Everything about Adrien-marie Legendre totally explained
Adrien-Marie Legendre (
September 18 1752 –
January 10 1833) was a
French mathematician. He made important contributions to
statistics,
number theory,
abstract algebra and
mathematical analysis.
The
Legendre crater on the
Moon is named after him.
Life
Born in a wealthy family, Legendre studied physics in Paris and later taught at a military academy out of interest, not because of financial need. His earliest work in physics concerned the
trajectories of cannonballs, but later he moved more towards mathematics.
In 1782, he was elected a member of the
French Academy of Sciences.
Legendre lost his money during the
French Revolution. His
Éléments de Géométrie was a lucrative book and was much reprinted and translated, but it was his various teaching positions and pensions that kept him at an acceptable standard of living. A mistake in office politics in
1824 led to the loss of his pension and he lived the rest of his years in poverty.
Scientific activity
Most of his work was brought to perfection by others: his work on roots of
polynomials inspired
Galois theory;
Abel's work on
elliptic functions was built on Legendre's; some of
Gauss' work in statistics and number theory completed that of Legendre. He developed the
least squares method, which has broad application in linear regression, signal processing, statistics, and curve fitting. Today, the term "least squares method" is used as a direct translation from the French
"méthode des moindres carrés".
In
1830 he gave a proof of
Fermat's last theorem for exponent
n = 5, which was also proven by
Dirichlet in
1828.
In number theory, he conjectured the
quadratic reciprocity law, subsequently proved by Gauss; in connection to this, the
Legendre symbol is named after him. He also did pioneering work on the distribution of
primes, and on the application of analysis to number theory. His
1796 conjecture of the
Prime number theorem was rigorously proved by
Hadamard and
de la Vallée-Poussin in
1898.
Legendre did an impressive amount of work on
elliptic functions, including the classification of
elliptic integrals, but it took
Abel's stroke of genius to study the inverses of
Jacobi's functions and solve the problem completely.
He is known for the
Legendre transform, which is used to go from the
Lagrangian to the
Hamiltonian formulation of
classical mechanics. In
thermodynamics it's also used to obtain the
enthalpy and the
Helmholtz and
Gibbs (free) energies from the
internal energy. He is also the namesake of the
Legendre polynomials which occur frequently in physics and engineering applications,
for example electrostatics.
He also wrote the influential
Éléments de géométrie in 1794.
Further Information
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