Euler's Constancy
by John Derbyshire

Who is the greatest mathematician of all time? In 1937, Eric Temple Bell, the most widely read historian and biographer of mathematics, placed Archi medes, Isaac Newton, and Karl Friedrich Gauss at the top of the list, adding, “It is not for ordinary mortals to attempt to arrange [these three] in order of merit.” This judgment, widely known among mathematicians, stirred a protest in 1997 from Charlie Marion and William Dunham in Mathematics Magazine. The protest was in eight stanzas of verse, of which the fourth and fifth read:



Without the Bard of Basel, Bell,

You’ve clearly dropped the ball.

Our votes are cast for Euler, L.

Whose Opera says it all.



Six dozen volumes— what a feat!

Profound and deep throughout.

Does Leonhard rank with the elite?

Of this there is no doubt.



Marion and Dunham were paying tribute to the mathematician Leonhard Euler (1707–83), one of the great yet little-known figures from Europe’s Age of Enlightenment. Euler’s discoveries continue to influence such disparate fields as computer networking, harmonics, and statistical analysis, and they did nothing less than transform pure mathematics. Children still learn Euler’s lessons in school. It was Euler, for instance, who gave the name i to the square root of –1. To mark his tercentenary, admirers are holding symposiums, concerts, and a two-week Euler tour, which will stop in St. Petersburg and Berlin, the two cities where he spent his working life, as well as Basel, Switzerland, the city of his birth. There is even an Euler comic book, A Man to Be Reckoned With, in German and English editions.

Compared to Gauss and Newton, both of whom published sparingly, Euler was prolific. This makes the assignment of precedence somewhat subjective. But Archimedes and Newton can hardly be excluded from the top ranks. For sheer breadth and quality of mathematical thought, I believe most scholars would place Gauss ahead of Euler. It is a close call, though, and nobody would disagree that Euler ranks with the crème de la crème in mathematical excellence. So who was he?

Leonhard Euler was born April 15, 1707, into a German- speaking family (the name is pronounced “Oiler”). His father, Paul Euler, was a Calvinist clergyman, and Leonhard remained a firm, uncritical Calvinist his whole life, believing that all events were preordained by God at the Creation. He once wrote a tract defending the truth of Revelation against Enlightenment skeptics. These beliefs did not make him a grim fatalist. To the contrary, he was a cheerful, industrious, and kind-hearted man, reliably humble despite his fame. Though given to “good-natured sarcasm,” as a contemporary noted, and short-lived outbursts of temper, he was altogether one of the more attractive personalities in the history of mathe matics.

When the precocious 13-year-old Euler commenced his studies at Basel University in 1720, Johann Ber noulli, another great name in the history of numbers, held the chair of mathematics. Bernoulli was also an old acquaintance of Leonhard’s father. Though a proud and prickly man with no great fondness for teaching, Bernoulli granted the boy individual seminars on Saturday afternoons, and must soon have recognized his mathematical ability. Paul Euler wanted his son to study theology and follow him into the clergy, but Bernoulli persuaded Rev. Euler to approve a switch to math and physics. Leonhard graduated in 1726, and published his first mathematical paper that same year.

At just that time, Johann Bernoulli’s eldest son, Nicholas, died in St. Petersburg. Both Nicholas and his brother Daniel had taken positions at the new St. Petersburg Academy, established in 1724 as part of Tsar Peter the Great’s grand plan to modernize his nation, and Daniel wrote to his father to suggest that Nicholas be succeeded by Leonhard Euler. Glad of the rare opportunity to attain an academician’s post at such a young age, Euler traveled to St. Petersburg in May 1727, a month after his 20th birthday, and a month and a half after the death of Newton. Unfortunately, Peter the Great was already dead, and his wife and successor died just as Euler arrived. The new regime was skeptical of the academy, so the scholars took pains to make themselves appear useful to the state. Euler secured a commission in the imperial navy, though he seems never to have gone to sea.

Through the 1730s, Euler worked on various projects for the Russian state—notably in the areas of cartography and shipbuilding—while making his international reputation as a mathematician . These were unhappy years for Russia, with the country descending into state terror during the reign of Empress Anna (1730–40). “Common prudence forced [Euler] into an unbreakable habit of industry,” E. T. Bell writes, suggesting that Euler’s extraordinary productivity had its foundations in this period. Another biographer remarks, “In all of Euler’s vast correspondence there is no mention of politics.” His Russian experiences either inoculated Euler against politics or confirmed an innately apolitical disposition.

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