Leonhard Euler (1707 – 1783) was a Swiss mathematician and scientist who made a prolific number of discoveries in mathematics. Amongst his many contributions, Euler made discoveries in infinitesimal calculus, graph theory and contributed to topology and analytic number theory. His work was remarkably prolific – running to 70-80 volumes on maths, physics, astronomy and logic. It is estimated Euler wrote a third of all the mathematic works of the 18th Century. Euler also introduced many modern mathematical notations such as π. His work served as a basis for many other mathematicians and he is widely regarded as the greatest mathematician of all time. Born in Switzerland he spent considerable time in Russia and Prussia.

Early life

Euler was born 15 April 1707 in Basel, Switzerland. His father was a pastor in the Protestant Reformed Church and also a friend of Johann Bernoulli, the greatest mathematician of the age. At the age of just 13, he enrolled at the University of Basel, gaining a degree in Philosophy, but he also studied mathematics at the weekend under the guidance of Johann Bernoulli. Bernoulli was soon aware of the child’s prodigious mathematical talent and Bernoulli successfully encouraged Euler’s father to allow his son to pursue mathematics rather than a career in the church. Euler was keen to pursue mathematics, though he never lost his interest in theology and philosophy.

In 1726, Euler was invited to St Petersburg to work at the Imperial Russian Academy of Sciences, with Daniel Bernoulli. While in Russia, Euler soon picked up the Russian language and also worked as a medic for the Russian Navy. The Academy of Sciences had been founded by Peter the Great to improve education in Russia. However, after the death of Peter and Catherine I, fewer funds were available.

In 1734, whilst living in Russia, he married Katharina Gsell. They had 13 children, but only five survived childhood. His wife died in 1773. He remarried Katherina’s half-sister in 1776. On the subject of death, Euler was resigned, offering a typical Calvinist view.

“It is also the influence of the soul upon the body which constitutes its life, which continues aslong as this union subsists. […] Death, then, is nothing but the dissolution of this union, andthe soul has no need to be transported elsewhere; for as it resides in no place, all places must beindifferent to it”

Letters on different subjects in natural philosophy addressed to a German Princess” January 13, 1761

In 1741, Euler was invited by Frederick the Great of Prussia to move to Berlin. Euler was happy to leave the increasing political turmoil in Russia and benefit from the patronage of Frederick, who allowed Euler to continue his investigations and publish his major works. His only other duties were some part-time teaching of Frederick’s family. Euler wrote over 380 articles on maths and natural philosophy. His books and letters were widely read, and it helped that Euler could communicate clearly with a lay audience. His prestige as an eminent mathematician rose around the world. However, his sometimes argumentative nature and simple, devout nature made him a target of court members, such as Voltaire. The court of Frederick the Great welcomed many free-thinkers and deists such as Voltaire, Euler stood for a different world view at odds with the dominant culture of the court, and this made him unpopular.

Blindness

In 1738, Euler all but lost his eyesight in one eye. In 1766, he lost eyesight in a second eye, leaving him effectively blind. However, he continued to work almost unhindered thanks to his great capacity for mental arithmetic. He employed scribes to write his maths down. He once said on his lost eyesight – “Now I will have fewer distractions.” Rather like Beethoven, Euler’s loss of a key sense did not hold him back.

In 1766, Catherine the Great became Queen of Russia, and she invited Euler to return to St Petersburg. Euler asked for a generous salary and once accepted, he agreed to return. He remained in Russia for the remainder of his life.

Scientific Contributions of Euler

While studying, Euler learnt about Sir Isaac Newton’s groundbreaking laws of motion and gravity, which he had discovered a few decades previously. Euler proved adept at implementing these theoretical laws to everyday situations. Euler developed equations for rigid bodies and made contributions to the theory of elasticity of objects.

Euler’s breadth of interest was remarkable, and he attempted to bring mathematics into many scientific problems. One of great interest to Euler – and particularly difficult – was the three-way gravitational attractions of the sun, moon and earth. Euler made progress in attempting to solve this. Euler even attempted to bring mathematics to music, though it gained little interest at the time.

Euler developed many of the important equations which have become the building blocks of modern mathematics. For example

The Lagrange equations (created by Joseph Louis Lagrange) on solving problems in mechanics, came from Euler’s initial equation and the calculus of variations.

Euler’s work also influenced John Baptiste Fourier, who created the Fourier technique for solving issues in the field of physics, acoustics and electromagnetic theory.

Perhaps Euler’s greatest breakthrough in mathematical terms was in the field of differential calculus and infinite series.

Euler’s equations have been very influential in mathematics. His equation on the complex exponential function.

Is one of the most widely used formulas in maths, and in 1988, was voted “the Most Beautiful Mathematical Formula Ever”

Although Euler was a great admirer of Isaac Newton, he didn’t take everything he proposed as gospel. Euler was influential in supporting and promoting the wave theory of light – initially proposed by Christiaan Huygens. At the time, Newton’s theory that light was made of particles held greater sway. Quantum theory would later prove Euler was correct.

Religious views of Euler

Euler was brought up by a Calvinist pastor and his childhood upbringing influenced his religious outlook. He remained deeply religious throughout his life and he remained a Calvinist. He believed the Bible was divinely inspired. Euler’s world outlook combined his belief in reason and inquisitive nature into scientific problems with the Calvinist view of pre-determination. While he was part of the Scientific Enlightenment, he vigorously defended religion against free-thinkers and atheists. To Euler, reason and science should be used to support the existence of God.

“Every man may rest assured that, from all eternity, he entered into the plan of the universe. […]How ought this consideration to increase our confidence and our joy in the providence of God, on which all religion is founded!”

Leonhard Euler, Letters to a German Princess, January 3, 1761.