Leonhard Euler (/ˈɔɪlər/ OY-lər;[2] German pronunciation: [ˈɔʏlɐ] ( listen), local pronunciation: [ˈɔɪlr̩] ( listen); 15 April 1707 – 18 September 1783) was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function.[3] He is also renowned for his work in mechanics, fluid dynamics, optics, astronomy, and music theory.[4]

Euler is considered to be the pre-eminent mathematician of the 18th century and one of the greatest mathematicians to have ever lived. He is also one of the most prolific mathematicians; his collected works fill 60–80 quarto volumes.[5] He spent most of his adult life in St. Petersburg,Russia, and inBerlin,Prussia.

A statement attributed to Pierre-Simon Laplace expresses Euler's influence on mathematics: "Read Euler, read Euler, he is the master of us all.

Early years

Old Swiss 10 Franc banknote honoring EulerEuler was born on 15 April 1707, inBaselto Paul Euler, a pastor of the Reformed Church, and Marguerite Brucker, a pastor's daughter. He had two younger sisters named Anna Maria and Maria Magdalena. Soon after the birth of Leonhard, the Eulers moved fromBaselto the town ofRiehen, where Euler spent most of his childhood. Paul Euler was a friend of the Bernoulli family—Johann Bernoulli, who was then regarded asEurope's foremost mathematician, would eventually be the most important influence on young Leonhard. Euler's early formal education started inBasel, where he was sent to live with his maternal grandmother. At the age of thirteen he enrolled at theUniversityofBasel, and in 1723, received his Master of Philosophy with a dissertation that compared the philosophies of Descartes andNewton. At this time, he was receiving Saturday afternoon lessons from Johann Bernoulli, who quickly discovered his new pupil's incredible talent for mathematics.[7] Euler was at this point studying theology, Greek, and Hebrew at his father's urging, in order to become a pastor, but Bernoulli convinced Paul Euler that Leonhard was destined to become a great mathematician. In 1726, Euler completed a dissertation on the propagation of sound with the title De Sono.[8] At that time, he was pursuing an (ultimately unsuccessful) attempt to obtain a position at theUniversityofBasel. In 1727, he first entered the Paris Academy Prize Problem competition; the problem that year was to find the best way to place the masts on a ship. Pierre Bouguer, a man who became known as "the father of naval architecture" won, and Euler took second place. Euler later won this annual prize twelve times.[9]

St. Petersburg

Around this time Johann Bernoulli's two sons, Daniel and Nicolas, were working at theImperialRussianAcademyof Sciences inSt Petersburg. On 10 July 1726, Nicolas died of appendicitis after spending a year inRussia, and when Daniel assumed his brother's position in the mathematics/physics division, he recommended that the post in physiology that he had vacated be filled by his friend Euler. In November 1726 Euler eagerly accepted the offer, but delayed making the trip toSt Petersburgwhile he unsuccessfully applied for a physics professorship at theUniversityofBasel.[10]

1957Soviet Unionstamp commemorating the 250th birthday of Euler. The text says: 250 years from the birth of the great mathematician, academician Leonhard Euler.Euler arrived in the Russian capital on 17 May 1727. He was promoted from his junior post in the medical department of the academy to a position in the mathematics department. He lodged with Daniel Bernoulli with whom he often worked in close collaboration. Euler mastered Russian and settled into life inSt Petersburg. He also took on an additional job as a medic in the Russian Navy.[11]

The Academy atSt. Petersburg, established by Peter the Great, was intended to improve education inRussiaand to close the scientific gap withWestern Europe. As a result, it was made especially attractive to foreign scholars like Euler. The academy possessed ample financial resources and a comprehensive library drawn from the private libraries of Peter himself and of the nobility. Very few students were enrolled in the academy in order to lessen the faculty's teaching burden, and the academy emphasized research and offered to its faculty both the time and the freedom to pursue scientific questions.[9]

The Academy's benefactress, Catherine I, who had continued the progressive policies of her late husband, died on the day of Euler's arrival. The Russian nobility then gained power upon the ascension of the twelve-year-old Peter II. The nobility were suspicious of the academy's foreign scientists, and thus cut funding and caused other difficulties for Euler and his colleagues.

Conditions improved slightly upon the death of Peter II, and Euler swiftly rose through the ranks in the academy and was made professor of physics in 1731. Two years later, Daniel Bernoulli, who was fed up with the censorship and hostility he faced atSt. Petersburg, left forBasel. Euler succeeded him as the head of the mathematics department.[12]

On 7 January 1734, he married Katharina Gsell (1707–1773), a daughter of Georg Gsell, a painter from the Academy Gymnasium.[13] The young couple bought a house by theNevaRiver. Of their thirteen children, only five survived childhood.[14]

Berlin

Stamp of the former German Democratic Republic honoring Euler on the 200th anniversary of his death. Across the centre it shows his polyhedral formula, nowadays written as v − e + f = 2.Concerned about the continuing turmoil in Russia, Euler left St. Petersburg on 19 June 1741 to take up a post at the Berlin Academy, which he had been offered by Frederick the Great of Prussia. He lived for twenty-five years inBerlin, where he wrote over 380 articles. InBerlin, he published the two works for which he would become most renowned: The Introductio in analysin infinitorum, a text on functions published in 1748, and the Institutiones calculi differentialis,[15] published in 1755 on differential calculus.[16] In 1755, he was elected a foreign member of theRoyalSwedishAcademyof Sciences.

In addition, Euler was asked to tutor Friederike Charlotte of Brandenburg-Schwedt, the Princess of Anhalt-Dessau andFrederick's niece. Euler wrote over 200 letters to her in the early 1760s, which were later compiled into a best-selling volume entitled Letters of Euler on different Subjects in Natural Philosophy Addressed to a German Princess.[17] This work contained Euler's exposition on various subjects pertaining to physics and mathematics, as well as offering valuable insights into Euler's personality and religious beliefs. This book became more widely read than any of his mathematical works, and was published across Europe and in theUnited States. The popularity of the 'Letters' testifies to Euler's ability to communicate scientific matters effectively to a lay audience, a rare ability for a dedicated research scientist.[16]

Despite Euler's immense contribution to the Academy's prestige, he was eventually forced to leaveBerlin. This was partly because of a conflict of personality with Frederick, who came to regard Euler as unsophisticated, especially in comparison to the circle of philosophers the German king brought to the Academy. Voltaire was among those inFrederick's employ, and the Frenchman enjoyed a prominent position within the king's social circle. Euler, a simple religious man and a hard worker, was very conventional in his beliefs and tastes. He was in many ways the antithesis of Voltaire. Euler had limited training in rhetoric, and tended to debate matters that he knew little about, making him a frequent target of Voltaire's wit.[16] Frederick also expressed disappointment with Euler's practical engineering abilities:

I wanted to have a water jet in my garden: Euler calculated the force of the wheels necessary to raise the water to a reservoir, from where it should fall back through channels, finally spurting out in Sanssouci. My mill was carried out geometrically and could not raise a mouthful of water closer than fifty paces to the reservoir. Vanity of vanities! Vanity of geometry