Leonhard Euler Essay, Research Paper

Leonhard Euler

Euler, Leonhard (1707-83), Swiss mathematician, whose major work was done in the

field of pure mathematics, a field that he helped to found. Euler was born in

Basel and studied at the University of Basel under the Swiss mathematician

Johann Bernoulli, obtaining his master’s degree at the age of 16. In 1727, at

the invitation of Catherine I, empress of Russia, Euler became a member of the

faculty of the Academy of Sciences in Saint Petersburg. He was appointed

professor of physics in 1730 and professor of mathematics in 1733. In 1741 he

became professor of mathematics at the Berlin Academy of Sciences at the urging

of the Prussian king Frederick the Great. Euler returned to St. Petersburg in

1766, remaining there until his death. Although hampered from his late 20s by

partial loss of vision and in later life by almost total blindness, Euler

produced a number of important mathematical works and hundreds of mathematical

and scientific memoirs.

In his Introduction to the Analysis of Infinities (1748; trans. 1748), Euler

gave the first full analytical treatment of algebra, the theory of equations,

trigonometry, and analytical geometry. In this work he treated the series

expansion of functions and formulated the rule that only convergent infinite

series can properly be evaluated. He also discussed three-dimensional surfaces

and proved that the conic sections are represented by the general equation of

the second degree in two dimensions. Other works dealt with calculus, including

the calculus of variations, number theory, imaginary numbers, and determinate

and indeterminate algebra. Euler, although principally a mathematician, made

contributions to astronomy, mechanics, optics, and acoustics