# Leonhard Euler

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Leonhard Paul Euler (15 April 1707 - 18 September 1783) was a pioneering Swiss mathematician and physicist and widely considered to be one of the greatest mathematicians of all time. His numerous works (over 900 publications) in many areas had a decisive influence on the development of mathematics.

## Biography

Leonhard Euler's father was pastor Paul Euler, who had studied theology at the University of Basel and had attended Jacob Bernoulli's lectures there. He also lived in Jacob's Bernoulli's house with Johann Bernoulli. Later he became a Protestant minister and married Margaret Brucker, the daughter of another Protestant minister.

Their son Leonhard Euler was born on 15 April 1707 in the town of Basel, Switzerland, but the family moved to Riehen when he was one year old. His father gave him the basic knowledge of mathematics.

At the age of 7, Euler returned to Basel and lived with his grandmother on his mother's side. During that time he went to school. However this school was known as a rather poor one, and Euler learnt no mathematics at all. Thus he read mathematics texts on his own and took some private lessons. His father wanted him to go to church and sent him to the University of Basel to prepare for the ministry. Euler entered the University in 1720, at the age of 14, first to obtain a general education. Johann Bernoulli soon discovered Euler's great potential for mathematics. Euler was writing that time:

... I soon found an opportunity to be introduced to a famous professor Johann Bernoulli. ... True, he was very busy and so refused flatly to give me private lessons; but he gave me much more valuable advice to start reading more difficult mathematical books on my own and to study them as diligently as I could; if I came across some obstacle or difficulty, I was given permission to visit him freely every Sunday afternoon and he kindly explained to me everything I could not understand ...

In 1723 he gained his Master's degree with a dissertation comparing the natural philosophy systems of Newton and Descartes. On his father's wishes, Euler he began to study theology, but spent all his spare time studying mathematics. He wrote two articles on reverse trajectory which were highly valued by his teacher Bernoulli. In 1727 Euler applied for a position as physics professor at Basel university, but was turned down.

At this time a new centre of science had appeared in Europe - the Petersburg Academy of Sciences. As Russia had few scientists of its own, many foreigners were invited to work at this centre - Euler among them. On the 24 May 1727 Euler arrived in Petersburg. His great talents were soon recognised. Among the areas he worked in include his theory of the production of the human voice, the theory of sound and music, the mechanics of vision, and his work on telescopic and microscopic perception. On the basis of this last work, not published until 1779, the construction of telescopes and microscopes was made possible.

In his study of colour effects, Euler hoped to make use of the observation of the conjunction of Venus and Moon, due to take place on the 8th of September 1729. However, no such effects were observed during this conjunction, and Euler was forced to wait for the eclipse of the sun which would take place in 1748. He observed this eclipse in Berlin, where he moved in 1741. Here he worked in the Prussian Academy of Sciences and was appointed as head of the Berlin Observatory, and was also tutor to the nieces of King Frederich II of Prussia.

Euler's works were not devoted solely to the natural sciences. A true renaissance man, he also involved himself in the philosophical debates of the day, and triumphantly declared himself a firm believer in the freedom of the will. Such views won him few friends in Germany, and the book in which he thus expressed himself was published for the first time in Russia, where Euler returned in 1766. Here he found many who agreed with his views, among them enemies of the views of Leibnitz and Voltaire.

In 1763 Catherine II came to the throne. She carried out reforms in the Academy of Sciences and aimed to make it a more prestigious institution. When Euler returned to Petersburg with his two elder sons they were given a two-storey house on the banks of the Neva and Euler given a position at the head of the Academy of Sciences.

When Euler renurned to Petersburg, he had already reconsidered his views on the atmosphere of planets. The work of Lomonosov and Bernoulli in this field led him to conclude that the atmosphere on the Earth and on other planets must be considerably more transparent than he had thought. Euler took a very active role in the observation of the movement of Venus across the face of the sun, despite the fact that at this time he was nearly blind. He had already lost one eye in the course of an experiment on light diffraction in 1738, and an eye disease and botched operation in 1771 led to an almost total loss of vision.

In contrast to most intellectuals of his time he was conservative and a convinced Christian. There is a story, which is often told in books, saying that once at the court of Catherine the Great he met the French philosopher Denis Diderot, who was a convinced atheist and tried to convince the Russians of atheism, much to the annoyance of Catherine. Therefore she asked Euler to stop him. Euler thought about it and when Catherine invited Diderot to have a theological discussion with Euler, Euler said: “${\displaystyle {\frac {a+b^{n}}{n}}=x}$, therefore God exists, answer!” Diderot, who knew almost nothing about algebra knew not what to answer and therefore returned to Paris. This story however is almost certainly an urban myth and Diderot knew enough algebra to answer Euler. However it is said that Euler published some not really serious proofs of the existence of God, which may well be, since at that time people were wondering about the possibility to give an algebraic proof of the existence of God.

This did not, however, stop Euler's creative output. Until his death in 18 September 1783, the Academy was presented with over 500 of his works. The Academy continued to publish them for another half century after the death of the great scientist. When Euler died the mathematician and philosopher Marquis de Condorcet said “...et il cessa de calculer et de vivre” ("and he stopped calculating and living").