Leonhard Euler

1707–1783, Basel, Switzerland, St Petersburg, Russia

AnalysisArithmetic and number theoryTopology

Swiss mathematician, the most prolific mathematician in history, who made foundational contributions to analysis, number theory, graph theory and mechanics and introduced much of modern mathematical notation.

Euler was born in Basel and studied at the University of Basel under Johann Bernoulli, who quickly recognised his exceptional talent. In 1727 he joined the new Imperial Academy of Sciences in St Petersburg, where he worked alongside Christian Goldbach and Daniel Bernoulli. In 1741 he moved to the Prussian Academy of Sciences in Berlin at the invitation of Frederick the Great, directing its mathematics section for 25 years before returning to St Petersburg in 1766.

Even after losing his sight almost completely in the 1760s, Euler continued to produce roughly half of his life's output through dictation, aided by his sons and assistants. He proved that $\zeta(2) = \pi^2/6$ (the Basel problem, 1735), founded graph theory by solving the Königsberg bridges problem (1736), introduced the notation f(x), e, i and Σ, and discovered the formula $e^{i\theta} = \cos\theta + i\sin\theta$ . He died in St Petersburg in 1783.

Workplaces: Imperial Academy of Sciences, St Petersburg, Prussian Academy of Sciences, Berlin

Switzerland, Russia, Germany

Contributions, linked to the library

Great problemBasel problemSolved the problem in 1735, showing ζ(2) = π²/6.Great problemSeven Bridges of KönigsbergFounded graph theory by solving the Königsberg bridges problem in 1736.TheoremEuler's formulaDiscovered

e^{i\theta} = \cos\theta + i\sin\theta

, connecting exponential and trigonometric functions.TheoremEuler's polyhedron formulaStated the polyhedron formula V − E + F = 2, an early result in topology.