Charles Émile Picard (; 24 July 1856 – 11 December 1941) was a French
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
. He was elected the fifteenth member to occupy seat 1 of the
Académie française in 1924.
Life
He was born in
Paris
Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), ma ...
on 24 July 1856 and educated there at the
Lycée Henri-IV
The Lycée Henri-IV is a public secondary school located in Paris. Along with the Lycée Louis-le-Grand, it is widely regarded as one of the most prestigious and demanding sixth-form colleges (''lycées'') in France.
The school educates more than ...
. He then studied mathematics at the
École Normale Supérieure
École may refer to:
* an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée)
* École (river), a tributary of the Seine flowing in région Île-de-France
* École, S ...
.
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.
Picard's little theorem states that every nonconstant
entire function
In complex analysis, an entire function, also called an integral function, is a complex-valued function that is holomorphic on the whole complex plane. Typical examples of entire functions are polynomials and the exponential function, and any fin ...
takes every value in the
complex plane, with perhaps one exception.
Picard's great theorem
In complex analysis, Picard's great theorem and Picard's little theorem are related theorems about the range of an analytic function. They are named after Émile Picard.
The theorems
Little Picard Theorem: If a function f: \mathbb \to\mathbb ...
states that an
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. Functions of each type are infinitely differentiable, but complex ...
with an
essential singularity
In complex analysis, an essential singularity of a function is a "severe" singularity near which the function exhibits odd behavior.
The category ''essential singularity'' is a "left-over" or default group of isolated singularities that a ...
takes every value infinitely often, with perhaps one exception, in any neighborhood of the singularity. He made important contributions in the theory of
differential equation
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...
s, including work on
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
In mathematics, a linear differential equation is a differential equation that is d ...
,
Painlevé transcendents and his introduction of a kind of
symmetry group for a
linear differential equation
In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form
:a_0(x)y + a_1(x)y' + a_2(x)y'' \cdots + a_n(x)y^ = b ...
. He also introduced the
Picard group
In mathematics, the Picard group of a ringed space ''X'', denoted by Pic(''X''), is the group of isomorphism classes of invertible sheaves (or line bundles) on ''X'', with the group operation being tensor product. This construction is a global ve ...
in the theory of
algebraic surfaces, which describes the classes of
algebraic curve
In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a homogeneous polynomial in three variables. An affine algebraic plane ...
s on the surface modulo linear equivalence. 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 is a branch of mathematics that 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 ...
. In addition to his theoretical work, Picard made contributions to
applied mathematics
Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathemati ...
, including the theories of
telegraphy
Telegraphy is the long-distance transmission of messages where the sender uses symbolic codes, known to the recipient, rather than a physical exchange of an object bearing the message. Thus flag semaphore is a method of telegraphy, whereas ...
and
elasticity. His collected papers run to four volumes.
Louis Couturat
Louis Couturat (; 17 January 1868 – 3 August 1914) was a French logician, mathematician, philosopher, and linguist. Couturat was a pioneer of the constructed language Ido.
Life and education
Born in Ris-Orangis, Essonne, France. In 1887 he ...
studied
integral calculus
In mathematics, an integral assigns numbers to Function (mathematics), functions in a way that describes Displacement (geometry), displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding ...
with Picard in 1891-1892, taking detailed notes of the lectures. These notes were preserved and now are available in three cahiers from
Internet Archive
The Internet Archive is an American digital library with the stated mission of "universal access to all knowledge". It provides free public access to collections of digitized materials, including websites, software applications/games, music, ...
.
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
Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (3 ...
and one of the first textbooks on the
theory of relativity
The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in ...
. Picard's popular writings include biographies of many leading French mathematicians, including his father in law,
Charles Hermite
Charles Hermite () FRS FRSE MIAS (24 December 1822 – 14 January 1901) was a French mathematician who did research concerning number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra.
Hermi ...
.
Family
In 1881 he married Marie, the daughter of
Charles Hermite
Charles Hermite () FRS FRSE MIAS (24 December 1822 – 14 January 1901) was a French mathematician who did research concerning number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra.
Hermi ...
.
Works
* 1891–96:
* 1905:
* 1906 : (with Georges Simart
Theorie des Fonctions Algebrique de deux Variables Independentevolume 2, via
Internet Archive
The Internet Archive is an American digital library with the stated mission of "universal access to all knowledge". It provides free public access to collections of digitized materials, including websites, software applications/games, music, ...
* 1922:
* 1922:
* 1931:
* 1978–81:
See also
*
Émile Picard Medal
*
Picard modular group
In mathematics, a Picard modular group, studied by , is a group of the form SU(''J'',''L''), where ''L'' is a 3-dimensional lattice over the ring of integers of an imaginary quadratic field and ''J'' is a hermitian form on ''L'' of signature ...
*
Picard modular surface In mathematics, a Picard modular surface, studied by , is a complex surface constructed as a quotient of the unit ball in C2 by a Picard modular group.
Picard modular surfaces are some of the simplest examples of Shimura varieties and are sometime ...
*
Picard horn A Picard horn, also called the Picard topology or Picard model, is one of the oldest known hyperbolic 3-manifolds, first described by Émile Picard in 1884. The manifold is the quotient of the upper half-plane model of hyperbolic 3-space by the pro ...
References
External links
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{{DEFAULTSORT:Picard, Charles Emile
1856 births
1941 deaths
Scientists from Paris
19th-century French mathematicians
20th-century French mathematicians
Lycée Henri-IV alumni
École Normale Supérieure alumni
Mathematical analysts
Grand Croix of the Légion d'honneur
Members of the Académie Française
Members of the French Academy of Sciences
Foreign Members of the Royal Society
Members of the Pontifical Academy of Sciences
Members of the Hungarian Academy of Sciences
Fellows of the American Academy of Arts and Sciences
Foreign associates of the National Academy of Sciences
Corresponding members of the Saint Petersburg Academy of Sciences
Honorary Members of the Russian Academy of Sciences (1917–1925)
Grand Crosses of the Order of Saint James of the Sword
Members of the Ligue de la patrie française
Members of the Royal Society of Sciences in Uppsala