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What are some of the accomplishments of Leonhard Euler?

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Leonhard Euler was an 18th century mathematician and physicist. He made important contributions to numerous branches of mathematics, including infinitesimal calculus, analytical geometry and number theory.

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As a child, Leonhard Euler showed an aptitude for the advanced mathematics of his day. Entering university at age 13, he studied mathematics, ancient languages and philosophy in preparation for a career in the clergy. Eventually, he gained his father's permission to switch to mathematics and almost immediately began to transform the field.

Euler was the first mathematician to introduce the concepts of sine, cosine and other functions on their own terms, rather than following the Ptolemaic tradition of treating them as chords. He developed a method for expressing repeating functions, such as an infinite string of factorials, in a way that made it easy to incorporate them into algebra. Euler was responsible for establishing a sizable fraction of modern mathematical notation conventions, including the use of the Greek letter sigma to denote summations and iota for the imaginary unit. Euler is also credited with inventing the entire field of analytic number theory.

Leonhard Euler was one of the most prolific publishers in the history of mathematics. So great was his output that, though he died in 1783, the St. Petersburg Academy continued publishing his papers into the 1830s.

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