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## Spectacular Mountain

# Leonhard Euler (1707-1783)

The greatest mathematician of the eighteenth century, **Leonhard Euler** was

born in Basel, Switzerland. There, he studied under another giant of

mathematics, **Jean Bernoulli**. In 1731 Euler became a professor of physics

and mathematics at St. Petersburg Academy of Sciences. Euler was the most

prolific mathematician of all time, publishing over *800 different books and
papers*. His influence was felt in physics and astronomy as well.

He is perhaps best known for his research into mathematical analysis. Euler’s

work, Introductio in analysin

infinitorum (1748), remained a standard textbook in the field for

well over a century. For the princess of Anhalt-Dessau he wrote

Lettres a une princesse d’Allemagne (1768-1772), giving a clear

non-technical outline of the main physical theories of the

time.

One can hardly write a mathematical equation without copying Euler.

Notations still in use today, such as e and pi, were introduced

in Euler’s writings. Leonhard Euler died in 1783, leaving behind

a legacy perhaps unmatched, and certainly unsurpassed, in the annals

of mathematics.

The Most Beautiful Theorem?

Euler’s Equation

cos(x) + isin(x) = e (ix)

demonstrates the relationship between algebra, complex analysis,

and trigonometry. From this equation, it’s easy to derive

the identity

e(pi i) + 1 = 0

which relates the fundamental constants: 0, 1, pi, e, and i in

a single beautiful and elegant statement. A poll of readers

conducted by The Mathematical Intelligencer magazine named

Euler’s Identity as the

most beautiful theorem in the history of mathematics.

Math High: A Site for Educators and Researchers