linking e, π, and i, the symbol he developed for the square root of -1.
In 1733 Bernoulli moved to a Chair in Switzerland. This enabled Euler to move from a post in Physics to take up Bernoulli's Chair in Mathematics. He married Katherine Gsell (d. 1773) and they had 13 children, only five of whom reached adolescence and three of whom survived him.
This was a period during which Euler did much consulting work for the Russian Government and publishing many results, including the solution to the much debated Basel Problem in 1735 (see below).
In 1736 Euler solved the Königsberg Bridges Problem, which is described below. This solution established the branch of mathematics now known as Graph Theory, and which is the basis of the understanding of networks, including computer networks.
Whereas Euler's research continued at an astonishing pace, there were some problems encountered during the next period, including the death of Catherine I, a subsequent backlash against the foreigners who dominated the Academy, and in 1738 the first signs of failing eyesight, with the loss of sight from his right eye.
During this time he still produced ground-breaking works, including work on shp-building, acoustics, music, Classical Number Theory in collaboration with Christian Goldbach (1690-1764), Analytic Number Theory, and a text Mechanica presenting Newtonian mechanics in a framework of Calculus.
In 1741, while still in the employ of the St Petersburg Academy, Euler and his family moved to Berlin at the invitation of Prussia's Frederick the Great (1712-1786) to join the revitalised Berlin Academy. He was to stay in Berlin until 1766.
In Berlin he published his most widely read book, Letters to a German Princess, which contains over 200 "letters" inspired by the instruction he was required to give to the Princess of Anhalt Dessau. The letters cover a wide range of topics in mathematics and physics, including the explanation of commonly observed phenomena. It is a classical example of excellent writing to explain science to the masses.
During his time in Berlin, Euler kept in excellent contact with the St Petersburg Academy, which was still paying him, and fell out gradually with Frederick the Great. While in Berlin he also fell out with the other leading identity Voltaire (1694-1778) who was more in favour with the King and was rather disdainful of Euler, who had not learned philosophy. While absent the St Petersburg Academy had also been revitalised under the influence of Catherine the Great (1729-1796) and in 1766 he returned to St Petersburg for the remainder of his life.
Euler's work in St Petersburg continued at a breathtaking pace despite the death of his wife (he later married her half-sister) and the substantial loss of sight in his good eye, forcing him to dictate all of his writings to scribes. He died of a massive haemhorrage on the afternoon of 18 September 1783, a day on which he had still been working at his normal pace. The St Petersburg Academy Journal had a massive backlog of his work to publish, a task which took a further 48 years to complete.
The complete works of Euler, Omnia Opera, was only published in the latter part of the twentieth century after a commitment by the Swiss Academy of Science in 1909. It is very expensive and can only be found in major research libraries. It comprises 29 volumes on mathematics, 31 on mechanics and astronomy, 12 on physics and other topics, 8 on correspondence. Further volumes on manuscripts is still to appear.
Euler's work took him into virtually every branch of mathematics and physics known during his life. Here we briefly discuss some problems for which he became famous. The individual problems discussed below indicate the flavour of Euler's work and do not indicate his massive contribution to what we now call applied mathematics.
The Königsberg Bridges Problem
Königsberg (now the Russian city of Kaliningrad, on the Baltic Sea) was a city in East Prussia laid out on the River Pregel, which had split into two courses forming two islands. The various regions of the city were connected by bridges.