Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

Gauß, Johann Carl Friedrich

  • Holm AltenbachEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-3-662-53605-6_114-1
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Johann Carl Friedrich Gauß (April 30, 1777, in Brunswick, Principality of Brunswick-Wolfenbüttel; February 23, 1855, in Göttingen, Kingdom of Hanover, German Confederation) was a mathematician and physicist with exceptional influence in many fields of mathematics and science (he is ranked among history’s most influential mathematicians).

Open image in new window Johann Carl Friedrich Gauß

Early Years and Education

Johann Carl Friedrich Gauß was the only one child of Gebhard Dietrich Gauß (1744–1808) and Dorothea Gauß nee Bentze (1743–1839). He attended the primary school in the age of 7 years. When he was 9 years old, his teacher Büttner formulated the problem to compute the sum of the numbers from 1 to 100. Gauß solved this problem very quick using the following algorithm: the sum is equal to 50 pairs with the sum 101 (1 + 100, 2 + 99, …, 50 + 51) and yields 5050. The teacher understood that Gauß had a great talent in mathematics. Finally, Gauß could attend in 1788 the Katharineum allowing to obtain a higher school degree.

In the age of 14, Gauß first time communicated with the duke Karl Wilhelm Ferdinand von Braunschweig, who supported him financially. With this support Gauß studied from 1792 up to 1795 at Collegium Carolinum. The level of education was in between of high school and university.

In October 1795, Gauß continued his studies at the University of Göttingen. He attended lectures in classical philology and mathematics. In summer term 1796, he attended lectures of experimental physics and later in astronomy. In 1796 he discovered a construction of the heptadecagon on March 30. After that he changed his study program to mathematics. In 1799 he defended his doctoral thesis at the Academia Julia (University of Helmstedt).

Gauß remained mentally active into his old age, even while suffering from gout and general unhappiness. For example, at the age of 62, he taught himself Russian.

Scientific Achievements

Among his contributions to mathematics and science, the following items can be mentioned:
  • algebra

    In 1799 in his PhD thesis on 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, Gauß proved the fundamental theorem of algebra which states that every nonconstant single-variable polynomial with complex coefficients has at least one complex root. In addition, he suggested Gaußian elimination, also known as row reduction, which is an algorithm in linear algebra for solving a system of linear equations.

  • non-Euclidean geometries

    Gauß claimed that he had discovered the possibility of non-Euclidean geometries. His main statement was that Euclid’s axioms were not the only one to make geometry consistent and noncontradictory.

  • magnetism

    In 1831, Gauß together with Wilhelm Weber (professor of physics) suggested new ideas in magnetism (including finding a representation for the unit of magnetism in terms of mass, charge).

  • statistics

    He introduced the most common bell curve of the normal distribution. In addition, the method of least squares was introduced by Gauß in regression analysis to approximate the solution of overdetermined systems.

  • mechanics

    Gauß suggested the principle of least constraint and the law for gravity (including the gravitational constant).

  • vector calculus

    The divergence theorem, also known as Gauß’ theorem or Ostrogradsky’s theorem, connects the flow (i.e., flux) of a vector field through a surface to the behavior of the tensor field inside the surface.

Honors

The Gauß (sometimes Gauss), symbol G, sometimes Gs, is in the cgs system of units based on centimeter–gram–second, the unit of measurement of magnetic flux density (or magnetic induction). It was named in honor after Gauß in 1936. One Gauß is defined as one Maxwell per square centimeter. In the International System of Units (SI), which uses the Tesla (symbol T) as the unit of magnetic flux density, one has 1 Gauß = 1 × 10−4 Tesla (or 100 μT) or 1 Tesla = 10,000 Gauß.

From 1989 through 2001, Gauß’ portrait together with the normal distribution curve, and some prominent Göttingen buildings were featured on the German ten-mark banknote.

The normal distribution, also known at the Gaußian distribution, the most common bell curve in statistics.

The Gauß Prize, one of the highest honors in mathematics, was established in 2006 by the International Mathematical Union and the German Mathematical Society for “outstanding mathematical contributions that have found significant applications outside of mathematics.” It is to be awarded every fourth year at the International Congress of Mathematicians.

Cross-References

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Fakultät für Maschinenbau, Institut für MechanikOtto-von-Guericke-Universität MagdeburgMagdeburgGermany

Section editors and affiliations

  • Holm Altenbach
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  1. 1.Fakultät für Maschinenbau, Institut für MechanikOtto-von-Guericke-Universität MagdeburgMagdeburgGermany