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; this was published in 1806 as an appendix to his book on the paths of comets. 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 transformation, which is used to go from the Lagrangian to the Hamiltonian formulation of classical mechanics. In thermodynamics it is also used to obtain the enthalpy and the Helmholtz and Gibbs (free) energies from the internal energy. He is also the namegiver of the Legendre polynomials, solutions to Legendre's differential equation, which occur frequently in physics and engineering applications, e.g. electrostatics.
Legendre is best known as the author of Éléments de géométrie, which was published in 1794 and was the leading elementary text on the topic for around 100 years. This text greatly rearranged and simplified many of the propositions from Euclid's Elements to create a more effective textbook.
Read more about this topic: Adrien-Marie Legendre
Famous quotes containing the words scientific and/or activity:
“Good resolutions are useless attempts to interfere with scientific laws. Their origin is pure vanity. Their result is absolutely nil. They give us, now and then, some of those luxurious sterile emotions that have a certain charm for the weak.... They are simply cheques that men draw on a bank where they have no account.”
—Oscar Wilde (1854–1900)
“A worm is as good a traveler as a grasshopper or a cricket, and a much wiser settler. With all their activity these do not hop away from drought nor forward to summer. We do not avoid evil by fleeing before it, but by rising above or diving below its plane; as the worm escapes drought and frost by boring a few inches deeper.”
—Henry David Thoreau (1817–1862)