Wednesday, November 26, 2008
Wednesday Math, Vol. 49: The Most Famous Mathematician
When discussing "the most famous _____", we deal more in opinion than fact. With mathematicians, the best known names include the ancient Greeks like Euclid, Pythagoras and Archimedes, but I'm going to go out on a limb and say that Isaac Newton is the best known mathematician in human history.
Why Newton over Einstein? Because Einstein was not a mathematician, but a physicist. Newton was both. Newton not only came up with the three laws of motion and the laws of optics and universal gravity, but he needed to invent the mathematical tools that would solve these problems in physics, and the most important tool he is given credit for developing is calculus. Einstein, in contrast, came up with relativity and the photoelectric effect and gravity being the natural consequence of curved space, but all the mathematical tools needed to solve these problems in physics already existed by the time Einstein was working. Perhaps the most important pre-existing concept Einstein used was the Riemannian manifold, which allows calculus methods to find areas not just over "easy" shapes like lines or planes or circles or spheres, but also on bendy, twisty things as well.
If we expand the list of mathematicians not just to people who spent their careers in the field, but to people who did advanced study, then a more famous name pops up on the list, Napoleon Bonaparte. Napoleon was a talented student, and at the age of 16 passed exams given to him by Pierre-Simon Laplace when the great mathematician was the Examiner of the Royal Artillery Corps. LaPlace not only worked for French royalty, but his career also survived the French Revolution and flourished when his former student became emperor.
Napoleon was of the opinion that Laplace was not the greatest mathematician of his day, but instead gave that place of honor to Giuseppe Lodovico Lagrangia, who Napoleon called "the lofty pyramid of the mathematical sciences." Lagrangia, like Napoleon, was of both Italian and French ancestry, and he is known to posterity as Joseph Louis Lagrange. Some put Lagrange as the greatest mathematician of the entire 18th Century, though the more popular modern view is that he was not quite as significant as the man who helped launch his career, Leonhard Euler, who has been mentioned on this blog many times already.
Napoleon and Laplace crossed paths after Napoleon became emperor when Laplace's masterwork on celestial mechanics was published. Their famous exchange is translated into English as follows.
Napoleon: "How can this be! You made the system of the world, you explain the laws of all creation, but in all your book you speak not once of the existence of God!"
Laplace: "Sire, I did not need to make such an assumption."
Napoleon was reported to be amused by this and told the story to Lagrange, who replied, "Ah, but it is such a lovely assumption. It explains so many things."
Napoleon served with distinction on the winning side during the French Revolution, and when the bloody battles were over, he said his plans were to return to private life and teach mathematics. But, you know, stuff came up.
Conquer Europe, proclaim yourself emperor... you know.
Even so, though he didn't make much time to pursue mathematics as an actual career, there is a theorem with Napoleon's name on it, a geometry proof shown here. Take any old triangle, like triangle ABC in bold in the illustration. Construct equilateral triangles on the outside of ABC using the sides AB, BC and AC. The new shape isn't a triangle at all, but if we link up the centers of the equilateral triangles, as shown in green with the triangle GHI, that triangle also has to be equilateral.
To this day, this is known as Napoleon's Theorem, and helps give credence to the idea that he is the most famous mathematician of all time, though his fame does not arise from his work in the field.
As my father is fond of saying, you learn something new every day, if you are not careful.