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 Connections
Associated With
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
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
Namesake Of
Derived from the theorem's own name (unambiguous possessive-token match to exactly one live mathematician entity, w-bfill-g5-0924 browse backfill)
Derived from the theorem's own name (unambiguous possessive-token match to exactly one live mathematician entity, w-bfill-g5-0924 browse backfill)
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
In the Other Atlases
- Also in Geography Atlas: Germany, nationality there.
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)
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