Leonhard Euler Essay, Research Paper

Leonhard Euler

Leonhard Euler, (born April 15, 1707, died Sept. 18, 1783), was the most

prolific mathematician in history. His 866 books and articles represent about

one third of the entire body of research on mathematics, theoretical physics,

and engineering mechanics published between 1726 and 1800. In pure mathematics,

he integrated Leibniz’s differential calculus and Newton’s method of fluxions

into mathematical analysis; refined the notion of a function; made common many

mathematical notations, including e, i, the pi symbol, and the sigma symbol; and

laid the foundation for the theory of special functions, introducing the beta

and gamma transcendal functions. He also worked on the origins of the calculus

of variations, but withheld his work in deference to J. L. Lagrange. He was a

pioneer in the field of topology and made number theory into a science, stating

the prime number theorem and the law of biquadratic reciprocity. In physics he

articulated Newtonian dynamics and laid the foundation of analytical mechanics,

especially in his Theory of the Motions of Rigid Bodies (1765). Like his teacher

Johann Bernoulli, he elaborated continuum mechanics, but he also set forth the

kinetic theory of gases with the molecular model. With Alexis Clairaut he

studied lunar theory. He also did fundamental research on elasticity, acoustics,

the wave theory of light, and the hydromechanics of ships.

Euler was born in Basel, Switzerland. His father, a pastor, wanted his

son to follow in his footsteps and sent him to the University of Basel to

prepare for the ministry, but geometry soon became his favorite subject. Through

the intercession of Bernoulli, Euler obtained his father’s consent to change his

major to mathematics. After failing to obtain a physics position at Basel in

1726, he joined the St. Petersburg Academy of Science in 1727. When funds were

withheld from the academy, he served as a medical lieutenant in the Russian navy

from 1727 to 1730. In St. Petersburg he boarded at the home of Bernoulli’s son

Daniel. He became professor of physics at the academy in 1730 and professor of

mathematics in 1733, when he married and left Bernoulli’s house. His reputation

grew after the publication of many articles and his book Mechanica (1736-37),

which extensively presented Newtonian dynamics in the form of mathematical

analysis for the first time.

In 1741, Euler joined the Berlin Academy of Science, where he remained

for 25 years. In 1744 he became director of the academy’s mathematics section.

During his stay in Berlin, he wrote over 200 articles, three books on

mathematical analysis, and a scientific popularization, Letters to a Princess of

Germany (3 vols., 1768-72). In 1755 he was elected a foreign member of the Paris

Academy of Science; during his career he received 12 of its prestigious biennial

prizes.

In 1766, Euler returned to Russia, after Catherine the Great had made

him a generous offer. At the time, Euler had been having differences with

Frederick the Great over academic freedom and other matters. Frederick was

greatly angered at his departure and invited Lagrange to replace him. In Russia,

Euler became almost entirely blind after a cataract operation, but was able to

continue with his research and writing. He had a phenomenal memory and was able

to dictate treatises on optics, algebra, and lunar motion. At his death in 1783,

he left a vast backlog of articles. The St. Petersburg Academy continued to

publish them for nearly 50 more years.