Leonhard Euler

Biography

Studied at the University of Basel under Johann Bernoulli. Worked at the St. Petersburg Academy of Sciences (1727–1741 and from 1766) and the Berlin Academy (1741–1766). Collaborated with Christian Goldbach and other scientists. Was an honorary member of many academies, including the Royal Society of London. Awarded the Order of St. Stanislaus and a prize of the Paris Academy of Sciences.

Key discoveries

• Euler's formula: e^(ix) = cos x + i sin x, connecting complex exponentials with trigonometric functions, fundamental for complex analysis and physics.
• Solution of the Basel problem: finding the sum of the reciprocals of squares (∑ 1/n² = π²/6), which was a triumph of analysis.
• Euler characteristic of polyhedra: formula V − E + F = 2, which laid the foundations of topology.
• Introduction of notations f(x), e, i, π and others, widely used to this day.