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About 1830

Babbage creates the first accurate actuarial tables for use in insurance calculations.

1830

Poisson introduces "Poisson's ratio" in elasticity which involves stresses and strains on materials.

1830

Peacock publishes his *Treatise on Algebra* which attempts to give algebra a logical treatment comparable to Euclid's *Elements*.

1831

Möbius publishes *Über eine besondere Art von Umkehrung der Reihen* which introduces the "Möbius function" and the "Möbius inversion formula".

1831

Cauchy gives power series expansions of analytic functions of a complex variable.

1832

Steiner publishes *Systematische Entwicklungen ...* (*Systematic Development of the Dependency of Geometrical Forms on One Another*) which gives a treatment of projective geometry based on metric considerations.

1832

János Bolyai's work on non-Euclidean geometry is published as an appendix to an essay by Farkas Bolyai, his father. (See this History Topic.)

1833

Legendre points out the flaws in 12 "proofs" of the parallel postulate. (See this History Topic.)

1834

Hamilton uses algebra in treating dynamics in *On a General Method in Dynamics*. This paper gives the first statement of the characteristic function applied to dynamics.

1835

Quetelet publishes *Sur l'homme et le développement de ses facultés* (*A treatise on Man and the Development of his Faculties*). He presents his conception of the "average man" as the central value about which measurements of a human trait are grouped according to the normal curve.

1835

Coriolis publishes *Sur les équations du mouvement relatif des systèmes de corps*. He introduces the "Coriolis force" and shows that the laws of motion can be used in a rotating frame of reference if an extra force called the "Coriolis acceleration" is added to the equations of motion. In the same year Coriolis publishes a work on a mathematical theory of billiards.

1836

Ostrogradski rediscovers Green's theorem.

1836

Liouville founds a mathematics journal *Journal de Mathématiques Pures et Appliquées*. This journal, sometimes known as *Journal de Liouville*, did much to advance mathematics in France throughout the 19th century.

1836

Poncelet publishes *Cours de mécanique appliquée aux machines* (*A Course in Mechanics Applied to Machines*). It is the first to propose the use of mathematics in machine design.

1837

Poisson publishes *Recherches sur la probabilité des jugements* (*Researches on the Probabilities of Opinions*). In this work he establishes the rules of probability, gives "Poisson's law of large numbers" and describes the "Poisson distribution" for a discrete random variable which is a limiting case of the binomial distribution.

1837

The Cambridge and Dublin Mathematical Journals begins publication.

1837

Dirichlet gives a general definition of a function.

1837

Liouville discusses integral equations and gives the "Sturm-Liouville theory" which is used in solving such equations.

1837

Wantzel proves that the classical problems of duplicating a cube and trisecting an angle could not be solved with ruler and compass.

1838

Bessel measures the parallax of the star 61 Cygni, the first star for which this is calculated.

1838

Cournot publishes *Recherches sur les principes mathématiques de la théorie des richesses* in which he discusses mathematical economics, in particular supply- and demand-functions.

1838

De Morgan invents the term "mathematical induction" and makes the method precise.

1839

Lamé proves Fermat's Last Theorem for *n* = 7. (See this History Topic.)

1840

Cauchy publishes the first volume of the four volume work *Exercises d'analyse et de physique mathematique*.

List of mathematicians alive in 1830.

List of mathematicians alive in 1840.

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