Legendre
Legendre, Adrien-Marie
ACHIEVEMENTS:
Advances in mathematical analysis
NICKNAME/ALIAS:
None
DATE AND PLACE OF BIRTH:
18 September 1752, Paris, France
DATE AND PLACE OF DEATH AND AGE AT DEATH:
10 January 1833, Paris, France. Aged 87
DISCIPLINE:
Mathematician
FIELD:
Mathematics
LANGUAGE:
French
PARENTS:
Father: ?
Mother:?
SIBLINGS:
?
SPOUSE:
Marguerite Couhin
CHILDREN:
None
EDUCATION:
College Mazarin, Paris
MAJOR WORK:
"Treatise on Elliptic Functions" (1825-37)
and
"Elements of Geography" (1794)
LIFE AND TIMES:
Legendre was brought up in comfortable circumstances and received an excellent education in science and mathematics. He had the money to follow an independent career in research and he also chose to teach mathematics at the Military Academy in Paris from 1775-80.
During the first years of his research, Legendre worked in the three areas to which he always returned: celestial mechanics, number theory and the theory of elliptic functions. In 1782 he was awarded the annual prize of the Berlin Academy for his essay on the trajectory of canon balls and bombs.
This brought him to the notice of Lagrange* but Legendre still wanted to be part of the wider scientific community. To this end he read a paper to the Academy of Sciences on the mutual attractions of planetary spheroids and also sent a number of essays to Laplace*, on probabilities, the rotation of bodies subject to no accelerating force, the properties of continued fractions, and second degree indeterminate equations. Much of Legendre's work was used by Laplace without acknowledgement but Legendre did become a member of the Academy of Sciences in 1783.
In the following year he presented a paper on number theory in which the renowned Legendre polynomials appeared for the first time. In 1785 he published a further paper in which he made his famous statement: "Every arithmetical progression whose first term and ratio are relatively prime contains an infinite number of prime numbers". He also stated the law of quadratic reciprocity. In 1786 he began his long investigations into integrations by elliptic arcs and published two works on the subject which show the basis of his mature theory of elliptic functions.
He was appointed by the Academy to take part in the meridian project set up jointly by the Paris and Greenwich observatories. In association with this, he was made a fellow of the Royal Society in London. In 1791 he was named by the Academy as one of the commissioners who would supervise the quantifying of the standard metre. However, a year later he requested his removal from this post.
In 1793, during the period of The Terror in the French Revolution, Legendre lost his modest inheritance and may even have been forced to go into hiding for a time. He survived and got on with preparing his textbook on geometry which was published in 1794.
He re-organized and simplified many of Euclid's* propositions and his book replaced that of Euclid as the standard textbook on geometry. Legendre was appointed head of the National Executive Commission of Public Instruction in 1794, with a brief to supervise weights and measures, and new inventions, and to promote science.
Legendre's first essay on the theory of numbers, which expanded and systemized his earlier work was published in 1798. Generally speaking, Legendre's contemporaries took very little notice of his work but the mathematician Germain* contacted him about his theory of numbers. Legendre supported Germain in her efforts for recognition which were obstructed by rivals like Poisson*.
Although he was not rewarded with a professorship, Legendre was appointed examiner in mathematics at the Military Academy in 1799. His publication on comet orbits in 1806 contains the first published account of the method of least squares.
He continued to publish papers on the theory of elliptic integrals on which he worked for over forty years, and his "Treatise on Elliptic Functions" was published between 1825-30. This was his most important work and in it he reduced elliptic integrals to the three standard forms known named after him. Soon after publication, the subject was revolutionized by the independent work of other mathematicians in the field.
In 1830 he published his final work on number theory, "Theory of Numbers" in which he collated his own researches and that of his predecessors. It contained the proof of his law of quadratic reciprocity and new material inspired mainly by Gauss*.
ASSESSMENT: Legendre is remembered for his work on number theory and his discovery of the law of quadratic reciprocity, and his extensive study of elliptic integrals which proved a fertile ground for future elaboration.
EXTRA CONNECTIONS: None
ONELINER: A-M Legendre, French mathematician
BIBLIOGRAPHY:
EB, DSB