Mathematician · 1707 – 1783
Leonhard Euler
Key Takeaways
- Euler is widely regarded as the most prolific mathematician of all time.
- He introduced much of the notation still used in mathematics today.
- He founded graph theory with the Seven Bridges of Königsberg problem.
- He made major advances in analysis, number theory and mechanics.
Leonhard Euler was a Swiss mathematician whose vast and varied output makes him the most prolific mathematician in history. A central figure of the Age of Enlightenment, he advanced nearly every branch of mathematics and much of physics.
A boundless output
Trained in Basel, Euler spent much of his career at the academies of Saint Petersburg and Berlin. His textbooks systematized calculus and analysis, and he introduced notation that remains standard today, including the symbol e for the base of natural logarithms, i for the imaginary unit, and the function notation f(x).
Founding new fields
Euler’s solution to the Seven Bridges of Königsberg problem launched graph theory and pointed toward topology. He solved the Basel problem, advanced analytic number theory, and produced his celebrated identity linking e, i, π, 1 and 0.
Legacy
Euler’s methods were carried forward by Carl Friedrich Gauss and built on the calculus of Isaac Newton and the analytic geometry of René Descartes. Remarkably, much of his greatest work came after he lost his sight, a testament to a mathematical mind of unrivaled fertility.
Influence
Euler's notation, methods and results pervade modern mathematics and physics, and his founding of graph theory shaped fields from computer science to network analysis.
Legacy
He remains a touchstone of mathematical creativity, and an extraordinary number of theorems, constants and concepts bear his name.
Major Works
- Introductio in analysin infinitorum
- Institutiones calculi differentialis
- Mechanica
Notable Quotes
“Logic is the foundation of the certainty of all the knowledge we acquire.”
Connections
Frequently Asked Questions
Who was Leonhard Euler?
Leonhard Euler (1707–1783) was a Swiss mathematician and physicist, the most prolific in history, who transformed analysis, number theory and notation and founded graph theory.
What is Euler's identity?
Euler's identity, e^{iπ} + 1 = 0, is a famous equation often praised as the most beautiful in mathematics for uniting fundamental constants.
Citations & Sources
People Like Leonhard
Carl Friedrich Gauss
95Carl Friedrich Gauss was a German mathematician and physicist whose profound contributions to number theory, statistics, geometry, astronomy and magnetism earned him the title "Prince of Mathematicians."
Why A later mathematician who extended Euler's work in analysis and number theory.
Isaac Newton
99Isaac Newton was an English physicist and mathematician whose laws of motion and universal gravitation laid the foundation of classical mechanics and the Scientific Revolution.
Why A predecessor whose calculus and mechanics Euler developed and systematized.
René Descartes
92René Descartes was a French philosopher, mathematician and scientist, the "father of modern philosophy", famous for "I think, therefore I am" and for founding analytic geometry.
Why An earlier thinker whose analytic methods underpinned the mathematics Euler advanced.
Pythagoras
90Pythagoras was an ancient Greek mathematician and philosopher who founded the Pythagorean school and is remembered for the Pythagorean theorem and the idea that number underlies the cosmos.
Why An ancient pioneer of number whose tradition Euler carried into modern number theory.
Galileo Galilei
95Galileo Galilei was an Italian astronomer, physicist and engineer, the "father of modern science", whose telescopic discoveries and championing of heliocentrism transformed our understanding of the cosmos.
Why Also a physicist & mathematician · Worked in astronomy & physics
Archimedes
94Archimedes was an ancient Greek mathematician, physicist and inventor, widely regarded as the greatest mathematician of antiquity and a founder of mathematical physics and engineering.
Why Also a mathematician & physicist · Worked in mathematics & physics