ProofWiki:Mathematicians/Carl Friedrich Gauss

Full name: Johann Carl Friedrich Gauss.

One of the most influential mathematicians of all time, contributing to many fields, including number theory, statistics, analysis and differential geometry.

Nationality

German

History

• Born: 30 April 1777 in Braunschweig, in the Electorate of Brunswick-Lüneburg (now part of Lower Saxony, Germany).
• 1792 to 1795: Attended the Collegium Carolinum (now Technische Universität Braunschweig).
• 1795 to 1798: University of Göttingen.
• 1807: Appointed Professor of Astronomy and Director of the astronomical observatory in Göttingen.
• Died: 23 February 1855 in Göttingen, Hannover (now part of Lower Saxony, Germany).

Theorems and Inventions

• Gauss-Bolyai-Lobachevsky Space
• Gauss-Bonnet Theorem and Generalized Gauss-Bonnet Theorem
• Gauss-Codazzi Equations
• Gauss-Jordan Elimination
• Gauss-Kronrod Quadrature Formula
• Gauss-Kuzmin-Wirsing Operator and Gauss-Kuzmin-Wirsing Constant
• Gauss-Manin Connection
• Gauss-Markov Theorem (with Andrey Andreyevich Markov)
• Gauss-Markov Process (with Andrey Andreyevich Markov)
• Gauss-Laplace Pyramid (with Pierre-Simon de Laplace)
• Gauss Linking Integral
• Gauss-Krüger Coordinate System
• Gauss-Seidel Method
• Gauss-Newton Algorithm
• Gauss-Legendre Algorithm
• Gauss-Lucas Theorem (with Édouard Lucas)
• Gauss's Principle of Least Constraint
• Gauss's Constant
• Gauss's Continued Fraction
• Gauss's Digamma Theorem
• Gauss Error Function
• Gauss's Generalization of Wilson's Theorem
• Gauss's Hypergeometric Theorem
• Gauss's Lemma (Polynomials)
• Gauss's Lemma (Number Theory)
• Gauss Map
• Gauss Sum
• Gauss's Theorem (otherwise known as the Divergence Theorem)
• Ostrogradsky-Gauss Theorem
• Gauss Composition
• Gaussian Integer
• Gaussian Rational
• Gaussian Integral

Also:

• Proved the Law of Quadratic Reciprocity.
• Invented the field of modular arithmetic.
• Conjectured the Prime Number Theorem.
• 1799: Proved the Fundamental Theorem of Algebra.

Books and Papers

• 1798: Disquisitiones Arithmeticae (not published until 1801)
• 1799: Demonstratio nova theorematis omnem functionem algebraicam rationalem integram unius variabilis in factores reales primi vel secundi gradus resolvi posse (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) (doctorate thesis)
• 1809: Theoria motus corporum coelestium in sectionibus conicis solem ambientum (theory of motion of the celestial bodies moving in conic sections around the sun)

Notable Quotes

• "The operation of distinguishing prime numbers from composites, and of resolving composite numbers into their prime factors, is one of the most important and useful in all of arithmetic. ... The dignity of science seems to demand that every aid to the solution of such an elegant and celebrated problem be zealously cultivated." -- Disquisitiones Arithmeticae, article 329.

Also see

• John J. O'Connor and Edmund F. Robertson: "Carl Friedrich Gauss": MacTutor History of Mathematics archive

• Eric Temple Bell: Men of Mathematics (1937): Chapter $\text{XIV}$
• George F. Simmons: Calculus Gems (1992): Chapter $\text{A}.25$