Leonhard Euler

Leonhard Euler ( OY-lər; 15 April 1707 – 18 September 1783) was a Swiss polymath who was active as a mathematician, physicist, astronomer, logician, geographer, music theorist and engineer. He founded the studies of graph theory and topology and made influential discoveries in many other branches of mathematics, such as analytic number theory, complex analysis, and infinitesimal calculus. He also introduced much of modern mathematical terminology and notation, including the notion of a mathematical function. He is known for his work in mechanics, fluid dynamics, optics, astronomy, and music theory. Euler has been called a "universal genius" who "was fully equipped with almost unlimited powers of imagination, intellectual gifts and extraordinary memory". He spent most of his adult life in Saint Petersburg, Russia, and in Berlin, then the capital of Prussia.

Euler is credited for popularizing the Greek letter

π

{\displaystyle \pi }

(lowercase pi) to denote the ratio of a circle's circumference to its diameter, as well as first using the notation

f

(

x

)

{\displaystyle f(x)}

for the value of a function, the letter

i

{\displaystyle i}

to express the imaginary unit

−

1

{\displaystyle {\sqrt {-1}}}

, the Greek letter

Σ

{\displaystyle \Sigma }

(capital sigma) to express summations, the Greek letter

Δ

{\displaystyle \Delta }

(capital delta) for finite differences, and lowercase letters to represent the sides of a triangle while representing the angles as capital letters. He gave the current definition of the constant

e

{\displaystyle e}

, the base of the natural logarithm, now known as Euler's number. Euler made contributions to applied mathematics and engineering, such as his study of ships helping navigation, his three volumes on optics, which contributed to the design of microscopes and telescopes, and his studies of beam bending and column critical loads.