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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.
In 1830Events February 3 The previously autonomous state of Greece gains full independence from the Ottoman Empire as the final result of the Greek War of Independence. Negotiations for the borders between the two states continue until 1832, under the supervisio he gave a proof of Fermat's last theoremFermat's last theorem (sometimes abbreviated as FLT and also called Fermat's great theorem is one of the most famous theorems in the history of mathematics. It states that: :There are no positive natural numbers a b and c such that where n is a natural nu for exponent n = 5, which was given almost simultaneously by DirichletJohann Peter Gustav Lejeune Dirichlet ( February 13, 1805 May 5, 1859) was a German mathematician credited with the modern "formal" definition of a function. His family hailed from the town of Richelet in Belgium, from which his surname "Lejeune Dirichlet in 1828Events January 4 The Vicomte de Martignac succeeds the Comte de Villele as Prime Minister of France. January 22 The Duke of Wellington succeeds Lord Goderich as Prime Minister of the United Kingdom. He repeals the Test Act, emancipating all Catholics, and.
In number theory, he conjectured the quadratic reciprocity law, subsequently proved by Gauss. He also did pioneering work on the distribution of primesIn mathematics, a prime number or prime for short, is a natural number whose only distinct positive divisors are 1 and itself; otherwise it is called a composite number . Hence a prime number has exactly two divisors. The number 1 is neither prime nor com, and on the application of analysis to number theory. His 1796Events Edward Jenner develops vaccination, using cowpox to protect against smallpox February 1 The capital of Upper Canada is moved from Newark to York March 9 Widow Josephine de Beauharnais marries General Napoleon Bonaparte. March 30 Carl Gauss obtained conjecture of the Prime number theoremIn number theory, the prime number theorem PNT describes the approximate, asymptotic distribution of the prime numbers. For any positive real number x define : The prime number theorem then states that : where ln x is the natural logarithm of x''. This no was rigorously proved by HadamardJacques Solomon Hadamard ( December 8, 1865 October 17, 1963) was a mathematician best known for his proof of the prime number theorem. He studied at the Ecole Normale Superieure. After the Dreyfus affair, which involved him personally, he became politica 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.
In theoretical mechanics, he is known for the Legendre transform, which is used to go from the Lagrangian to the Hamiltonian formulation of mechanics.