Euler

Leonhard Euler (7 April 1707 – 18 September 1783) was a Swiss mathematician and physicist whose work laid foundational advances across mathematics, mechanics, and astronomy. Born in Basel, he studied at the University of Basel and spent the early part of his career at the St. Petersburg Academy of Sciences before moving to the Berlin Academy in 1741. He returned to St. Petersburg in 1766 and remained there until his death, becoming one of the most prolific and influential figures in the history of mathematics.

Euler made wide-ranging contributions. In analysis and mathematical notation, he advanced calculus, popularized the use of the exponential base e, and helped establish function notation such as f(x). He is associated with the famous identities e^{iπ}+1=0 and e^{iθ}=cos θ + i sin θ, which connect analysis and trigonometry. In graph theory, his solution to the Königsberg bridges problem laid the foundations of the field and introduced the concept of an Eulerian path. In number theory he introduced the totient function φ(n) and developed early product formulas for primes, notably the Euler product for the zeta function. In geometry and topology he stated the polyhedron formula V−E+F=2 for convex polyhedra. In physics and applied mathematics he derived the Euler equations for rigid body rotation and for inviscid fluid flow, and he contributed to numerical methods, including what is now known as Euler’s method for solving differential equations.

Euler’s extensive output—comprising hundreds of papers and books—shaped many areas of mathematics and its applications. His notation, insights, and techniques influenced subsequent generations and remain central to multiple fields.