Adrien-Marie Legendre is a mathematician who is most famous for writing Elements de Geometrie and for his obsession in trying to prove Euclid's fifth postulate.  In Elements de Geometrie he attempted a pedagogical improvement of Euclid's Elements by rearranging and simplifying the proposition.  He spent over 30 years trying to prove the parallel postulate.

Legendre was born on September 18, 1752 in Paris France.  He was educated at College Mazarin in Paris.  From 1775 to 1780 he taught at the Ecole Militaire and he was appointed to the Academie des Sciences in 1783.  He remained there until it closed in 1793.

His most famous book is Elements de Geometrie.  In his book he gave a simple proof on why p is irrational.  He also proved that p² is irrational and conjectured that p is not the root of any algebraic equation of finite degree with rational coefficients, in other words, that p is not algebraic.  Legendre made many contributions to the field of number theory, elliptic functions, the method of least squares, and integrals.  Based on experimental evidence, which depends on extensive calculations, Legendre suggested that for a large n the density of primes behaves like the function 1/log(n).  He gave the following expression, which is said to "fit the distribution of primes well":

Sadly to say, Legendre did not die "well".  What I mean by that is that although he made considerable advances in mathematics, he died in poverty.  The reason for this is that in 1824, he refused to vote for the government's candidate for Institut National.  As a result the government took his pension away.

Author: Sergio Gonzalez

References:
Eves, Howard.  An introduction to the History of Mathematics, 6th edition. Published by Saunders College Publishing, Florida, 1992.

Greenberg, Marvin Jay.  Euclidean and non-Euclidean Geometries; development and history.  Published by W. H. Freeman and Company, New York, 1993.

O'Connor, John J and Robertson, Edmund F Mathematical MacTutor. 1996.  1998.  www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Legendre.html, www-groups.dcs.st-and.ac.uk/~history/Diagrams/PrimeNumTheorem.gif, and www-groups.dcs.st-and.ac.uk/~history/HistTopics/Non-Euclidean_geomtery.html.