Leonhard Euler :: essays research papers

Leonhard EulerLeonhard Euler, (born April 15, 1707, died Sept. 18, 1783), was the most productive mathematician in history. His 866 books and articles represent aboutone third of the entire system of research on mathematics, theoretical natural philosophy,and engineering mechanics published surrounded by 1726 and 1800. In pure mathematics,he integrated Leibnizs differential calculus and Newtons order of fluxionsinto numerical analysis refined the notion of a function make common manymathematical notations, including e, i, the pi symbol, and the sigma symbol andlaid the induction for the speculation of special functions, introducing the betaand gamma transcendal functions. He in addition worked on the origins of the calculusof variations, but withheld his work in deference to J. L. Lagrange. He was apioneer in the field of topology and made number theory into a science, statingthe prime number theorem and the law of biquadratic reciprocity. In physics hearticulated Newtonian d ynamics and laid the foundation of analytical mechanics,especially in his Theory of the Motions of Rigid Bodies (1765). Like his teacherJohann Bernoulli, he elaborated continuum mechanics, but he also set forth theenergizing theory of gases with the molecular model. With Alexis Clairaut hestudied 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 give-and-take to follow in his footsteps and sent him to the University of Basel to wangle for the ministry, but geometry soon became his favorite subject. Throughthe intercession of Bernoulli, Euler obtained his fathers consent to change hismajor to mathematics. After failing to obtain a physics rig at Basel in1726, he joined the St. Petersburg academy of Science in 1727. When funds werewithheld from the academy, he served as a medical lieutenant in the Russian navyfrom 1727 to 1730. In St. Petersburg he boarded at the home of Bernoullis sonDaniel. He became professor of physics at the academy in 1730 and professor ofmathematics in 1733, when he married and left Bernoullis house. His reputationgrew afterwards the publication of many articles and his book Mechanica (1736-37),which extensively presented Newtonian dynamics in the form of mathematicalanalysis for the first time.In 1741, Euler joined the Berlin Academy of Science, where he remainedfor 25 years. In 1744 he became director of the academys mathematics section.During his tarry in Berlin, he wrote over 200 articles, three books onmathematical analysis, and a scientific popularization, Letters to a Princess ofGermany (3 vols., 1768-72).