date=July 2007}} He supported monarchy and opposed [[Napoleon I of France|Napoleon]], whom he saw as an outgrowth of [[revolution]].

== Commemorations ==

<!-- Image with inadequate rationale removed: [[Image:1993-DM-10.jpg|frame|A 10 [[Deutsche Mark]] [[banknote]] from Germany 1993 showing Gauss]] -->

The [[Centimetre gram second system of units|CGS]] [[units of measurement|unit]] for [[Faraday's law of induction|magnetic induction]] was named [[Gauss (unit)|gauss]] in his honour.

From 1989 until the end of 2001, his portrait and a normal distribution curve as well as some prominent buildings of [[Göttingen]] were featured on the German ten-mark banknote. The other side of the note features the [[Heliotrope (instrument)|heliotrope]] and a [[triangulation]] approach for [[Kingdom of Hanover|Hanover]]. Germany has issued three stamps honouring Gauss, as well. A righteous stamp (no. 725), was issued in 1955 on the hundredth anniversary of his death; two other stamps, no. 1246 and 1811, were issued in 1977, the 200th anniversary of his birth.

In 2007, his [[Bust (sculpture)|bust]] was introduced to the [[Walhalla temple]].<ref>http://www.stmwfk.bayern.de/downloads/aviso/2004_1_aviso_48-49.pdf</ref>

Places, vessels and events named in honour of Gauss:

* [[Gauss (crater)|Gauss crater]] on the [[Moon]]<ref>Andersson, L. E.; Whitaker, E. A., (1982). NASA Catalogue of Lunar Nomenclature. NASA RP-1097.</ref>
* [[Asteroid]] [[1001 Gaussia]].
* The ship ''[[Gauss (ship)|Gauss]]'', used in the [[Gauss expedition]] to the Antarctic.
* [[Gaussberg]], an extinct volcano discovered by the above mentioned expedition
* [[Gauss Tower]], an observation tower
* In Canadian junior high schools, an annual national mathematics competition administered by the [[Centre for Education in Mathematics and Computing]] is named in honour of Gauss.
* In [[Crown College, University of California, Santa Cruz|University of California, Santa Cruz, in Crown College]], a dormitory building is named after Gauss.
* The Gauss Haus, an [[Nuclear magnetic resonance|NMR]] center at the [[University of Utah]].
* The Carl-Friedrich-Gauß School for Mathematics, Computer Science, Business Administration, Economics, and Social Sciences of [[Technical University at Brunswick|University of Braunschweig]]

==See also==
*[[List of topics named after Carl Friedrich Gauss]]

==References==
===Notes===
{{reflist|2}}
== Writings ==
* 1799: [[Doctoral dissertation]] on the [[Fundamental theorem of algebra]], with the title: ''Demonstratio nova theorematis omnem functionem algebraicam rationalem integram unius variabilis in factores reales primi vel secundi gradus resolvi posse'' ("New proof of the theorem that every integral algebraic function of one variable can be resolved into real factors [i.e. polynomials] of the first or second degree")
* 1801: ''Disquisitiones Arithmeticae'', online at [http://gallica.bnf.fr/Catalogue/noticesInd/FRBNF37264814.htm]
* 1809: ''Theoria Motus Corporum Coelestium in sectionibus conicis solem ambientium'' (Theorie der Bewegung der Himmelskörper, die die Sonne in Kegelschnitten umkreisen), online at [http://gallica.bnf.fr/Catalogue/noticesInd/FRBNF37258151.htm] English translation by C. H. Davis, reprinted 1963, Dover, New York.
* 1821, 1823 und 1826: ''Theoria combinationis observationum erroribus minimis obnoxiae''. Drei Abhandlungen betreffend die Wahrscheinlichkeitsrechnung als Grundlage des Gauß'schen Fehlerfortpflanzungsgesetzes. English translation by G. W. Stewart, 1987, Society for Industrial Mathematics. 
* 1827: ''[http://dz-srv1.sub.uni-goettingen.de/contentserver/contentserver?command=docconvert&docid=D234039 Disquisitiones generales circa superficies curvas]'' (Allgemeine Untersuchung über gekrümmte Flächen), [http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN35283028X_0006_2NS Commentationes Societatis Regiae Scientiarum Gottingesis Recentiores. Volumen VI], S. 99-146
* 1843/44: ''[http://dz-srv1.sub.uni-goettingen.de/contentserver/contentserver?command=docconvert&docid=D39018 Untersuchungen über Gegenstände der Höheren Geodäsie. Erste Abhandlung]'', [http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN250442582_0002 Abhandlungen der Königlichen Gesellschaft der Wissenschaften in Göttingen. Zweiter Band], S. 3-46
* 1846/47: ''[http://dz-srv1.sub.uni-goettingen.de/contentserver/contentserver?command=docconvert&docid=D39036 Untersuchungen über Gegenstände der Höheren Geodäsie. Zweite Abhandlung]'', [http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN250442582_0003 Abhandlungen der Königlichen Gesellschaft der Wissenschaften in Göttingen. Dritter Band], S. 3-44
* ''Mathematisches Tagebuch 1796–1814'', Ostwaldts Klassiker, Harri Deutsch Verlag 2005, mit Anmerkungen von Neumamn, ISBN 978-3-8171-3402-1 (es gibt auch engl. Übers. mit Anmerkungen von Jeremy Gray, Expositiones Math. 1984)

Die Gesammelten Werke von Gauß are online here: [http://dz-srv1.sub.uni-goettingen.de/cache/toc/D38910.html]. 
This includes German translations of Latin texts and commentaries by various authorities

==Further reading==
* {{cite web
 | title = Carl Friedrich Gauss
 | url = http://www.geocities.com/RainForest/Vines/2977/gauss/english.html
 | accessmonthday=June| accessyear = 2005
 }}
* {{planetmath reference | id = 5594 | title = Carl Friedrich Gauss }}
* {{cite book
 | last = Dunnington
 | first = G. Waldo.
 | title = Carl Friedrich Gauss: Titan of Science
 | publisher = The Mathematical Association of America
 | date = June 2003
 | id = ISBN 0-88385-547-X
 }}
* {{cite book
 | last = Gauss
 | first = Carl Friedrich
 | others = tr. Arthur A. Clarke
 | title = [[Disquisitiones Arithmeticae]]
 | publisher = Yale University Press
 | date = 1965
 | id = ISBN 0-300-09473-6
 }}
* {{cite book
 | last = Hall
 | first = Tord
 | title = Carl Friedrich Gauss: A Biography
 | location = Cambridge, MA
 | publisher = MIT Press
 | date = 1970
 | id = ISBN 0-262-08040-0
 }}
* {{cite web
 | title = Gauss and His Children
 | url = http://www.gausschildren.org
 | accessmonthday=June| accessyear = 2005
 }}
* {{cite book
 | last = Simmons
 | first = J.
 | title = The Giant Book of Scientists: The 100 Greatest Minds of All Time
 | location = Sydney
 | publisher = The Book Company
 | date = 1996
 }}

==External links==
{{wikiquote}}
{{commons|Johann Carl Friedrich Gauß}}
{{wikisource author|Carl Friedrich Gauss}}
* [http://www.corrosion-doctors.org/Biographies/GaussBio.htm Gauss biography]
* {{MacTutor Biography|id=Gauss}}
*{{MathGenealogy|id=18231}} 
* [http://fermatslasttheorem.blogspot.com/2005/06/carl-friedrich-gauss.html Carl Friedrich Gauss], Biography at [http://fermatslasttheorem.blogspot.com Fermat's Last Theorem Blog].
* [http://www.idsia.ch/~juergen/gauss.html Gauss: mathematician of the millennium], by [[Jürgen Schmidhuber]]
* [http://books.google.com/books?id=yh0PAAAAIAAJ Digitized English Translation of Waltershausen's Gauss biography, ''Gauss zum Gedächtnis'', 1862, translated by Gauss' great-granddaughter]
* [http://www.gauss.info Gauss], general information, submit your site about Gauss.
* Obituary: [http://adsabs.harvard.edu//full/seri/MNRAS/0016//0000080.000.html MNRAS '''16''' (1856) 80]
* [http://www.americanscientist.org/template/AssetDetail/assetid/50686?&print=yes A discussion of childhood problem and the sources]
* [http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN235957348 Complete works]
* [http://www-personal.umich.edu/~jbourj/money1.htm Carl Friedrich Gauss on the 10 Deutsch Mark banknote.]

==Further reading==

* {{cite book
 | last = Kehlmann
 | first = Daniel
 | title = [[Measuring the World|Die Vermessung der Welt]]
 | publisher = Rowohlt
 | date = 2005
 | id = ISBN 3-498-03528-2
 }}

{{s-start}}
{{s-awards}}
{{s-bef|before=[[Antoine César Becquerel]] and [[John Frederic Daniell]]}}
{{s-ttl|title=[[Copley Medal]]|years=1838<br/>''jointly with [[Michael Faraday]]''}}
{{s-aft|after=[[Robert Brown (botanist)|Robert Brown]]}}
{{s-end}}

{{Enlightenment}}
<!-- Metadata: see [[Wikipedia:Persondata]] -->

{{Persondata
|NAME= Gauss, Johann Carl Friedrich
|ALTERNATIVE NAMES=
|SHORT DESCRIPTION= [[Mathematics|Mathematician]] and [[Physics|physicist]]
|DATE OF BIRTH= {{birth date|1777|4|30|df=y}}
|PLACE OF BIRTH= [[Braunschweig]], Germany
|DATE OF DEATH= {{death date|1855|2|23|df=y}}
|PLACE OF DEATH= [[Göttingen]], [[Kingdom of Hanover|Hanover]], Germany
}}
{{BD|1777|1855|Gauss, Carl Friedrich}}
[[Category:Carl Friedrich Gauss| ]]
[[Category:18th century mathematicians]]
[[Category:19th century mathematicians]]
[[Category:Calculating prodigies]]
[[Category:Differential geometers]]
[[Category:German astronomers]]
[[Category:German Lutherans]]
[[Category:German mathematicians]]
[[Category:German physicists]]
[[Category:German scientists]]
[[Category:Number theorists]]
[[Category:People from Braunschweig]]
[[Category:People from Brunswick]]
[[Category:Recipients of the Copley Medal]]
[[Category:Recipients of the Pour le Mérite (civil class)]]
[[Category:Walhalla enshrinees]]
[[Category:Technical University of Braunschweig alumni]]
[[Category:University of Helmstedt alumni]]
[[Category:University of Göttingen alumni]]
[[Category:University of Göttingen faculty]]

{{Link FA|hu}}
{{Link FA|ka}}

[[ar:كارل فريدرش غاوس]]
[[ast:Carl Friedrich Gauss]]
[[az:Karl Qauss]]
[[bn:কার্ল ফ্রিড্‌রিশ গাউস]]
[[bs:Carl Friedrich Gauss]]
[[br:Carl Friedrich Gauss]]
[[bg:Карл Фридрих Гаус]]
[[ca:Carl Friedrich Gauß]]
[[cs:Carl Friedrich Gauss]]
[[da:Carl Friedrich Gauss]]
[[de:Carl Friedrich Gauß]]
[[el:Καρλ Φρίντριχ Γκάους]]
[[es:Carl Friedrich Gauss]]
[[eo:Carl Friedrich Gauss]]
[[eu:Carl Friedrich Gauss]]
[[fa:کارل فریدریش گاوس]]
[[fr:Carl Friedrich Gauss]]
[[gl:Carl Friedrich Gauss]]
[[zh-classical:高斯]]
[[ko:카를 프리드리히 가우스]]
[[hr:Carl Friedrich Gauss]]
[[io:Carl Friedrich Gauss]]
[[id:Carl Friedrich Gauss]]
[[is:Carl Friedrich Gauss]]
[[it:Carl Friedrich Gauss]]
[[he:קרל פרידריך גאוס]]
[[ka:კარლ ფრიდრიხ გაუსი]]
[[la:Carolus Fridericus Gauss]]
[[lv:Kārlis Frīdrihs Gauss]]
[[lb:Carl Friedrich Gauß]]
[[lt:Carl Friedrich Gauß]]
[[hu:Carl Friedrich Gauss]]
[[mr:कार्ल फ्रिदरिश गाउस]]
[[nl:Carl Friedrich Gauss]]
[[ja:カール・フリードリヒ・ガウス]]
[[no:Carl Friedrich Gauss]]
[[oc:Carl Friedrich Gauss]]
[[pms:Carl Friedrich Gauss]]
[[pl:Carl Friedrich Gauss]]
[[pt:Carl Friedrich Gauss]]
[[ro:Carl Friedrich Gauss]]
[[ru:Гаусс, Карл Фридрих]]
[[sco:Carl Friedrich Gauss]]
[[sq:Carl Friedrich Gauss]]
[[scn:Karl Friedrich Gauss]]
[[simple:Carl Friedrich Gauss]]
[[sk:Carl Friedrich Gauß]]
[[sl:Carl Friedrich Gauss]]
[[sr:Карл Фридрих Гаус]]
[[sh:Karl Friedrich Gauss]]
[[fi:Carl Friedrich Gauss]]
[[sv:Carl Friedrich Gauss]]
[[tl:Karl Friedrich Gauss]]
[[ta:கார்ல் ஃப்ரெடெரிக் காஸ்]]
[[th:คาร์ล ฟรีดริช เกาส์]]
[[vi:Carl Friedrich Gauß]]
[[tr:Carl Friedrich Gauss]]
[[uk:Ґаусс Карл Фрідріх]]
[[vo:Carl Friedrich Gauss]]
[[fiu-vro:Gaussi Carl Friedrich]]
[[zh:卡爾·弗里德里希·高斯]]