# Hommage to Leonhard Euler

### by Emil A. Fellmann

Leonhard Euler was by far the most productive mathematician in the history of humankind and one of the greatest scholars of all time. He was cosmopolitan in the truest sense of the word: he spent his first 20 years in Basel, and worked altogether more than 30 years in St. Petersburg and a quarter century in Berlin. As happens to only a very few scholars, Euler's work brought him fame and popularity, comparable to that of Galileo, Newton, and Einstein.

**Euler the man**

All of Euler's contemporaries and biographers are unanimous in their estimation of his character: he had an open, cheerful nature; he was uncomplicated, good-humored, and sociable. Although prosperous, even wealthy - at least in the second half of his life - with respect to material things he was absolutely unassuming. Free of all arrogance, he never held a grudge, yet at the same time he was self-confident, critical, and "daring". Although once in a while he might fly off the handle, it was only for a brief moment, after which he would immediately dissolve into laughter again.

**On belief**

Euler did not, however, find the question of religion and Christian belief at all amusing, as revealed in his Rettung der göttlichen Offenbarung gegen die Anwürfe der Freygeister (Rescuing divine revelation from the slings of freethinkers), published anonymously in 1747. In general, Euler's strict belief is the key to understanding many important aspects of his life, for example, his stubborn opposition to Wolff's interpretation of Leibnizian monadology as well as his fierce attacks on certain Encyclopedists and other "freethinkers". Nevertheless, Euler - the "moderate philosopher of the Enlightenment" - actively practiced a humane tolerance that was far more honest and more "lived" than that of his royal employer Friedrich II, who availed himself of the word for purposes of impact and propaganda and immediately forgot it if its application proved in any way a hindrance.

**Personal style**

Scientific claims of ownership were also foreign to Euler; unlike most scholars and artists throughout history, he never engaged in disputes over authorship; just the opposite - occasionally he generously gave away new discoveries and knowledge, and not only to his sons. Euler's work hides nothing; he always lays his cards openly on the table, offering the reader the same conditions and opportunities to find something new. Often he even leads the reader very close to the discovery, but leaves to him the joy of finding it out. This genuine education makes Euler's books an exciting and entertaining learning experience. He seems to have been incapable of envy; he never begrudged anyone anything, and was always delighted at the discoveries of others, as his correspondence in hundreds of cases demonstrates. All of this was possible owing to Euler's immeasurable intellectual powers and his unusually well-balanced psyche.

**The "Euler phenomenon"**

Three factors go a long way to explaining the "Euler phenomenon": First of all, his - perhaps uniquely - gifted memory. Whatever Euler heard, saw, thought, or wrote he seems to have remembered his whole life long, as countless of his contemporaries would attest. So it is, for example, that at an advanced age he was able to delight his relatives, friends, and acquaintances with a literal (Latin) recitation of any song from Virgil's Aeneis, and that he could recall by heart minutes of academy meetings decades later, to say nothing of his memory for mathematical things. Second, Euler's prodigious memory went hand in hand with a rare ability to concentrate. Noise and bustle in his immediate environment hardly disturbed his thinking: "A child on his knees, a cat on his back - this is how he wrote his immortal works," reported Thiébault, his colleague from the Berlin academy. The third factor in the "Euler mystery" is, quite simply, constant, calm work.

**Reputation**

Leonhard Euler's influence and reputation were already impressive during his lifetime. He was (according to Andreas Speiser) for roughly two decades the intellectual leader of the Protestant part of Germany, and (according to Eduard Winter) he performed inestimable services as the "golden bridge between two academies". The 10 volumes of his correspondence testify to this role, as does the fact that, during his Berlin years, Euler published 109 papers in the Petersburger Kommentare as opposed to the 119 he published in the Mémoires of the Berlin academy. And although Euler's energy was sufficient for him to keep up his activities at both institutions, the institutions themselves could not easily cope with the almost inexhaustible tide of Euler's productivity. To judge simply from the extent of his work, Euler is in the company of the most prolific members of the human race, for instance, Voltaire, Leibniz, Telemann or Goethe. The directory of Euler's writings published by G. Eneström (1910-1913) takes up an entire volume and lists almost 900 titles, among them some 40 books.

**Productivity**

The following table summarizes the extent of Euler's writings specified by him as ready for publication, arranged according to decades (not included are a few dozen works that have not yet been dated):

*Year Range Works Percentage*

1725–1734 35 5%

1735–1744 50 10%

1745–1754 150 19%

1755–1764 110 14%

1765–1774 145 18%

1775–1783 270 34%

*Technical range*

With respect to technical discipline, the writings break down approximately as follows:

Algebra, number theory, analysis 40%

Mechanics and other physics 28%

Geometry, including trigonometry 18%

Astronomy 11%

Ship theory, artillery, architecture 2%

Philosophy, music theory, theology, and anything else not included above 1%

*Mathematical works*

The distribution of Euler's purely mathematical works is approximately as follows:

Algebra, combinatorics, and probability theory 10%

Number theory 13%

Fundamental analysis and differential calculus 7%

Infinite series 13%

Integral calculus 20%

Differential equations 13%

Calculus of variations 7%

Geometry, including differential geometry 17%

**Prizes**

Altogether Leonhard Euler won 12 international academy prizes, not counting the prizes of his sons Johann Albrecht (7) and Karl (1), which can essentially also be credited to Euler's account. The Frenchman King Louis XVI awarded Euler 1000 rubles for his "second ship theory", and the Russian empress Katharina II gave him double that amount so that the blind doyen of Petersburg could collect a supplementary salary in 1773.

**Influence**

On the subject of Euler the judgment of the most important mathematicians is unanimous. Laplace used to say to his students: "Read Euler, read Euler! He is the master of us all!" and Gauss explained emphatically: "The study of Euler's works remains the best instruction in the various areas of mathematics and can be replaced by no other." Indeed, through his books, which are consistently characterized by the highest striving for clarity and simplicity and which represent the first actual textbooks in the modern sense, Euler became the premier teacher of Europe not only of his time but well into the 19th century.