# Chronology

### 1880 - 1890

#### 1880

- Poincaré publishes important results on automorphic functions.

#### 1881

- Venn introduces his "Venn diagrams" which become a useful tools in set theory.
- Gibbs develops vector analysis in a pamphlet written for the use of his own students. The methods will be important in Maxwell's mathematical analysis of electromagnetic waves.

#### 1882

- Lindemann proves that π is transcendental. This proves that it is impossible to construct a square with the same area as a given circle using a ruler and compass. The classic mathematical problem of squaring the circle dates back to ancient Greece and had proved a driving force for mathematical ideas through many centuries.
- Mittag-Leffler founds the journal
*Acta Mathematica*.

#### 1883

- Reynolds publishes
*An experimental investigation of the circumstances which determine whether the motion of water in parallel channels shall be direct or sinuous and of the law of resistance in parallel channels*. The "Reynolds number" (as it is now called) used in modelling fluid flow appears in this work. - Poincaré publishes a paper which initiates the study of the theory of analytic functions of several complex variables.
- The Edinburgh Mathematical Society is founded. (See THIS LINK.)

#### 1884

- Volterra begins his study of integral equations.
- Frege publishes
*The Foundations of Arithmetic*. - Hölder discovers the "Hölder inequality".
- Mittag-Leffler publishes
*Sur la représentation analytique fes fonctions monogènes uniformes d'une variable indépendante*which gives his theorem on the construction of a meromorphic function with prescribed poles and singular parts. - Frobenius proves Sylow's theorems for abstract groups.
- Ricci-Curbastro begins work on the absolute differential calculus.
*Circolo Matematico di Palermo*is founded.

#### 1885

- Weierstrass shows that a continuous function on a finite subinterval of the real line can be uniformly approximated arbitrarily closely by a polynomial.
- Edgeworth publishes
*Methods of Statistics*which presents an exposition of the application and interpretation of significance tests for the comparison of means.

#### 1886

- Reynolds formulates a theory of lubrication
- Peano proves that if $f(x, y)$ is continuous then the first order differential equation ${{dy}\over{dx}} = f(x, y)$ has a solution.

#### 1887

- Levi-Civita publishes a paper developing the calculus of tensors.

#### 1888

- Dedekind publishes
*Was sind und was sollen die Zahlen?*(*The Nature and Meaning of Numbers*). He puts arithmetic on a rigorous foundation giving what were later known as the "Peano axioms". - Galton introduces the notion of correlation.
- Engel and Lie publish the first of three volumes of
*Theorie der Transformationsgruppen*(*Theory of Transformation Groups*) which is a major work on continuous groups of transformations.

#### 1889

- Peano publishes
*Arithmetices principia, nova methodo exposita*(*The Principles of Arithmetic*) which gives the Peano axioms defining the natural numbers in terms of sets. - FitzGerald suggests what is now called the FitzGerald-Lorentz contraction to explain the "Michelson-Morley experiment".