Leonhard Euler: Biography, Contributions & Discoveries

Instructor: Betsy Chesnutt

Betsy teaches college physics, biology, and engineering and has a Ph.D. in Biomedical Engineering

Leonhard Euler was one of the most influential and prolific mathematicians of all time. In this lesson, we discuss his life and his contributions to mathematics.

Who Was Leonhard Euler?

Why do mathematicians represent imaginary numbers using the symbol i? Why are functions usually written as f(x)? Today, we take this standard system of notation and symbols for granted. However, it wasn't always like this! It took the work of one of the greatest mathematicians of all time, Leonhard Euler, to standardize and invent most of the mathematical notation that we use today.

Leonhard Euler
Leonhard Euler

We still use the notation and symbols developed by Euler, and that alone is a huge accomplishment. However, Euler was also one of the most important mathematicians of his time, and his groundbreaking work remains important even today.

Early Life and Education

Leonhard Euler was born in Basel, Switzerland in 1707. His father, Paul Euler, was educated at the University of Basel. Although he was a minister and not a mathematician, he studied under one of the great mathematicians of the time, Jacob Bernoulli. Euler's father even lived in Bernoulli's house and studied with his son Johann while they were both students.

When Euler was a child, he learned the basics of mathematics from his father, but his family expected him to enter the ministry. However, Euler was more interested in reading mathematics books than the Bible, and becoming a minister was not something he really wanted to do.

At fourteen years old, he enrolled in the University of Basel to study theology, but he quickly convinced his father's old friend Johann Bernoulli--now a renowned mathematics professor--to give him some private lessons. Bernoulli quickly recognized the enormous talent of the young Euler, and convinced Paul Euler to allow his son to switch from theology to mathematics.

Euler graduated in 1726 at only nineteen years old, and by the time he graduated, he had already published his first paper. The next year, he published another paper and won second place in the competition for the Grand Prize of the Paris Academy, which was a major accomplishment for such a young mathematician. He would later win the Paris prize twice, in 1738 and 1740.

Work in St. Petersburg

Although he wanted to stay close to home in Switzerland, Euler was unable to find a position at the university. Instead, he accepted a position as a professor in the newly formed St. Petersburg Academy of Sciences in St. Petersburg, Russia. He arrived in St. Petersburg in May of 1727, and it was here that he would do much of his most revolutionary work. Initially, Euler worked for the Russian navy as well as at the academy, but in 1730, he was given a full time position as a professor of physics. Then, in 1733, he became a senior professor of mathematics at only 26 years old.

Euler would spend most of his life in St. Petersburg, and during this time he published 380 papers. He defined the trigonometric functions sine, cosine, and tangent; combined and improved on the early forms of calculus developed by Leibniz and Newton; and did work in fields ranging from optics, musical analysis, and acoustics. He introduced many new forms of mathematical notation, including the use of f(x) for functions, the symbol i for imaginary numbers, and the symbol e for the base of the natural logarithm.

Personal Life

In 1734, Euler married Katharinia Gsell, who was also a Swiss expatriate living in St. Petersburg. They had thirteen children total, but only five survived. Not long after his marriage, Euler began to suffer from problems with his eyesight that would plague him for the rest of his life. After he recovered from a fever in 1735, the vision in his right eye was damaged. It got progressively worse over the next few years, and by 1766, he was almost entirely blind.

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