Marie Ennemond Camille Jordan
Born: 5 Jan 1838 in Lyon, France
Died: 22 Jan 1922 in Milan, Italy
Previous (Chronologically) Next Biographies Index Previous ( Alphabetically) Next Welcome page
Previous (Chronologically) Next Biographies Index Previous ( Alphabetically) Next Welcome page
Camille Jordan was highly regarded by his contemporaries for his work in algebra and group theory.
Jordan studied mathematics at the École Polytechnique and from 1873 taught there and at the Collège de France.
He introduced important topological concepts in 1866. He was aware of Riemann's work in topology but did not know of the work by Möbius. Jordan introduced the notion of homotopy of paths looking at deformation of paths one into the other. He defined a homotopy group of a surface without explicitly using group terminology.
Jordan was particularly interested in the theory of finite groups. His introduction to the group concept in geometry (1869) was motivated by studies of crystal structure. In this work he considers classification of groups of Euclidean motions.
His Traité des substitutions et des équations algebraique in 1870 gave a comprehensive study of Galois theory. For this work he was awarded the Poncelet Prize of the Académie des Science. The work contains the 'Jordan normal form' for matrices, not over the complex numbers but over a finite field. He appears not to have known of earlier results of this type by Weierstrass. It also brings permutation groups to a central role in mathematics.
Jordan is best remembered today for his proof that a simply closed curve divides a plane into exactly two regions. He originated the concept of functions of bounded variation and is known especially for his definition of the length of a curve. This appears in his Cours d'analyse de l'École Polytechnique 3 volumes (1882), the Jordan curve theorem appearing in the 3rd edition (1909-1915).
He also generalised the criteria for convergence of Fourier series.
Two of Jordan's students, Sophus Lie and Felix Klein, drew upon his studies to produce their own theories of continuous and discontinuous groups.
References elsewhere in this archive:
Tell me about Jordan's work on matrices and determinants
Tell me about Jordan's work on topology
References:
Previous (Chronologically) Next Biographies Index Previous ( Alphabetically) Next Welcome page History Topics Index Famous curves index Chronologies Birthplace Map Mathematicians of the day Anniversaries for the year Search Form Simple Search Form Search Suggestions