Lagrange
NAME:
Lagrange, Joseph-Louis, Count of the Empire
ACHIEVEMENTS:
Advances in mathematics
NICKNAME/ALIAS:
None
DATE AND PLACE OF BIRTH:
25 January 1736, Turin, Italy
DATE AND PLACE OF DEATH AND AGE AT DEATH:
10 April 1813, Paris, France. Aged 77
DISCIPLINE:
Mathematician
FIELD:
Mathematics
PARENTS:
Father: Guiseppe Lagrange
Mother: Marie-Therese Gros
SIBLINGS:
None survived beyond infancy
SPOUSE:
- Vittoria Conti
- Renee-Francoise Le Monnier
CHILDREN:
None
EDUCATION:
Schools in Turin
MAJOR WORK:
"Analytical Mechanics" (1788)
LIFE AND TIMES:
Lagrange’s interest in mathematics started when he read an essay by the English astronomer <influenced by> Halley* on the advantages of calculus over Greek geometry.
Lagrange mastered analysis in an exceptionally short time and at the age of sixteen is said to have been teaching mathematics to older boys at the artillery school in Turin. He later organised the brighter students into a research society which became the Turin Academy of Sciences. The Academy published its first papers in 1759.
Lagrange’s papers on the propagation of sound were immediately recognised for their brilliance. Lagrange had solved a problem on variations which had puzzled the distinguished German mathematician <collaborated with> Euler*, who generously delayed his own publication so Lagrange could have credit for his work.
Lagrange was stimulated to apply analytic methods to celestial mechanics through competitions set by the Paris Academy of Sciences. In 1764 they set the task set of calculating, from the Newtonian law of gravitation, why the moon always showed the same face to Earth, with only slight variations which could be accounted for. Lagrange won the prize.
Two years later the Academy set a more difficult task: the formulation of a theory for the motions of the satellites of Jupiter. Only four of Jupiter's satellites had then been discovered, but Lagrange used methods of approximation and his prize-winning essay was a major advance in celestial mechanics.
On Euler's recommendation, <made Academician by> Frederick the Great*, king
of Germany, appointed Lagrange to the Berlin Academy, declaring that "the greatest King in Europe" wanted "the greatest mathematician" at his court. Lagrange arrived in Berlin in 1766 and stayed for twenty-two years, during which time he produced most of his best work.
He spent most of his time on the theory of numbers, and the numerical and algebraic solutions of equations. His papers "On the Solution of Numerical Equations" (1767) and "Reflections on the Algebraic Resolution of Equations" (1770) did not resolve the questions he raised, but they triggered a new period in algebra and inspired the leading algebraists of the early nineteenth century.
Like many of his colleagues, he tried providing the proof for <worked on theorems of> Fermat's* theorems and later recalled that arithmetical research had "cost him most trouble" and that arithmetic is always "more difficult than it seems at first”.
He published papers on differential and integral calculus, and was interested in investigating a calculus of probabilities, but complained he did not have the time to do so.
In connection with his work on probability, he began to translate <started translation of> de Moivre's* book on "The Doctrine of Chance" but did not complete it.
Lagrange produced papers on more aspects of the "Problem of the Three Bodies" (the mutual attraction of three bodies according to the law of the inverse square of the distances between their centres of gravity).
In 1782 he finished writing "Analytical Mechanics," the work which marked the first total break with the Greek tradition. Where Newton, and others who followed him, had used diagrams in their analysis of mechanics Lagrange did not. He based his explanation on his calculus of variations, and in doing so produced the so-called “Lagrange equations” for a classical mechanical system.
After the death of Frederick, Lagrange accepted an invitation from the French king, <accepted invitation of> Louis XVI*. He arrived in Paris in 1787 and was treated as an honored guest by the royal family and the Academy. He was given rooms at the Louvre, and was particularly friendly with the French queen, Marie Antoinette, who tried to lift him out of the depression into which he had fallen.
Lagrange had become indifferent to mathematics and it was two years before he could be bothered to publish "Analytical Mechanics". The Revolution of 1789 cured his depression. He refused to leave Paris, saying he wanted to see the experiment through something he came to regret when he witnessed the barbarism of The Terror in 1793/4. (When the chemist <knew> Lavoisier* was guillotined, Lagrange commented that "it required only a moment to sever that head, and perhaps a century will not be sufficient to produce another like it".)
His own position was not threatened and he was called to help with the reform of the <developed> metric system* and given committee jobs to supplement his pay. In 1795 he was appointed professor of mathematics when the Ecole Normale was established and when it was replaced in 1797 by the Ecole Polytechnic, he became the first professor of mathematics, teaching the young military engineers being promoted by Napoleon.
When his students found it difficult to understand the concept of the infinitely small and the infinitely great in the traditional form of the calculus, Lagrange attempted a development of the calculus based on algebra without the use of <work related to> Leibniz's* infinitesimals. He failed to do so, but his work inspired later mathematicians to construct a satisfactory calculus.
His "Theory of Analytic Functions" (1797) and "Lessons on the Calculus of Functions" (1804) provided the first textbooks on real analytic functions. Among his pupils were <taught> Poisson* and <taught> Germain*.
Lagrange was made a Count of the empire and remained in Paris until his death.
ASSESSMENT: Responsible for major advances in the theory of numbers and in analytic and celestial mechanics.
EXTRA CONNECTIONS:
He knew the work of <knew work of>Legendre*
ONELINER: JL Lagrange, major French 18th century mathematician
BIBLIOGRAPHY:
Bell, ET, Men of Mathematics, Victor Gollancz Ltd., London, 1937