- Carl Friedrich Gauss
Infobox Scientist

box_width = 300px

name = Carl Friedrich Gauss

caption = Johann Carl Friedrich Gauss (1777-1855), painted byChristian Albrecht Jensen

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 =Kingdom of Hanover

citizenship =

nationality = German

ethnicity =

fields = Mathematician and physicist

workplaces =University of Göttingen

alma_mater =University of Helmstedt

doctoral_advisor =Johann Friedrich Pfaff

academic_advisors =Johann Christian Martin Bartels

doctoral_students =Friedrich Bessel Christoph Gudermann Christian Ludwig Gerling Richard Dedekind

Johann Encke

Johann ListingBernhard Riemann

Christian PetersMoritz Cantor

notable_students =August Ferdinand Möbius Julius Weisbach L. C. Schnürlein

known_for =

footnotes =**Johann Carl Friedrich Gauss**(IPAEng|ˈɡaʊs, audio|De-carlfriedrichgauss.ogg|Audio, _de. Gauß, _la. Carolus Fridericus Gauss) (30 April 1777 –23 February 1855 ) was a Germanmathematician andscientist who contributed significantly to many fields, includingnumber theory ,statistics , analysis, differential geometry,geodesy ,electrostatics ,astronomy , andoptics . Sometimes known as the "princeps mathematicorum" [*cite book*] (

last=Zeidler

first=Eberhard

title=Oxford User's Guide to Mathematics

location=Oxford, UK

publisher=Oxford University Press

year=2004

isbn=0198507631

pages=1188Latin , 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.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.]Gauss was a

child prodigy . There are manyanecdote s pertaining to his precocity while a toddler, and he made his first ground-breaking mathematical discoveries while still a teenager. He completed "Disquisitiones Arithmeticae ", hismagnum opus , in 1798 at the age of 21, though it would not be published until 1801.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 (1777–1798)**Carl Friedrich Gauss was born in

Braunschweig , in theElectorate of Brunswick-Lüneburg , now part ofLower Saxony ,Germany , as the only son of poor working-class parents. [*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*] There are several stories of his early genius. 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 ofinteger s. The young Gauss reputedly produced the correct answer within seconds, to the astonishment of his teacher and his assistant Martin Bartels. Gauss's 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 series andsummation "). [*http://www.americanscientist.org/issues/pub/gausss-day-of-reckoning/2 for discussion of original*] However whilst the method works, the incident itself is probablyWolfgang Sartorius von Waltershausen source.apocryphal ; some, such as Joseph Rotman in his book "A first course in Abstract Algebra", question whether it ever happened.As his father wanted him to follow in his footsteps and become a 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 Duke of Braunschweig, who awarded Gauss a fellowship to the Collegium Carolinum (now Technische Universität Braunschweig), which he attended from 1792 to 1795, and subsequently he moved to the 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 prime (and, consequently, those polygons with any number of sides which is the product of distinct Fermat primes and a power of 2) can be constructed by 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 Greeks, and the discovery ultimately led Gauss to choose mathematics instead ofphilology as a career. Gauss was so pleased by this result that he requested that a regularheptadecagon be inscribed on his tombstone. The stonemason declined, stating that the difficult construction would essentially look like a circle.Fact|date=September 2008The year 1796 was most productive for both Gauss and number theory. He discovered a construction of the

heptadecagon on March 30. [] He invented**Carl Friedrich Gauss**§§365-366 inDisquisitiones Arithmeticae . Leipzig, Germany, 1801. New Haven, CT: Yale University Press, 1965.modular arithmetic , greatly simplifying manipulations in number theory. He became the first to prove thequadratic reciprocity law onApril 8 . This remarkably general law allows mathematicians to determine the solvability of any quadratic equation in modular arithmetic. Theprime number theorem , conjectured onMay 31 , gives a good understanding of how theprime number s are distributed among the integers. Gauss also discovered that every positive integer is representable as a sum of at most threetriangular number s onJuly 10 and then jotted down in his diary the famous words, "Heureka! num = $Delta+Delta+Delta$." On October 1 he published a result on the number of solutions of polynomials with coefficients infinite field s, which ultimately led to theWeil conjectures 150 years later.**Middle years (1799–1830)**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-variablepolynomial over thecomplex number s has at least one root. Mathematicians includingJean 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 theJordan 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 ofmodular arithmetic and the first proof of the law ofquadratic reciprocity ., 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 method of least squares, a procedure used in all sciences to this day to minimize the impact of measurement error. Gauss was able to prove the method in 1809 under the assumption of normally distributed errors (seeGauss–Markov theorem ; see also Gaussian). The method had been described earlier byAdrien-Marie Legendre in 1805, but Gauss claimed that he had been using it since 1795.Fact|date=July 2007Gauss 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 usedlogarithm 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!"Fact|date=September 2008In 1818 Gauss, putting his calculation skills to practical use, carried out a geodesic survey of the state of Hanover, linking up with previous Danish surveys. To aid in the survey, Gauss invented the 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 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, Einstein's theory of general relativity, which describes the universe as non-Euclidean. His friend 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, , 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.

The survey of Hanover fueled Gauss's interest in differential geometry, a field of mathematics dealing with

curve s andsurface s. This led in 1828 to an important theorem, theTheorema Egregium ("remarkable theorem" inLatin ), establishing an important property of the notion ofcurvature . Informally, the theorem says that the curvature of a surface can be determined entirely by measuringangle s anddistance s on the surface. That is, curvature does not depend on how the surface might be embedded in 3-dimensional space.**Later years and death (1831–1855)**In 1831 Gauss developed a fruitful collaboration with the physics professor 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 ofKirchhoff's circuit laws in electricity. They constructed the first electromagnetic telegraph in 1833, which connected the observatory with the institute for physics in Göttingen. Gauss ordered a magneticobservatory to be built in the garden of the observatory, and with Weber founded themagnetischer Verein ("magnetic club" in 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 (core and crust) and outer (magnetospheric) sources of Earth's magnetic field.Gauss died in Göttingen, Hannover (now part of

Lower Saxony , Germany) in 1855 and is interred in the cemeteryAlbanifriedhof there. Two individuals gave eulogies at his funeral, Gauss's son-in-lawHeinrich Ewald andWolfgang Sartorius von Waltershausen , who was Gauss's close friend and biographer. His brain was preserved and was studied byRudolf Wagner who found its weight to be 1,492 grams and the cerebral area equal to 219,588 square millimeters [*This reference from 1891 (cite journal*] (340.362 square inches). Highly developed convolutions were also found, which in the early 20th century was suggested as the explanation of his genius. [

last=Donaldson

first=Henry H.

authorlink=

coauthors=

title=Anatomical Observations on the Brain and Several Sense-Organs of the Blind Deaf-Mute, Laura Dewey Bridgman

journal=The American Journal of Psychology

volume=4

issue=2

pages=248–294

publisher=E. C. Sanford

location=

year=1891

url=

doi=10.2307/1411270

id=

accessdate=) says: "Gauss, 1492 grm. 957 grm. 219588. sq. mm. ", i.e the unit is "square mm". In the later reference: Dunnington (1927), the unit is erroneously reported as square cm, which gives an unreasonably large area, the 1891 reference is more reliable.*Dunnington, 1927*]**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 depression from which he never fully recovered. He married again, to Johanna's best friend named Friederica Wilhelmine Waldeck but commonly known as Minna. When his second wife died in 1831 after a long illness, [

*cite web|url=http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Gauss.html |title=Gauss biography|publisher=Groups.dcs.st-and.ac.uk |date= |accessdate=2008-09-01*] 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.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.Fact|date=July 2007 Wilhelm also settled in Missouri, starting as afarmer and later becoming wealthy in the shoe business in 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".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 onSeptember 3 ,1912 .**Personality**Gauss was an ardent 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." [*cite book*] This anecdote is briefly discussed in Waldo Dunnington's "Gauss, Titan of Science" where it is suggested that it is an apocryphal story.

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

year=1972He 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"). His personal diaries indicate that he had made several important mathematical discoveries years or decades before his contemporaries published them. Mathematical historian

Eric Temple Bell estimated that had Gauss timely published all of his discoveries, Gauss would have advanced mathematics by fifty years. [*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

year=1986

isbn=0-671-46400-0Though 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 themRichard Dedekind ,Bernhard Riemann , andFriedrich 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 supported monarchy and opposed Napoleon, whom he saw as an outgrowth of

revolution .**Commemorations**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 and atriangulation approach for Hannover. 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 was introduced to the

Walhalla temple . [*http://www.stmwfk.bayern.de/downloads/aviso/2004_1_aviso_48-49.pdf*]Things named in honour of Gauss:

* The CGS unit for magnetic induction was named gauss in his honour.

* Gauss crater on theMoon [*Andersson, L. E.; Whitaker, E. A., (1982). NASA Catalogue of Lunar Nomenclature. NASA RP-1097.*]

*Asteroid 1001 Gaussia .

* The ship "Gauss", used in theGauss expedition to the Antarctic.

*Gaussberg , an extinct volcano discovered by the above mentioned expedition

*Gauss Tower , an observation tower inDransfeld ,Germany .

* In Canadian junior high schools, an annual national mathematics competition administered by theCentre for Education in Mathematics and Computing is named in honour of Gauss.

* In University of California, Santa Cruz, in Crown College, a dormitory building is named after Gauss.

* The Gauss Haus, an NMR center at theUniversity of Utah .

* The Carl-Friedrich-Gauß School for Mathematics, Computer Science, Business Administration, Economics, and Social Sciences of University of Braunschweig**ee also***

List of topics named after Carl Friedrich Gauss **References****Writings***1799:

Doctoral dissertation on theFundamental 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: [*http://resolver.sub.uni-goettingen.de/purl?PPN235993352 "Disquisitiones Arithmeticae"*]

*1809: [*http://books.google.com/books?id=ORUOAAAAQAAJ&dq=Theoria+Motus+Corporum+Coelestium+in+sectionibus+conicis+solem+ambientium&source=gbs_summary_s&cad=0 "Theoria Motus Corporum Coelestium in sectionibus conicis solem ambientium"*] (Theorie der Bewegung der Himmelskörper, die die Sonne in Kegelschnitten umkreisen), 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://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN35283028X_0006_2NS "Disquisitiones generales circa superficies curvas"*] , Commentationes Societatis Regiae Scientiarum Gottingesis Recentiores. Volume**VI**, pp. 99-146. " [*http://quod.lib.umich.edu/cgi/t/text/text-idx?c=umhistmath;idno=ABR1255 General Investigations of Curved Surfaces*] " (published 1965) Raven Press, New York, translated by A.M.Hiltebeitel and J.C.Morehead.

*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*] , pp. 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*] , pp. 3-44

*"Mathematisches Tagebuch 1796–1814", Ostwaldts Klassiker, Harri Deutsch Verlag 2005, mit Anmerkungen von Neumamn, ISBN 978-3-8171-3402-1 (English translation with annotations by Jeremy Gray: Expositiones Math. 1984)

* [*http://dz-srv1.sub.uni-goettingen.de/cache/toc/D38910.html Gauss' collective works are online here*] This includes German translations of Latin texts and commentaries by various authorities**Further reading***citebook |last=Dunnington|first=G. Waldo.|title=Carl Friedrich Gauss: Titan of Science

publisher=The Mathematical Association of America|year=2003|isbn=088385547X |oclc=53933110

*citebook |last=Gauss|first=Carl Friedrich|others=tr. Arthur A. Clarke|title=Disquisitiones Arithmeticae |publisher=Yale University Press|year=1965|isbn=0300094736

*cite book

last=Hall

first=Tord

title=Carl Friedrich Gauss: A Biography

location=Cambridge, MA

publisher=MIT Press

year=1970

isbn=0262080400

oclc=185662235

*cite book

last=Kehlmann

first=Daniel

title=Die Vermessung der Welt

publisher=Rowohlt

year=2005

isbn=3498035282

oclc=144590801

*cite book

last=Simmons

first=J.

title=The Giant Book of Scientists: The 100 Greatest Minds of All Time

publisher=The Book Company

location=Sydney

isbn=

year=1996**External links***planetmath reference |id=5594 |title=Carl Friedrich Gauss

* [*http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN235957348 Complete works*]

* [*http://www.gausschildren.org Gauss and his children*]

* [*http://www.corrosion-doctors.org/Biographies/GaussBio.htm Gauss biography*]

*MathGenealogy|id=18231

* [*http://fermatslasttheorem.blogspot.com/2005/06/carl-friedrich-gauss.html Carl Friedrich Gauss*] , Biography at Fermat's Last Theorem Blog.

* [*http://www.idsia.ch/~juergen/gauss.html Gauss: mathematician of the millennium*] , byJürgen Schmidhuber

* [*http://books.google.com/books?id=yh0PAAAAIAAJ English translation of Waltershausen's 1862 biography*]

* [*http://www.gauss.info Gauss*] general website on Gauss

* [*http://adsabs.harvard.edu//full/seri/MNRAS/0016//0000080.000.html MNRAS*] Obituary**16**(1856) 80

* [*http://www.americanscientist.org/template/AssetDetail/assetid/50686?&print=yes A discussion of childhood problem and the sources*]

* [*http://www-personal.umich.edu/~jbourj/money1.htm Carl Friedrich Gauss on the 10 Deutsche Mark banknote*]

*MacTutor Biography|id=GaussPersondata

NAME= Gauss, Johann Carl Friedrich

ALTERNATIVE NAMES=

SHORT DESCRIPTION= Mathematician and 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 , Hannover, Germany

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