Today we, along with Google Doodle, celebrate the birthday of Swiss mathematician Leonhard Euler (1707-1783). Euler completed work in astronomy, physics, and mechanics, but he remains most famous for his work in mathematics.
Leonhard Euler is responsible for many of our modern mathematical terminology, including the principle of a function. A function, noted as f(x), is a formula or algorithm that is applied to argument x, producing exactly one specific output for each input. He’s also responsible for the modern notation of trigonometric functions, such as sine, cosine, and tangent. And although he didn’t discover the constants e and pi, he’s responsible for popularizing the letter e as the base of the natural logarithm – to this day referred to as “Euler’s number” – and the Greek letter pi for the ratio of a circle’s circumference to its diameter. He also popularized using the Greek letter sigma for summation and the letter i for irrational numbers.
If it sounds like Euler didn’t do much but make up notation for other people’s work, think again! He contributed significant advancement to infinitesimal calculus (Euler’s formula, Euler’s identity, Euler-Lagrange equation), graph theory (Eulerian path, Euler characteristic), number theory (Euler’s theorem, Euler product formula for the Riemann zeta function), applied mathematics (Euler numbers, Euler’s method, Euler-Maclaurin formula, Euler-Mascheroni constant), and logic (Euler’s diagram). In fact, if you put together all of Euler’s published work, you’d have a small library.
Please join me in celebrating Euler’s birthday today!