# Leonhard Euler – a blind man leading mathematics

Euler was born the same year as Carl Linnaeus. He was born in Basel in 1707 and died in St. Petersburg in 1783. His teacher was Johann Bernoulli. He took a post at the newly opened Academy of Science in St. Petersburg in 1727. In the years 1741–1766 he worked at the Berlin Academy of Science and then returned to St. Petersburg where he was buried. Despite the fact that he became blind in one eye in the late 1730s and totally blind in 1766, he was clearly the greatest mathematician of the 18^{th} century and produced an enormous number of mathematical publications, toward the end of his life [among others] with the Finnish mathematician Anders Lexell (1740–1784) as his secretary.

Euler created order in differential and integral calculus, developed the number theory, introduced symbols like *f(x)*, e, *π*, and *i*. He developed the theory for solving differential equations and thereby contributed to the solution of many problems in applied physics.

## Number theory

Pythagoras, Diophantos, and Fermat are precursors to Euler in regard to number theory. Many of their mutual problems had to do with prime numbers. A theorem by Fermat that Euler proved reads: A prime number of the form 4*n* + 1 (*n* is a positive whole integer) can always be expressed as the sum of two squares, but only in one way.

Example: for the prime number 29 and the number *n* = 7, thus 4·7 + 1 = 29 = 2^{2} + 5^{2}.

## Differential equations

A differential equation is an equation that contains derivatives of one or more functions. The equation is solved when the function or functions have been found. In Euler's day, there were no derivatives. Equations were then expressed by differentials.