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Leonard Eulers Scientific Heritage
February 7, 2008 23:25

Euler equations

Leonard Euler’s scientific heritage is enormous. Euler is the author of classic result in mathematical analysis. Leonard Euler develops its basis, makes significant contribution to integral calculus and techniques for integrating ordinary differential equations and partial differential equations. Euler is the proud author of the famous six volumes of mathematical analysis, which include “Introduction to infinitesimal analysis”, “Differential Calculus” and “Integral Calculus” (1748-1770). This “analytic trilogy” brings up many generations of mathematicians of the world.

Leonard Euler works out main equations of calculus of variations and predicts its further development in his monograph “Method for finding curves, showing maximum or minimum property”, published in 1744. His contribution to theory of functions, differential geometry, computing mathematics and theory of numbers is also enormous. Two volumes of Euler’s “Complete guide to algebra” (1770) went through 30 editions in six European languages.


Leonard Euler obtains fundamental results in rational mechanics. He is the first to give consistently analytical summary of mechanics of a particle, covering issues of movement of free particle and constrained particle in empty space and in resisting medium. Later Euler develops basis for kinematics and solid-state dynamics by creating appropriate general equations. Summaries of this research are collected into his “Theory of solid bodies’ movement” of 1765. Famous American mathematician and physics historian of the XX century Clifford Truesdell suggests calling the complex of equations in dynamics, describing moment of momentum and momentum principles, “Euler’s laws of mechanics”.

In 1752 Leonard Euler formulates general aspects of Newtonian motion equations for fixed coordinates thus opening the way for studying continuum mechanics. The genius also derives classic equations of hydrodynamics for an ideal liquid and makes significant contribution to acoustics. Euler does a lot for mathematical astronomy with his “New theory of Moon moving process”, which becomes essential for navigation.

The mathematician contributes to applied sciences as well – ship theory (Ship Science of 1749), artillery, ballistics and geometrical optics owe a lot to the genius. Modern Encyclopedia of Mathematics lists 20 mathematical objects, named after Euler. Physics also has fundamental equations, proudly bearing the name of great mathematician.


The Archive of Saint-Petersburg’s Academy of Sciences keeps thousands of unpublished scientific works of Leonard Euler, his mathematical notebooks and enormous scientific correspondence.

Authority of Leonard Euler as a scientist is infinite – he is an honoured member of all possible science academies and societies of the world. Total of Euler’s works boggles imagination – over 800 published works amount to 30 000 printed pages and consist of 600 articles for Saint-Petersburg’s Academy of Sciences, 130 articles published in Berlin, 30 articles for various European journals, 15 memoir volumes and 40 other books – all this will come off the press as 72 volumes of Euler’s scientific heritage (Opera omnia).

Euler is a guardian angel for Russian Academy of Sciences together with Peter the Great and Mikhail Lomonosov, who are Academy’s fame and strong foundation. Euler’s grandsons and students were responsible for Academy’s affairs for almost a century. Euler’s three sons dedicate themselves to the Russian state and Academy of Science. His other descendants became citizens of Russia.


Kizilova Anna

Tags: Russian scientists Russian science    

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