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1880

Poincaré publishes important results on automorphic functions.

1881

Venn introduces his "Venn diagrams" which become a useful tools in set theory.

1881

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.

1882

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.

1883

Poincaré publishes a paper which initiates the study of the theory of analytic functions of several complex variables.

1883

The Edinburgh Mathematical Society is founded. (See this Article.)

1884

Volterra begins his study of integral equations.

1884

Frege publishes *The Foundations of Arithmetic*.

1884

Hölder discovers the "Hölder inequality".

1884

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.

1884

Frobenius proves Sylow's theorems for abstract groups.

1884

Ricci-Curbastro begins work on the absolute differential calculus.

1884

*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.

1885

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

1886

Peano proves that if *f*(*x*, *y*) is continuous then the first order differential equation ^{dy}/_{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".

1888

Galton introduces the notion of correlation.

1888

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.

1889

FitzGerald suggests what is now called the FitzGerald-Lorentz contraction to explain the "Michelson-Morley experiment".

1890

Peano discovers a space filling curve.

1890

St Petersburg Mathematical Society is founded.

1890

Heawood publishes *Map colour theorems* in which he points out the error in Kempe's proof of the Four Colour Theorem. He proves that *five* colours suffice. (See this History Topic.)

List of mathematicians alive in 1880.

List of mathematicians alive in 1890.

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