Joseph-Louis Lagrange / zho-SEF loo-EE, la-GRAHNZH /
Italian-Born French Mathematician
Mathematics Ranking 15th of 46
Portrait of Lagrange on a French stamp.
Joseph-Louis Lagrange’s most influential work was the Traite de mecanique analytique (Characteristics of Analytical Mechanics, 1788), which was the culmination of his extensive work on mechanics and its application to the description of planetary and lunar motion.(1) All later work in this field was based on his book. Second, and just as significant, Lagrange became the leading spirit in formulating the metric system. The metric system was adopted by the French government on November 25, 1792, and became the most widely used system of weights and measures in the world.
Lagrange was one of eleven children born to a French couple living in Turin; of these eleven, he alone survived infancy. He was turned from the classics to science by reading a memoir addressed by Edmund Halley to the Royal Society of London. At once he devoted himself to mathematics, and with such success that at 18 he became professor of geometry at the Turin Artillery Academy. At 19, he sent Leonard Euler a new method for treating the calculus of variations. Euler replied that this procedure solved difficulties which he himself had been unable to overcome. The kindly Euler delayed making public his own results, “so as not to deprive you of any part of the glory which is your due.”(2) Lagrange announced his method in the first volume issued by the Turin Academy (1759). When Euler left Prussia, he recommended Lagrange as his successor at the Academy, and in 1766 Lagrange moved to Berlin. He greeted Frederick II as “the greatest king in Europe”; Frederick welcomed him as “the greatest mathematician in Europe.”(3)
During his twenty years in Berlin, Lagrange gradually put together his masterpiece, Mecanique Analytique. Incidentally to this basic enterprise, he delved into astronomy, and offered a theory of Jupiter’s satellites. In 1786, Frederick the Great died and was succeeded by Frederick William II, who cared little for science. Lagrange accepted an invitation from Louis XVI to join the Academie des Sciences in Paris. He was given comfortable quarters in the Louvre, and became a favorite of Marie Antoinette. He brought the manuscript of Mecanique Analytique but could find no publisher for so difficult a printing problem in a city seething with revolution. His friends Adrien Legendre and the Abbé Marie finally prevailed upon a printer to undertake the task, but only after the abbé promised to buy all copies unsold after a stated date. When the book that summed up his life’s work was placed in Lagrange’s hands (1788), he did not care to look at it. He was in a periodic depression in which he lost all interest in mathematics, even in life. For two years, the book remained unopened on his desk.
The Mecanique Analytique is rated by general consent as the summit of eighteenth-century mathematics. Second only to Newton’s Principia Mathematica in their field, it advanced upon Newton’s book by using “analysis”—algebraic calculus—instead of geometry in the discovery and exposition of solutions. In the preface it states, “No diagrams will be found in this work.” By this method Lagrange reduced mechanics to general formulas—the calculus of variations—from which specific equations could be derived for each particular problem. These general equations still dominate mechanics, and bear his name. Ernst Mach described them as one of the greatest contributions ever made to the economy of thought.(4)
When the French Revolution broke out with the fall of the Bastille (July 14, 1789), Lagrange, as a favorite of royalty, was advised to return to Berlin. He refused. He was horrified by the massacres of September 1792 and the execution of his friend Antoine Lavoisier (regarded as the father of modern chemistry), but his moody silence saved him from the guillotine. In 1797, he became the first professor at the newly established Ecole Polytechnique. The mathematical basis and bent of French education are part of Lagrange’s enduring influence.(5)
The common measurements since ancient times had been the product of usage in the local market. They came from the bodily measurements that were available everywhere. The “digit” was the width of a finger, the “palm” was the width of four fingers, the “cubit” was the distance between the elbow and the top of the middle finger, the “pace” was one step, and the “fathom” the distance between outstretched arms. The variety of common units across Europe caused daily inconvenience and was an incentive for fraud. Every trade had its own vocabulary. In England, apothecaries had minims and drams, for seamen fathoms, knots, and cable lengths. A gallon of wine was not the same measure as a gallon of ale. A bushel of wheat was sold rounded or “heaped,” but corn was leveled. Elsewhere in Europe, the practice was not much simpler. A dictionary of local units of weights and measures used in France before the Revolution came to 200 printed pages. The chaos and the local variety everywhere expressed the variety of needs.
In 1791, to end all the problems and confusion caused by so many local units of weights and measures, the French government appointed a committee to devise a new system of weights and measures. Lagrange, Lavoisier, and Pierre Laplace (a prominent French mathematician and physicist) were among its first members; two of the three were “purged” after three months, and Lagrange became the leading spirit in formulating the metric system. The committee chose as the
basis of length a quadrant of the earth—a quarter of the great circle passing around the earth at sea level through the poles. One ten-millionth of this was taken as the new unit of length and was called a “metre”—a meter. A subcommittee chose as the new unit of weight a gram: the weight of distilled water, at zero temperature centigrade, occupying a cube each side of which measured one centimeter–one hundredth of a meter. In this way, all lengths and weights were based upon one physical constant, and upon the number ten (like the base-10 counting system adopted worldwide). There were still many defenders of the duodecimal system, which took twelve as its base, as in England and generally in our measurement of time (two 12-hour periods make up the 24-hour day). Lagrange stood firmly for ten, and had his way. The metric system was adopted by the French government on November 25, 1792, and became the most widely used system of weights and measures in the world.
The influence of the metric system, because it was adopted by more and more countries until it became the international standard in commerce and the sciences, is, ironically, immeasurable. The metric system is understood across the globe so everyone has a shared frame of reference when exchanging measurement information; just consider all the confusion that is avoided in the world of commerce because of this. The metric system also allowed scientists from different countries to more easily confirm the results of each other’s experiments.
Commonly used metric system units and symbols
(1) Judy Pearsall and Bill Trumble (editors), The Oxford Encyclopedic English Dictionary (New York, 1996), p. 800.
(2) Will Durant, The Age of Voltaire – The Story of Civilization: Volume 9 (New York, 1950), p. 511.
(3)Ibid., p. 511.
(4) Ibid., p. 512.
(5) Ibid., p. 512