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# Leonhard Euler

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### Leonhard Euler

Leonhard Euler ( ;[1] German pronunciation:  ( ), local pronunciation:  ( ); 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.[2] He is also renowned for his work in mechanics, fluid dynamics, optics, astronomy, and music theory.[3]

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.[4] He spent most of his adult life in St. Petersburg, Russia, and in Berlin, 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."[5][6]

## Contents

• Life 1
• Early years 1.1
• St. Petersburg 1.2
• Berlin 1.3
• Eyesight deterioration 1.4
• Contributions to mathematics and physics 2
• Mathematical notation 2.1
• Analysis 2.2
• Number theory 2.3
• Graph theory 2.4
• Applied mathematics 2.5
• Physics and astronomy 2.6
• Logic 2.7
• Personal philosophy and religious beliefs 3
• Commemorations 4
• Selected bibliography 5
• References and notes 7

## Life

### Early years

Old Swiss 10 Franc banknote honoring Euler

Euler was born on 15 April 1707, in Basel to 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 from Basel to the town of Riehen, where Euler spent most of his childhood. Paul Euler was a friend of the Bernoulli familyJohann Bernoulli, who was then regarded as Europe's foremost mathematician, would eventually be the most important influence on young Leonhard. Euler's early formal education started in Basel, where he was sent to live with his maternal grandmother. At the age of 13 he enrolled at the University of Basel, and in 1723, received his Master of Philosophy with a dissertation that compared the philosophies of Descartes and Newton. 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 the University of Basel. 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 the Imperial Russian Academy of Sciences in St Petersburg. On 10 July 1726, Nicolas died of appendicitis after spending a year in Russia, 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 to St Petersburg while he unsuccessfully applied for a physics professorship at the University of Basel.[10]

1957 Soviet Union stamp 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 in St Petersburg. He also took on an additional job as a medic in the Russian Navy.[11]

The Academy at St. Petersburg, established by Peter the Great, was intended to improve education in Russia and to close the scientific gap with Western 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 at St. Petersburg, left for Basel. Euler succeeded him as the head of the mathematics department.[12]

On 7 January 1734, he married Katharina Gsell (1707–1773), a daughter of

• LeonhardEuler.com
• Weisstein, Eric W., Euler, Leonhard (1707–1783) from ScienceWorld.
• Encyclopædia Britannica article
• Leonhard Euler at the Mathematics Genealogy Project
• How Euler did it contains columns explaining how Euler solved various problems
• Euler Archive
• Leonhard Euler – Œuvres complètes Gallica-Math
• Euler Committee of the Swiss Academy of Sciences
• References for Leonhard Euler
• Euler Tercentenary 2007
• The Euler Society
• Euler Family Tree
• Euler's Correspondence with Frederick the Great, King of Prussia
• "Euler – 300th anniversary lecture", given by Robin Wilson at Gresham College, 9 May 2007 (can download as video or audio files)
• .
• Euler Quartic Conjecture