# Chronology

### 1830 - 1840

#### 1830

- Babbage creates the first accurate actuarial tables for use in insurance calculations.
- Poisson introduces "Poisson's ratio" in elasticity which involves stresses and strains on materials.
- 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". - 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. - 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. - 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.
- 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. - 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. - The Cambridge and Dublin Mathematical Journals begins publication.
- Dirichlet gives a general definition of a function.
- Liouville discusses integral equations and gives the "Sturm-Liouville theory" which is used in solving such equations.
- 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.
- Cournot publishes
*Recherches sur les principes mathématiques de la théorie des richesses*in which he discusses mathematical economics, in particular supply- and demand-functions. - De Morgan invents the term "mathematical induction" and makes the method precise.

#### 1839

- Lamé proves Fermat's Last Theorem for $n = 7$. (See THIS LINK.)