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Leonhard Euler
1707–1783 · Mathematician and Physicist
A Swiss mathematician and physicist whose enormous body of work transformed analysis, number theory, mechanics, geometry and many other areas of mathematics.
“Mathematics is the science of the necessary.”
Why is this scientist famous?
Making fundamental contributions across mathematics and physics, including mathematical analysis, number theory, mechanics and graph theory, while introducing or popularising notation still used today.
Leonhard's story
A Pastor's Son in Basel
Leonhard Euler was born on 15 April 1707 in Basel, Switzerland, the son of a Calvinist pastor who had studied mathematics under Jakob Bernoulli. His father hoped Leonhard would follow him into the church, but the boy's extraordinary talent for numbers was impossible to ignore. He entered the University of Basel at just 13, and completed a master's degree in philosophy in 1723. Mathematician Johann Bernoulli declined to give Euler regular private lessons but encouraged him to study difficult mathematical books independently and allowed him to visit on Sunday afternoons to discuss problems he could not solve. Bernoulli told Euler's father that his son was destined to be a great mathematician, not a pastor.
To Russia and St Petersburg
At 20, Euler moved to St Petersburg, Russia, to join the newly established Academy of Sciences. The Academy had been founded by Peter the Great, and Euler was initially offered a position in the medical section, but a vacancy in mathematics soon opened. He threw himself into research with extraordinary energy, publishing on navigation, ballistics, artillery, and shipbuilding alongside his pure mathematical work. He married Katharina Gsell, the daughter of a Swiss painter at the Academy, and they had 13 children, though only five survived to adulthood. Euler often said he did some of his best mathematics while holding a baby in one arm.
The Bridges of Königsberg
In the 1730s, Euler analysed a puzzle that had been nagging the citizens of Königsberg (now Kaliningrad): could you walk through the city crossing each of its seven bridges exactly once? Euler proved it was impossible, producing work that became foundational to the later field of graph theory. His insight was to strip away all the irrelevant detail and focus only on which pieces of land were connected to which. His abstraction of the problem into vertices and connections became one of the foundational ideas of graph theory and also influenced the later development of topology.
Berlin and the Academy
In 1741, Euler left St Petersburg for Berlin, where Frederick the Great had invited him to join the Prussian Academy of Sciences. He spent 25 years there, producing an astonishing flood of work — hundreds of papers on calculus, astronomy, optics, and lunar motion. He wrote textbooks that became the standard for generations, including his Introductio in Analysin Infinitorum, which laid out the foundations of mathematical analysis. Frederick the Great, however, found Euler too quiet and unworldly for his glittering court, once calling him 'my cyclops' — a cruel reference to Euler's blind eye. The relationship cooled, and in 1766 Euler returned to St Petersburg.
Blindness and the Golden Flood
Euler had been losing his eyesight for years. A fever in 1735 damaged his right eye, and after returning to St Petersburg in 1766 his sight deteriorated further. After a cataract operation in 1771 briefly restored some vision, he became totally blind. For most mathematicians this would have been the end. For Euler, it was the beginning of his most productive period. He had a remarkable memory — he could recite the entire Aeneid from memory and tell you the first and last lines on any page — and he dictated his ideas to a team of assistants. After returning to St Petersburg he produced almost half of his total body of work despite severe and eventually total blindness. His assistants and collaborators played an important role in calculating, preparing and developing this work.
A Legacy in Every Equation
Euler died on 18 September 1783, collapsing while playing with his grandson. He was 76. His collected works, which scholars are still cataloguing today, fill more than 80 large volumes — the largest body of mathematical work ever produced by a single person. His name is everywhere in mathematics: Euler's number e, Euler's constant gamma, Euler's formula, Euler's identity, Euler's totient function, Euler angles, Euler diagrams. Pierre-Simon Laplace once said: 'Read Euler, read Euler, he is the master of us all.'
What did they discover?
Euler's Identity
Euler's formula e^(ix) = cos(x) + i sin(x) links exponential and trigonometric functions. Setting x = π gives the celebrated identity e^(iπ) + 1 = 0.
Foundations of Graph Theory
Euler's analysis of the Seven Bridges of Königsberg reduced the problem to a network of points and connections, becoming a foundational result in graph theory.
Modern Mathematical Notation
Introduced or popularised notation including f(x) for a function, e for the base of natural logarithms, i for the imaginary unit and Σ for summation, and helped establish widespread use of π.
Euler's Formula for Polyhedra
He proved that for any convex polyhedron, the number of vertices minus edges plus faces always equals two (V − E + F = 2), a foundational result in topology that connects geometry to the study of shapes.
Seven Bridges of Königsberg
His analysis of the Seven Bridges of Königsberg became a foundational result in graph theory and introduced the type of route now known as an Eulerian path.
Lunar Motion Calculations
His precise calculations of the Moon's orbit were so accurate that the British Navy used them for navigation, and the method helped solve the longitude problem that had plagued sailors for centuries.
Amazing facts
Euler published over 800 papers and books — more than any other mathematician in history. His collected works fill over 80 large volumes, and scholars are still cataloguing them.
After returning to St Petersburg in 1766, Euler produced almost half of his total body of work despite becoming almost completely and eventually totally blind.
He could recite Virgil's Aeneid from memory and tell you the first and last line on any page you named.
He had 13 children with his wife Katharina, though only five survived to adulthood. He often did mathematics with a baby in one arm.
Frederick the Great called Euler 'my cyclops' because of his damaged right eye — a cruel nickname that contributed to Euler leaving Berlin.
Euler introduced the symbol e for the base of natural logarithms and made major contributions to understanding exponential functions.
His Letters to a German Princess, a collection of popular science lessons written in plain language, became one of the bestselling science books of the 18th century.
Euler introduced the notation f(x) for a function and made the concept of functions central to mathematical analysis.
Laplace, one of history's greatest mathematicians, told his students: 'Read Euler, read Euler, he is the master of us all.'
Timeline
Born in Basel, Switzerland
Entered the University of Basel at age 13
Completed a master's degree in philosophy at the University of Basel
Moved to St Petersburg to join the Russian Academy of Sciences
Suffered a severe illness; serious eyesight problems developed during the following years
Discussed his solution to the Seven Bridges of Königsberg problem in correspondence; the resulting paper was published in 1741
Moved to Berlin to join the Prussian Academy of Sciences at Frederick the Great's invitation
Published Introductio in Analysin Infinitorum, a landmark work in mathematical analysis
Published Institutiones Calculi Differentialis, a foundational calculus textbook
Returned to St Petersburg as his eyesight continued to deteriorate
Published Letters to a German Princess, a bestselling popular science book
Became totally blind after a cataract operation briefly restored some sight
Published a major treatise on lunar motion with assistance from collaborators
Died in St Petersburg, aged 76
Awards & honours
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