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Legendre's major work on elliptic integrals provided basic analytical tools for mathematical physics.
Legendre was educated at Collège Mazarin in Paris. From 1775 to 1780 he taught with Laplace at École Militaire where his appointment was made on the advice of d'Alembert. Legendre was appointed to the Académie des Sciences in 1783 and remained there until it closed in 1793.
In 1782 Legendre determined the attractive force for certain solids of revolution by introducing an infinite series of polynomials P
which are now called Legendre polynomials.
His major work on elliptic functions in Exercises du Calcul Intégral (1811,1817,1819) and elliptic integrals in Traité des Fonctions Elliptiques (1825,1826,1830) provided basic analytical tools for mathematical physics.
In his famous textbook Éléments de géométrie
(1794 )he gave a simple proof that
is irrational as well as the first proof that 
is irrational and conjectured that
is not the root of any algebraic equation of finite degree with rational coefficients i.e.
is not algebraic.
His attempt to prove the parallel postulate extended over 40 years.
In 1824 Legendre refused to vote for the government's candidate for Institut National. Because of this his pension was stopped and he died in poverty. Abel wrote in October 1826
Legendre is an extremely amiable man, but unfortunately as old as the stones.
References elsewhere in this archive:
Tell me about the Prime Number Theorem
Show me Legendre's estimates for the density of primes
Tell me about Legendre's part in investigating prime numbers
Tell me about his work on Fermat's last theorem and on non-Euclidean geometry
References:
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