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Leonhard Euler: The jewel of three courts


When someone in America once asked me who the three greatest mathematicians of all time were, I immediately responded: Archimedes, Newton and Gauss. “Goddamnit, why do you mathematicians always come up with the same three names?” demanded my interlocutor. Probably because we have all read Men of Mathematics by E.T. Bell, which features portraits of this trio on its cover. To pick a fourth, a name often mentioned is Leonhard Euler, and Bell’s chapter on this prolific 18th-century genius, whose collected works fill 80 volumes, quotes mathematician, physicist, astronomer and one-time president of France, François Arago: “Euler calculated without apparent effort, as men breathe, or as eagles sustain themselves on the wing.”

Born in 1707 in Basel, where Johann Bernoulli, the greatest mathematician of the day worked, Euler got off to a good start and in 1726 was offered a position at the new Academy in St Petersburg founded by Peter the Great, whose aim was to draw Russia into the European Enlightenment, and away from 17th-century attitudes that branded arithmetic and geometry as magic. Still, it was not easy. The Church censored the idea of a solar system centred at the sun, and the Old Believer nobles treated foreign academicians — mainly German, Swiss and French — with suspicion, even hostility.

After Peter’s death in 1725, benevolent control of the Academy continued under his successors until Empress Anna died in 1740, but even in the 1730s censors blocked the astronomical idea of heliocentricity, and publications from outside Russia were considered heretical. Meanwhile, Euler threw himself wholeheartedly into mathematics both pure and applied, even dealing with cartography for expeditions to Kamchatka in the far east of Russia.

Newton had died in 1727 but his differential calculus and principles of dynamics still needed substantial development, and it fell to the young Euler to lead the 18th-century creation of what we now call Newtonian dynamics and mechanics. Indeed, his two-volume Mechanica, published in 1736, became a landmark in the history of physics, and although the book was in Latin, Euler was equally at home writing in French or his native German. During the early St Petersburg years he also learned to read and write Russian, publishing in all these languages across the entire span of mathematics, including applications to optics, mechanics, fluid dynamics, navigation, ship construction and even music, which for Euler formed part of the quadrivium: arithmetic, geometry, music and astronomy. His teaching was superb, and in later years his Letters to a German Princess formed one of the finest explanations of science ever written. Yet he also took administrative duties very seriously, and found ample time for family. In the mid-1730s he married Katharina, daughter of another Swiss gentleman, the Petersburg Court painter Georg Gsell, and would happily work with a child on his knee and a cat on his shoulder.

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