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Carl Gauss. Lived and died. 30 April 1777 – 23 February 1855.

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Lived and died

30 April 1777 – 23 February 1855

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Sometimes referred to as the Princepsmathematicorum(Latin, "the Prince of Mathematicians" or "the foremost of mathematicians") 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.[2] He referred to mathematics as "the queen of sciences".

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1799: Doctoral dissertation on the Fundamental theorem of algebra, with the title: Demonstratio nova theorematisomnemfunctionemalgebraicamrationalemintegramuniusvariabilis in factoresrealesprimivelsecundigradusresolvi 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: DisquisitionesArithmeticae. German translation by H. Maser UntersuchungenüberhöhereArithmetik (DisquisitionesArithmeticae & other papers on number theory) (Second edition). New York: Chelsea. 1965. ISBN 0-8284-0191-8, pp. 1–453. English translation by Arthur A. Clarke DisquisitionesArithemeticae (Second, corrected edition). New York: Springer. 1986. ISBN 0387962549.
  • 1808: Theorematisarithmeticidemonstratio nova. Göttingen: Comment. Soc. regiaesci, Göttingen XVI. German translation by H. Maser UntersuchungenüberhöhereArithmetik (DisquisitionesArithmeticae & other papers on number theory) (Second edition). New York: Chelsea. 1965. ISBN 0-8284-0191-8, pp. 457–462 [Introduces Gauss's lemma, uses it in the third proof of quadratic reciprocity]
  • 1809: TheoriaMotusCorporumCoelestium in sectionibusconicissolemambientium(Theorieder Bewegung der Himmelskörper, die dieSonne in Kegelschnittenumkreisen), English translation by C. H. Davis, reprinted 1963, Dover, New York.
  • 1811: Summatioserierunquarundamsingularium. Göttingen: Comment. Soc. regiaesci, Göttingen. German translation by H. Maser UntersuchungenüberhöhereArithmetik (DisquisitionesArithmeticae & other papers on number theory) (Second edition). New York: Chelsea. 1965. ISBN 0-8284-0191-8, pp. 463–495 [Determination of the sign of the quadratic Gauss sum, uses this to give the fourth proof of quadratic reciprocity]

Writings

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1812: Disquisitiones Generales Circa SeriemInfinitam

  • 1818: Theorematisfundamentallis in doctrina de residuisquadraticisdemonstrationes et amplicationesnovae. Göttingen: Comment. Soc. regiaesci, Göttingen. German translation by H. Maser UntersuchungenüberhöhereArithmetik (DisquisitionesArithmeticae & other papers on number theory) (Second edition). New York: Chelsea. 1965. ISBN 0-8284-0191-8, pp. 496–510 [Fifth and sixth proofs of quadratic reciprocity]
  • 1821, 1823 und 1826: Theoriacombinationisobservationumerroribusminimisobnoxiae. DreiAbhandlungenbetreffend die WahrscheinlichkeitsrechnungalsGrundlage des Gauß'schenFehlerfortpflanzungsgesetzes. English translation by G. W. Stewart, 1987, Society for Industrial Mathematics.
  • 1827: Disquisitionesgenerales circa superficies curvas, CommentationesSocietatisRegiaeScientiarumGottingesisRecentiores. Volume VI, pp. 99–146. "General Investigations of Curved Surfaces" (published 1965) Raven Press, New York, translated by A.M.Hiltebeitel and J.C.Morehead.
  • 1828: Theoriaresiduorumbiquadraticorum, Commentatio prima. Göttingen: Comment. Soc. regiaesci, Göttingen 6. German translation by H. Maser UntersuchungenüberhöhereArithmetik (DisquisitionesArithmeticae & other papers on number theory) (Second edition). New York: Chelsea. 1965. ISBN 0-8284-0191-8, pp. 511–533 [Elementary facts about biquadratic residues, proves one of the supplements of the law of biquadratic reciprocity (the biquadratic character of 2)]

More Writings

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1832: Theoriaresiduorumbiquadraticorum, Commentatio secunda. Göttingen: Comment. Soc. regiaesci, Göttingen 7. German translation by H. Maser UntersuchungenüberhöhereArithmetik (DisquisitionesArithmeticae & other papers on number theory) (Second edition). New York: Chelsea. 1965. ISBN 0-8284-0191-8, pp. 534–586 [Introduces the Gaussian integers, states (without proof) the law of biquadratic reciprocity, proves the supplementary law for 1 + i]

  • 1843/44: UntersuchungenüberGegenstände der HöherenGeodäsie. ErsteAbhandlung, Abhandlungen der KöniglichenGesellschaft der Wissenschaften in Göttingen. Zweiter Band, pp. 3–46
  • 1846/47: UntersuchungenüberGegenstände der HöherenGeodäsie. ZweiteAbhandlung, Abhandlungen der KöniglichenGesellschaft der Wissenschaften in Göttingen. Dritter Band, pp. 3–44
  • MathematischesTagebuch1796–1814, OstwaldtsKlassiker, Harri Deutsch Verlag 2005, mitAnmerkungen von Neumamn, ISBN 978-3-8171-3402-1 (English translation with annotations by Jeremy Gray: Expositiones Math. 1984)

Even More Writings