Essay/Term paper: Leonhard euler

Essay, term paper, research paper:  Science

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.