Leonhard Euler, his famous formula, and why he's so revered

Today’s Google Doodle celebrates mathematics, and the 306th birthday of the 18th century’s pre-eminent mathematician, Leonhard Euler. Born and educated in Basel, Switzerland, Euler was responsible for much of the modern mathematical terminology and notation still used today. 

Euler was a prolific mathematician whose work spanned the fields of geometry, calculus, trigonometry, algebra, number theory, physics, lunar theory, and even astronomy.

Euler was the first to introduce the notation for a function f(x). He also popularized the use of the Greek letter π to denote the ratio of a circle’s circumference to its diameter.

Arguably, his most notable contribution to the field was Euler’s identity formula, (e^iπ + 1 = 0) 

Euler also made contributions in the fields of number theory, graph theory, logic, and applied mathematics. He received a number of Paris Academy Prizes for his work in astronomy, which mostly focused on understanding comets and determining their orbits. Euler's contemporary colleagues, and even mathematicians working today, recognize him as one of the greatest mathematicians to have ever lived. 

“He calculated without any apparent effort, just as men breathe, as eagles sustain themselves in the air."

– François Arago, French mathematician, physicist, and astronomer.

“Read Euler: he is our master in everything.”

– Pierre-Simon Laplace (attributed), French mathematician and astronomer.

“Euler calculated the force of the wheels necessary to raise the water in a reservoir … My mill was carried out geometrically and could not raise a drop of water fifty yards from the reservoir. Vanity of vanities! Vanity of geometry!”

– Frederick the Great in letters to Voltaire.

“Our jewel ... one of the most remarkable, almost astounding, formulas in all of mathematics.”

– Richard Feynman, 20th century American physicist on Euler’s identity formula.

 “Like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence.”

– Keith J. Devlin, 20th century British mathematician and popular science writer on Euler’s identity formula.

“Perhaps the most surprising thing about mathematics is that it is so surprising. The rules which we make up at the beginning seem ordinary and inevitable, but it is impossible to foresee their consequences. These have only been found out by long study, extending over many centuries. Much of our knowledge is due to a comparatively few great mathematicians such as Newton, Euler, Gauss, or Riemann; few careers can have been more satisfying than theirs. They have contributed something to human thought even more lasting than great literature, since it is independent of language.”

– Edward Charles Titchmarsh, 20th century British mathematician.