Charles Émile Picard
Encyclopedia
Charles Émile Picard FRS (ʃaʁl emil pikaʁ; 24 July 1856 – 12 December 1941) was a French mathematician
. He was elected the fifteenth member to occupy seat 1 of the Académie Française
in 1924.
are probably familiar with two of his named theorems. His lesser theorem states that every nonconstant entire function
takes every value in the complex plane
, with perhaps one exception. His greater theorem states that an analytic function
with an essential singularity
takes every value infinitely often, with perhaps one exception, in any neighborhood of the singularity. He also made important contributions in the theory of differential equation
s, including work on Picard–Vessiot theory
, Painlevé transcendents
and his introduction of a kind of symmetry group
for a linear differential equation
, the Picard group. In connection with his work on function theory, he was one of the first mathematicians to use the emerging ideas of algebraic topology
.
In addition to his path-breaking theoretical work, Picard also made important contributions to applied mathematics
, including the theories of telegraphy and elasticity. His collected papers run to four volumes.
Like his contemporary, Henri Poincaré
, Picard was much concerned with the training of mathematics, physics, and engineering students.
He wrote a classic textbook on analysis
and one of the first textbooks on the theory of relativity
.
Picard's popular writings include biographies of many leading French mathematicians, including his father in law, Charles Hermite
.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. He was elected the fifteenth member to occupy seat 1 of the Académie Française
Académie française
L'Académie française , also called the French Academy, is the pre-eminent French learned body on matters pertaining to the French language. The Académie was officially established in 1635 by Cardinal Richelieu, the chief minister to King Louis XIII. Suppressed in 1793 during the French Revolution,...
in 1924.
Biography
Picard's mathematical papers, textbooks, and many popular writings exhibit an extraordinary range of interests, as well as an impressive mastery of the mathematics of his time. Modern students of complex variablesComplex variables
In mathematics, the term complex variables may be taken to mean one of* Complex analysis* Several complex variables* Quaternion variable* Motor variable* Multicomplex numbers* Hypercomplex numbers* Tricomplex numbers...
are probably familiar with two of his named theorems. His lesser theorem states that every nonconstant entire function
Entire function
In complex analysis, an entire function, also called an integral function, is a complex-valued function that is holomorphic over the whole complex plane...
takes every value in the complex plane
Complex plane
In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the orthogonal imaginary axis...
, with perhaps one exception. His greater theorem states that an analytic function
Analytic function
In mathematics, an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions, categories that are similar in some ways, but different in others...
with an essential singularity
Essential singularity
In complex analysis, an essential singularity of a function is a "severe" singularity near which the function exhibits extreme behavior.The category essential singularity is a "left-over" or default group of singularities that are especially unmanageable: by definition they fit into neither of the...
takes every value infinitely often, with perhaps one exception, in any neighborhood of the singularity. He also made important contributions in the theory of differential equation
Differential equation
A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders...
s, including work on Picard–Vessiot theory
Picard–Vessiot theory
In differential algebra, Picard–Vessiot theory is the study of the differential field extension generated by the solutions of a linear differential equation, using the differential Galois group of the field extension. A major goal is to describe when the differential equation can be solved by...
, Painlevé transcendents
Painlevé transcendents
In mathematics, Painlevé transcendents are solutions to certain nonlinear second-order ordinary differential equations in the complex plane with the Painlevé property , but which are not generally solvable in terms of elementary functions...
and his introduction of a kind of symmetry group
Symmetry group
The symmetry group of an object is the group of all isometries under which it is invariant with composition as the operation...
for a linear differential equation
Linear differential equation
Linear differential equations are of the formwhere the differential operator L is a linear operator, y is the unknown function , and the right hand side ƒ is a given function of the same nature as y...
, the Picard group. In connection with his work on function theory, he was one of the first mathematicians to use the emerging ideas of algebraic topology
Algebraic topology
Algebraic topology is a branch of mathematics which uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence.Although algebraic topology...
.
In addition to his path-breaking theoretical work, Picard also made important contributions to applied mathematics
Applied mathematics
Applied mathematics is a branch of mathematics that concerns itself with mathematical methods that are typically used in science, engineering, business, and industry. Thus, "applied mathematics" is a mathematical science with specialized knowledge...
, including the theories of telegraphy and elasticity. His collected papers run to four volumes.
Like his contemporary, Henri Poincaré
Henri Poincaré
Jules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and a philosopher of science...
, Picard was much concerned with the training of mathematics, physics, and engineering students.
He wrote a classic textbook on analysis
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
and one of the first textbooks on the theory of relativity
Theory of relativity
The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....
.
Picard's popular writings include biographies of many leading French mathematicians, including his father in law, Charles Hermite
Charles Hermite
Charles Hermite was a French mathematician who did research on number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra....
.