Adrien marie legendre biography of williams

1. Biography of Adrien-Marie Legendre
2. Early Education and Career
3. Academic Achievements
4. Legacy and Personal Life

Biography of Adrien-Marie Legendre

Adrien-Marie Legendre was a prominent French mathematician who lived from 1752 to 1833. He was born on September 18, 1752, in Paris, France.

Early Education and Career

Legendre completed his education at the Collège Mazarin and later became a professor at the Military School in Paris in 1775. He was known for his contributions to the field of mathematics and was elected as a member of the Paris Academy of Sciences in 1783.

During the French Revolution, Legendre, along with Lagrange and Laplace, actively participated in the Commission for the Introduction of the Metric System. They were involved in measuring the length of one degree between Dunkirk and Barcelona to establish the meter standard.

Academic Achievements

In 1795, Legendre became a professor at the École Normale, and in 1799, he replaced Laplace as an examiner at the Polytechnic School. He continued his academic career and became a professor at the Polytechnic School in 1816.

Legendre made several significant contributions to mathematics. He formulated the quadratic reciprocity law and introduced Legendre symbols, which had a modern formulation. However, some of his proofs in his fundamental work, "Essai sur la théorie des nombres" (Essay on the Theory of Numbers), were not rigorous or absent altogether. These gaps were later filled by Gauss.

He also developed the theory of continuous fractions and their applications in solving Diophantine equations. In the final edition of his work, he presented a proof for Fermat's Last Theorem for n = 5 in 1830.

Legendre further advanced geodetic measurements and spherical trigonometry. He introduced Legendre polynomials, Legendre transformation, and investigated Euler's integrals of the first and second kind. He demonstrated the reducibility of elliptic integrals to canonical forms, compiled tables of their values, and established a criterion for the existence of extrema in variational calculus.

Legacy and Personal Life

Despite his significant contributions to mathematics, Legendre's career was marked by several instances where his discoveries were overshadowed or preceded by other mathematicians. His priority dispute with Gauss over the method of least squares is an example of this.

Legendre's textbook, "Elements of Geometry," published in 1794, had a lasting impact on mathematics education. It went through multiple editions during his lifetime and was translated into numerous languages. Although his attempts to prove Euclid's fifth postulate in the book were unsuccessful, it remained a highly regarded textbook in Russia.

Unfortunately, Legendre faced financial difficulties in his later years due to a bureaucratic error that resulted in the cancellation of his pension in 1824. He passed away in Paris on January 10, 1833. He is remembered as one of the greatest scientists of France, with his name included in the list of eminent scientists displayed on the first floor of the Eiffel Tower.

In honor of Legendre's contributions, a crater on the moon and numerous mathematical theorems and concepts bear his name.