Joseph-Louis Lagrange (1736-1813) Historical Sketch
Today, it is almost impossible to listen to a newscast featuring a politician without hearing what we must do, now that we are in "the 21st century." The phrase is used so often that it has become trite, but we wouldn't even hear it had it not been for Lagrange! You see, he was a member of the French Academy of Sciences, and the Academy appointed him to head the Comité International des Poids et Mesures (International Committee of Weights and Measures) in 1790. He persuaded the Committee to adopt the base ten metric system instead of a base twelve system, proposed by the British who held a lot of sway in the world of that time and who favored groupings by dozens. Had the base twelve people won the argument, the first year of what we call the 21st century, 2001, would be the small-looking number 11T9 (do you think we would have called that the year "eleventy-nine"?). And 2001 in base twelve wouldn't occur until the year we call 3457.
There is a story to tell about the previous paragraph. It seems to be accepted mathematical folklore that in the voting about base ten versus base twelve, the vote on the issue was a tie, and that therefore Lagrange as Chairman would vote to break the tie. The story has it that to satirize the tight situation, Lagrange moved to make eleven the base for numeration, causing a stir among the delegates. And then only after that did Lagrange vote for base ten to break the tie. Is this story true? Well, no one knows, for there were no minutes kept of these proceedings----indeed, there were no recorded minutes of any of the issues of the Comité International, due to the fact that all this happened during the turmoil of the French Revolution, and so it was dangerous to have records of meetings, lest a committee member's vote on an issue cause him possibly fatal troubles.
The luminary of this Sketch, Joseph Louis Lagrange, is described in Boyer's History of Mathematics as being "generally regarded as the keenest of mathematicians of the eighteenth century, only Euler being a close rival, ... . " See [1].
There are those who might argue with this assessment, but none could assert that Lagrange was anything less than a remarkable and dominant mathematician of his time. Turnbull says in his little book, The Great Mathematicians, that Lagrange "would set to mathematics all the little themes on physical inquiries which his friends brought him, much as Schubert would set to music any stray rhyme that took his fancy." See [2].
Joseph-Louis Lagrange was born in 1736 to a wealthy French family of Turin, Italy, the first of his parents' eleven children; and he remains to this day a heroic figure in Turin, though he spent most of his life elsewhere.
In school, he was not at first attracted to mathematics, finding geometry rather dull. He preferred instead the study of classical Greek. He also studied astronomy (Lagrange is today recognized as one of the founders of modern astronomy). In astronomy, he saw some work of Halley, and at about age 17 became enamored with mathematics. After some fits and starts in pursuing original ideas in his self-taught mathematics, it became clear that he was deeply talented in the subject, and he was at age 19 appointed Professor of Mathematics at the Royal Artillery School in Turin. This attraction to astronomy continued, and he made important contributions to the field of celestial mechanics.
- In an English-speaking society with base 12 numeration, do you think "common folks" would pronounce the year 11T9 as "eleventy nine"? If not, how do you think they would say that? Explain.
- The first discovery that Lagrange made when he first met mathematics seriously was to notice that successive differentiation of a product of two functions exhibits the Pascal Triangle pattern. He sent this in a letter to Euler, only to find that this property had already been discovered by Euler himself (remember that calculus was then yet in the development stage). Show the first four steps of the pattern Lagrange wrote about.
[1] A History of Mathematics, Second Ed., by Boyer and Merzbach, Wiley & Sons, 1991, p. 490
[2] The Great Mathematicians, by Herbert Westren Turnbull, Simon & Schuster, 1962, p. 117-8