Leonhard Euler

# Leonhard Euler

## Leonhard Euler

Born:  15th April, 1707, Basel, Switzerland
Died:  18th September, 1783, Saint Petersburg, Russia
Education: University of Basel (1720–1723)
Influenced: Carl Friedrich Gauss, Joseph-Louis Lagrange

Leonhard Euler, a Swiss mathematician, physicist, astronomer, logician and engineer who made important and influential discoveries in many branches of mathematics like graph theory and infinitesimal calculus. He also made pioneering contributions to several branches such as topology and analytic number theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function.

Euler worked in almost all areas of mathematics, such as algebra, trigonometry, geometrycalculusand number theory, as well as in physicslunar theory and other areas of physics.

Euler is the only mathematician to have two numbers named after him: the important Euler's number in calculuswhose value is approximately equal to 2.71828, and the Euler–Mascheroni constant Î³ (gamma) which is referred to as Euler's constant, and whose value is approximately equal to 0.57721.

Euler introduced and popularized several conventions through his numerous and widely circulated textbooks. Most notably, he introduced the concept of a function and was the first to write f(x) to denote the function f applied to the argument x. He also introduced the modern notation for the trigonometric functions, the letter e for the base of the natural logarithm (now also known as Euler's number), the Greek letter  for summations and the letter i to denote the imaginary unit.

Euler introduced the use of the logarithms and exponential function in analytic proofs. He discovered different methods to express the logarithmic functions using power series, and he successfully defined logarithms for negative and complex numbers.

He greatly expanded the scope of mathematical applications of logarithms.