Leonhard Euler (1707-1783) was born in Basel [Switzerland]. His father ... gave him his first instruction in mathematics. ... In his nineteenth year he composed a dissertation on the masting of ships, which received the second prize from the French Academy of Sciences. ... In 1735 the solving of an astronomical problem, proposed by the Academy, for which several eminent mathematicians had demanded some months' time, was achieved in three days by Euler with aid of improved methods of his own. But the effort threw him into a fever and deprived him of the use of his right eye.
[Later] he became blind [in both eyes], but this did not stop his wonderful literary productiveness. ... Euler wrote an immense number of works. ... [He] introduced (simultaneously with Thomas Simpson in England) the now current abbreviations for trigonometric functions, and simplified formulas by ... designating the angles of a triangle by A,B,C, and the opposite sides by a, b, c. ...
He pointed out the relation between trigonometric and exponential functions. ... Euler laid down the rules for the transformation of co-ordinates in space. ... [He] proved a well-known theorem, giving the relation between the number of vertices, faces, and edges of certain polyhedra, which, however, appears to have been known to Descartes. The powers of Euler were directed also towards the fascinating subject of ... probability, in which he solved some difficult problems.
Astronomy owes [a great deal] to Euler. ... These researches on the moon's motion, which captured two prizes, were carried on while he was blind, with the assistance of his sons and two of his pupils.
It has been said that an edition of Euler's complete works would fill [about 90 modern day books]. His mode of working was, first to concentrate his powers upon a special problem. Then [he would] solve separately all problems growing out of the first. ... It is easy to see that mathematicians could not long continue...
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