Mathematician:Carl Friedrich Gauss

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

According to legend, he was correcting his father's arithmetic at the age of $3$.

Nationality
German

History

 * Born: 30 April 1777 in Braunschweig, in the Electorate of Brunswick-Lüneburg (now part of Lower Saxony, Germany)
 * 1792 -- 1795: Attended the Collegium Carolinum (now Technische Universität Braunschweig)
 * 1795 -- 1798: University of Göttingen
 * 1807: Appointed Professor of Astronomy and Director of the astronomical observatory in Göttingen
 * 1820: Embarked on an exercise to supervise a geodetic survey of the Kingdom of Hanover
 * 1833: Constructed the first electromagnetic telegraph with
 * Died: 23 February 1855 in Göttingen, Hannover (now part of Lower Saxony, Germany)

Theorems and Definitions

 * Gauss's Constant
 * Gauss Error Function
 * Gauss Map
 * Gaussian Binomial Coefficient
 * Gaussian Curvature
 * Gaussian Distribution
 * Gaussian Domain, another term for Unique Factorization Domain
 * Gaussian Elimination
 * Gaussian Field
 * Gaussian Hypergeometric Function
 * Gaussian Integer
 * Gaussian Rational


 * Gauss-Bolyai-Lobachevsky Space (with and )
 * Gauss-Jordan Elimination (with )
 * Gauss-Laplace Pyramid (with )
 * Gauss-Kuzmin-Wirsing Constant (with and )
 * Gauss-Manin Connection (with )
 * Gauss-Markov Process (with )


 * Gauss-Bonnet Theorem and Generalized Gauss-Bonnet Theorem (with )
 * Gauss-Chebyshev Rule (with ), also known as the Gaussian Integration Rule
 * Gauss-Codazzi Equations (with )
 * Gauss-Kronrod Quadrature Formula (with )
 * Gauss-Krüger Coordinate System (with )
 * Gauss-Kuzmin-Wirsing Operator (with and )
 * Gauss-Laguerre Quadrature (with )
 * Gauss-Legendre Algorithm (with )
 * Gauss-Lucas Theorem (with )
 * Gauss-Markov Theorem (with )
 * Gauss-Newton Algorithm (with )
 * Gauss-Ostrogradsky Theorem (with ), also known as Ostrogradsky-Gauss Theorem, Ostrogradsky's Theorem, Gauss's Theorem and the Divergence Theorem
 * Gauss-Seidel Method (with )


 * Gauss Composition
 * Gauss's Continued Fraction
 * Gauss's Digamma Theorem
 * Gauss's Eureka Theorem
 * Gauss's Formulas (also known as Delambre's Analogies, for )
 * Gauss's Generalization of Wilson's Theorem
 * Gauss's Hypergeometric Theorem
 * Gauss's Interpolation Formula (also known as Gregory-Newton Interpolation, for and )
 * Gauss's Lemma (Polynomials)
 * Gauss's Lemma (Number Theory)
 * Gauss Linking Integral
 * Gauss Multiplication Formula
 * Gauss's Principle of Least Constraint
 * Gauss Sum
 * Gaussian Binomial Theorem
 * Gaussian Integral
 * Gaussian Isoperimetric Inequality


 * Theorema Egregium

Also:
 * Invented the Method of Least Squares
 * Proved the Law of Quadratic Reciprocity
 * Invented the field of modulo arithmetic
 * Conjectured the Prime Number Theorem
 * Demonstrated Construction of Regular Heptadecagon
 * Proved Construction of Regular Prime $p$-Gon Exists iff $p$ is Fermat Prime
 * 1799: Proved the Fundamental Theorem of Algebra

Publications

 * 1798: (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:
 * 1827:
 * 1827:

Notable Quotes

 * Mathematics is the Queen of the Sciences, and Arithmetic the Queen of Mathematics.
 * -- Quoted in : They Say: What Say They? : Let Them Say


 * 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. It has engaged the industry and wisdom of ancient and modern geometers to such an extent ... 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 $329$.
 * -- Quoted at the end of of : Section $4.5$
 * -- Quoted by  in Section $257$ of his  of $1986$, requoting


 * I mean the word proof not in the sense of the lawyers, who set two half proofs equal to a whole one, but in the sense of the mathematician, where $\frac 1 2$ proof $= 0$ and it is demanded for proof that every doubt becomes impossible.


 * You know that I write slowly. This is chiefly because I am never satisfied until I have said as much as possible in a few words, and writing briefly takes far more time than writing at length.


 * It is not knowledge but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment. When I have clarified and exhausted a subject, then I turn away from it in order to go into darkness again.
 * -- Letter to


 * The higher arithmetic presents us with an inexhaustible store of interesting truths -- of truths too, which are not isolated, but stand in a close internal connection, and between which, as our knowledge increases, we are continually discovering new and sometimes wholly unexpected ties. A great part of its theories derives an additional charm from the peculiarity that important propositions, with the impress of simplicity upon them, are often easily discoverable by induction, and yet are of so profound a character that we cannot find their demonstration till after many vain attempts; and even then, when we do succeed, it is often by some tedious and artificial process, while the simpler methods may long remain concealed.
 * -- Translated by from Gauss's introduction to the collected papers of
 * -- Quoted in : Chapter $\text{IV}$: The Prince of Amateurs


 * In arithmetic the most elegant theorems frequently arise experimentally as the result of a more or less unexpected stroke of good fortune, while their proofs lie so deeply embedded in darkness that they defeat the sharpest enquiries.
 * -- Quoted in : Introduction

Critical View

 * He is like the fox, who effaces his tracks in the sand with his tail.


 * The name of Gauss is linked to almost everything that the mathematics of our century [ the nineteenth ] has brought forth in the way of original scientific ideas.

Also known as
Full name: Johann Carl Friedrich Gauss.

Some sources (perhaps in error) report his first name as Karl.