He was born in
Paris on 24 July 1856 and educated there at the
Lycée Henri-IV. He then studied mathematics at the
École Normale Supérieure. 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 takes every value in the
complex plane, with perhaps one exception.
Picard's great 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 made important contributions in the theory of
differential equations, including work on
Picard–Vessiot theory,
Painlevé transcendents and his introduction of a kind of
symmetry group for a
linear differential equation. He also introduced the
Picard group in the theory of
algebraic surfaces, which describes the classes of
algebraic curves 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. In addition to his theoretical work, Picard made contributions to
applied mathematics, including the theories of
telegraphy and
elasticity. His collected papers run to four volumes.
Louis Couturat studied
integral calculus 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. 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. Picard was an International Honorary Member of the
American Academy of Arts and Sciences, an International Member of the United States
National Academy of Sciences, and an International Member of the
American Philosophical Society. ==Family==