Leonhard Euler
(1707-1783)

Leonhard Euler made many remarkable contributions to mathematics and mechanics. He was the most productive mathematician of all time and Newman refers to him as "a hero for mathematicians". His name, which is pronounced "'oiler," appears repeatedly in present-day textbooks; for instance, in mechanics we have Euler's equations of motion of a rigid body, Euler's angles, Euler's equations of fluid flow, the Euler load in column buckling, and much more; and in mathematics we encounter the famous Euler constant, as well as Euler's numbers, the Euler identity (e^iq = cos q + i sin q), Euler's formula (e^ip + 1 = 0), Euler's differential equation, Euler's equation of a variational problem, Euler's quadrature formula, the Euler summation formula, Euler's theorem on homogeneous functions, Euler's integrals, and even Euler squares (square arrays of numbers possessing special properties).

In applied mechanics, Euler was the first to derive the formula for the critical buckling load of an ideal, slender column and the first to solve the problem of the elastica. This work was published in 1744. He dealt with a column that is fixed at the base and free at the top. Later, he extended his work on columns. Euler's numerous books include treatises on celestial mechanics, dynamics, and hydromechanics, and his papers include subjects such as vibrations of beams and plates and statically indeterminate structures.

In the field of mathematics, Euler made outstanding contributions to trigonometry, algebra, number theory, differential and integral calculus, infinite series, analytic geometry, differential equations, calculus of variations, and many other subjects. He was the first to conceive of trigonometric values as the ratios of numbers and the first to present the famous equation e^iq = cos q + i sin q. Within his books on mathematics, all of which were classical references for many generations, we find the first development of the calculus of variations as well as such intriguing items as the proof of Fermat's "last theorem" for n = 3 and n = 4. Euler also solved the famous problem of the seven bridges of Konigsberg, a problem of topology, another field in which he pioneered.

Euler was born near Basel, Switzerland, and attended the University of Basel, where he studied under John Bernoulli (1667-1748). From 1727 to 1741 he lived and worked in St. Petersburg, where he established a great reputation as a mathematician. In 1741 he moved to Berlin upon the invitation of Frederick the Great, King of Prussia. He continued his mathematical research in Berlin until the year 1766, when he returned to St. Petersburg at the request of Catherine II, Empress of Russia. Euler continued to be prolific until his death in St. Petersburg at the age of 76; during this final period of his life he wrote more than 400 papers. In his entire lifetime, the number of books and papers written by Euler totaled 886; he left many manuscripts at his death and they continued to be published by the Russian Academy of Sciences in St. Petersburg for 47 years afterward. All this in spite of the fact that one of his eyes went blind in 1735 and the other in 1766!

From Mechanics of Materials, 4th Ed., by J.M. Gere and S.P. Timoshenko, PWS Publishing, 1997, pp. 835-42.