**Leonhard Euler**

**Born:**15

^{th}April, 1707, Basel, Switzerland

**Died:**18

^{th}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,
geometry, calculus, and number theory, as well as in physics, lunar theory and
other areas of physics.

Euler is the only mathematician to have

*two*numbers named after him: the important**Euler's number**in calculus, whose 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.