German mathematician and physicist often called the Prince of Mathematicians, a child prodigy who at nineteen proved that a regular seventeen-sided polygon (the heptadecagon) could be constructed with compass and straightedge, the first advance on the classical constructibility problem since antiquity, and chose the result for his own gravestone. His doctoral thesis proved the fundamental theorem of algebra, and his Disquisitiones Arithmeticae (1801) founded modern number theory as a systematic subject. He also did foundational work in statistics (the Gaussian, or normal, distribution) and differential geometry.
Facts
BirthplaceBraunschweig (Brunswick), Duchy of Brunswick-Wolfenbuttel 2 Death PlaceGottingen, Kingdom of Hanover 2 Nationality / Culture Defining ContributionProved the heptadecagon (17-gon) constructible by compass and straightedge (1796); proved the fundamental theorem of algebra; founded modern number theory with the Disquisitiones Arithmeticae. 2 Notable WorkDisquisitiones Arithmeticae (1801); Theoria Motus (1809) 2 Carl Friedrich Gauss
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Gauss discovered the method of least squares before Legendre, who was the first to officially publish it in 1805; a documented priority dispute in the history of statistics.
Source Complex Number (Wikipedia)
Gauss introduced the Gaussian integers in his 1832 monograph on quartic reciprocity.
Source Gaussian Integer (Wikipedia)
Source MacTutor History of Mathematics Archive
Attributed Works
Source Wikipedia: Error function
Source Gauss Sum (Wikipedia)
Source Gaussian Integer (Wikipedia)
Source Generalized Hypergeometric Function (Wikipedia)
Source Hypergeometric Function (Wikipedia)
Source Modular Arithmetic (Wikipedia)
Conjectures Posed
In Branch
Source Differential Geometry (Wikipedia)
Source MacTutor History of Mathematics Archive
Source MacTutor History of Mathematics Archive
Source MacTutor History of Mathematics Archive
Mentored
Source Peter Gustav Lejeune Dirichlet (Wikipedia)
Namesake Of
Proofs Credited
Source MacTutor History of Mathematics Archive
Additional Source Wikipedia: HeptadecagonConstructibility section
Source MacTutor History of Mathematics Archive
Additional Source Fundamental Theorem of Algebra (Wikipedia)History section
Source MacTutor History of Mathematics Archive
Additional Source Fundamental Theorem of Arithmetic (Wikipedia)History section
Source Gauss congruence, Wikipedia
Source Gauss-Lucas theorem (Wikipedia)
Source Squeeze Theorem (Wikipedia)
In the Other Atlases
Nationality
Also in Geography Atlas: the nationality of this subject.
Sources
1. Wikipedia: Carl Friedrich Gauss
WikipediaLead section, gender referenceQuote, Lead section, gender reference
His mathematical contributions spanned the branches of number theory, algebra, analysis, geometry, statistics, and probability.
2. MacTutor History of Mathematics Archive
University of St Andrews, School of Mathematics and StatisticsAssociated With: Matrix, https://mathshistory.st-andrews.ac.uk/HistTopics/Matrices_and_determinants/Quote, Associated With: Matrix, https://mathshistory.st-andrews.ac.uk/HistTopics/Matrices_and_determinants/
Gaussian elimination, which first appeared in the text Nine Chapters on the Mathematical Art written in 200 BC, was used by Gauss in his work which studied the orbit of the asteroid Pallas.
Complex Number (Wikipedia)
Wikimedia FoundationAssociated With: Complex Number, history sectionQuote, Associated With: Complex Number, history section
It was not until 1831 that he overcame these doubts and published his treatise on complex numbers as points in the plane, largely establishing modern notation and terminology
Differential Geometry (Wikipedia)
WikipediaIn Branch: Differential Geometry, Intrinsic geometry sectionQuote, In Branch: Differential Geometry, Intrinsic geometry section
Gauss introduced the Gauss map, Gaussian curvature, first and second fundamental forms, proved the Theorema Egregium.
Fundamental Theorem of Arithmetic (Wikipedia)
Wikimedia FoundationProofs Credited: Fundamental Theorem of Arithmetic, History sectionQuote, Proofs Credited: Fundamental Theorem of Arithmetic, History section
Article 16 of Gauss's Disquisitiones Arithmeticae seems to be the first proof of the uniqueness part of the theorem.
Fundamental Theorem of Algebra (Wikipedia)
Wikimedia FoundationProofs Credited: Fundamental Theorem of Algebra, History sectionQuote, Proofs Credited: Fundamental Theorem of Algebra, History section
The other one was published by Gauss in 1799 and it was mainly geometric, but it had a topological gap, only filled by Alexander Ostrowski in 1920
Wikipedia: Heptadecagon
Wikimedia FoundationProofs Credited: Constructibility of the Regular Heptadecagon, Constructibility sectionQuote, Proofs Credited: Constructibility of the Regular Heptadecagon, Constructibility section
this was shown by Carl Friedrich Gauss in 1796.
Gaussian Integer (Wikipedia)
Wikimedia Foundation- Associated With: Gaussian Integers
Attributed Works: Gaussian Integers, Lead section
Gaussian integers are named after the German mathematician Carl Friedrich Gauss.
View the Source Peter Gustav Lejeune Dirichlet (Wikipedia)
Mentored: Peter Gustav Lejeune Dirichlet, Infobox, doctoral advisor or academic advisorsView the Source Modular Arithmetic (Wikipedia)
Wikimedia FoundationAttributed Works: Modular Arithmetic, LeadQuote, Attributed Works: Modular Arithmetic, Lead
The modern approach to number theory using modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in 1801.
Squeeze Theorem (Wikipedia)
Proofs Credited: Squeeze Theorem, LeadQuote, Proofs Credited: Squeeze Theorem, Lead
It was first used geometrically by the mathematicians Archimedes and Eudoxus in an effort to compute π, and was formulated in modern terms by Carl Friedrich Gauss.
Wikipedia: Error function
Attributed Works: Error Function, Lead sectionQuote, Attributed Works: Error Function, Lead section
the error function (also called the Gauss error function)
Gauss-Lucas theorem (Wikipedia)
Proofs Credited: Gauss-Lucas Theorem, Lead sectionQuote, Proofs Credited: Gauss-Lucas Theorem, Lead section
The Gauss-Lucas theorem, named after Carl Friedrich Gauss and Félix Lucas
Gauss congruence, Wikipedia
Proofs Credited: Gauss Congruence, Lead sectionQuote, Proofs Credited: Gauss Congruence, Lead section
The property is named after Carl Friedrich Gauss (1777-1855)
Hypergeometric Function (Wikipedia)
Attributed Works: Hypergeometric Function, LeadQuote, Attributed Works: Hypergeometric Function, Lead
Hypergeometric series were studied by Leonhard Euler, but the first full systematic treatment was given by Carl Friedrich Gauss (1813)
Gauss Sum (Wikipedia)
Attributed Works: Gauss Sum, LeadQuote, Attributed Works: Gauss Sum, Lead
The case originally considered by Carl Friedrich Gauss was the quadratic Gauss sum, for R the field of residues modulo a prime number p, and χ the Legendre symbol
Generalized Hypergeometric Function (Wikipedia)
Attributed Works: Generalized Hypergeometric Function, LeadQuote, Attributed Works: Generalized Hypergeometric Function, Lead
This function was first studied in detail by Carl Friedrich Gauss, who explored the conditions for its convergence
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