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 An academy (Attic Greek: Ἀκαδήμεια; Koine Greek Ἀκαδημία) is an institution of secondary education, secondary or tertiary education, tertiary higher education, higher learning (and generally also research or honorary membershi ...

in 1924.

Life

He was born in

Paris Paris () is the capital and 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), making it the 30th most densely populated city in the world in 2020. S ...

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, Savoi ...

. 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 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 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 In mathematics, the complex plane is the plane formed by the complex numbers, with a Cartesian coordinate system such that the -axis, called the real axis, is formed by the real numbers, and the -axis, called the imaginary axis, is formed by the ...

, 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 an ...

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 In mathematics, Painlevé transcendents are solutions to certain nonlinear second-order ordinary differential equations in the complex plane with the Painlevé property (the only movable singularities are poles), but which are not generally solvabl ...

and his introduction of a kind of

symmetry group In group theory, the symmetry group of a geometric object is the group of all transformations under which the object is invariant, endowed with the group operation of composition. Such a transformation is an invertible mapping of the ambient ...

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 surface In mathematics, an algebraic surface is an algebraic variety of dimension two. In the case of geometry over the field of complex numbers, an algebraic surface has complex dimension two (as a complex manifold, when it is non-singular) and so of di ...

s, 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 c ...

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 invariant (mathematics), invariants that classification theorem, classify topological spaces up t ...

. 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 mathematical s ...

, 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 p ...

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 Jules Henri Poincaré ( S: stress final syllable ; 29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "The ...

, 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 (38 ...

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

Works

* 1891–96: * 1905: * 1906 : (with Georges Simart
Theorie des Fonctions Algebrique de deux Variables Independente
volume 2, via

* 1922: * 1922: * 1931: * 1978–81:

References

External links

* * * {{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

Life

Family

Works

See also

References

External links