Leonhard Euler

Now I will have less distraction.
(upon losing the use of his right eye)
Quoted in H Eves In Mathematical Circles (Boston 1969).

b. 15 April 1707, Basel, Switzerland
d. 18 Sept 1783, St. Petersburg, Russia

Leonhard Euler is considered to be the father of fluid mechanics and was an amazingly productive writer of mathematics. He advanced modern analytic geometry and trigonometry by considering sin, cos, etc. as functions rather than as chords. He integrated Leibniz's differential calculus and Isaac Newton's method of fluxions into mathematical analysis. He studied the three body problem, continuum mechanics, lunar theory with Clairaut, acoustics, the wave theory of light, hydraulics, elasticity, and music. Euler also laid the foundation of analytical mechanics in his Theory of the Motions of Rigid Bodies (1765).

As for fluid mechanics, Euler laid the formulas for the continuity equation, the Laplace velocity potential equation, and the Euler equations for the motion of an inviscid incompressible fluid.

Background

Euler went to a second-rate school in Basel that had no mathematics (and probably no heat, and bad plumbing...and no sense of fashion!), so he studied texts on his own and soon began private study with Johann Bernoulli, one of the venerable Bernoulli family. Actually, Leonhard's father, Paul, had lived with Johann in older brother Jakob's house when they were ungraduates. So Johann cut Leonhard a twig.

Euler studied philosophy and theology and completed his studies at the University of Basel by 1726, by which time he had a short article published on isochronous curves in a resisting medium. In 1727 he published another article on reciprocal trajectories and submitted an entry for the 1727 Grand Prize of the Paris Academy on the best arrangement of masts on a ship (which won second place). In Russia he continued the tradition of Euler-Bernoulli flat-sharing when he lived with Daniel Bernoulli. He made full physics professor at St. Petersburg in 1730. His career to this point is summarized below:

... after 1730 he carried out state projects dealing with cartography, science education, magnetism, fire engines, machines, and ship building. The core of his research program was now set in place: number theory; infinitary analysis including its emerging branches, differential equations and the calculus of variations; and rational mechanics. He viewed these three fields as intimately interconnected. Studies of number theory were vital to the foundations of calculus, and special functions and differential equations were essential to rational mechanics, which supplied concrete problems. - Historia Mathematica 23 (1996), 121-166.

Euler then went to Berlin to work at the Berlin Academy, where he

... supervised the observatory and the botanical gardens; selected the personnel oversaw various financial matters; and, in particular, managed the publication of various calendars and geographical maps, the sale of which was a source of income for the Academy. The king (Frederick the Great) also charged Euler with practical problems, such as the project in 1749 of correcting the level of the Finow Canal ... At that time he also supervised the work on pumps and pipes of the hydraulic system at Sans Souci, the royal summer residence. - Dictionary of Scientific Biography (New York 1970-1990).

A shout-out to the School of Mathematics and Statistics, University of St. Andrews, Scotland, for most of the info.

Leonhard Euler (pronounced Oiler as ccunning points out) was born in 1707 at Basle, Switzerland. At the age of 20 having already graduated from Basle University, he moved to St. Petersburg where within ten years he became professor of physics and mathematics. For a while he taught in Berlin but towards the end of his life, beset by total blindness yet still able to perform astounding mathematical feats in his head, he returned to Russia where he taught until his death at the age of 76.

One of the greatest mathematicians to have ever lived, his many published works dealt with the diverse subjects of number theory, geometry, calculus (still a new and unproven concept then), astronomy and physics. His name lives on through a number of important mathematical concepts:

Euler's Constant (usually denoted by the Greek letter gamma γ) is the limit, as n->s, of 1 + ¹/₂ + ¹/₃ + ¹/₄ n -> infinity ... ¹/_n - log_en, approximately 0.577.

Euler's Function (denoted by φ(n)) refers in the number of integers in the set 1,2,3,...,n-1 which are prime to n; thus φ(9) = 6, since 6 of the integers 1,2,3,...8 are prime to 9.

Euler's Formula for Polyhedra states that if a polyhedron has v vertices, f faces and e edges, v + f - e = 2 for all polyhedra; thus a cube has 8 vertices, 12 edges and 6 faces, and 8 + 6 - 12 = 2.

Leonhard Euler wrote over 1100 books and papers and left so much unpublished work that it took 47 years after he died for all his work to be published. During his life his papers accumulated so quickly that he kept a large pile of articles awaiting publication. The Berlin Academy published the papers on top of this pile so later results were often published before results they depended on or superseded. Euler had 13 children and was able to continue his work while a child or two bounced on his knees. He was blind for the last 17 years of his life, but because of his fantastic memory this did not diminish his matematical output. The project of publishing his collected works, undertaken by the Swiss Society of Natural Science, is still going on and will require more than 75 volumes.

The correct pronunciation of Leonhard Euler's last name sounds like oiler.

Sources: Interactive Real Analysis, Encyclopedia Britannica, Discrete Math and Its Applications