  Leonhard Euler was born in Switzerland in 1707, and he studied mathematics there under Johann Bernoulli. Euler was a genius, and a very prolific writer, perhaps more so than any other mathematician in history. He has his name attached to ideas in just about every branch of mathematics. Amazingly, his productivity was not the least impaired by becoming blind in 1768.Euler is particularly known for his contributions to early Western algebra; the incredible number of contributions he made to mathematics as a whole could fill many textbooks (in fact, they do!) Here are a few of the ideas for which he is responsible, most of which should be familiar to senior high school mathematics students. Euler was responsible for the following notations, which he invented and used in his work:
Euler also discovered the very remarkable formula:  ... a relation connecting five of the most important numbers in mathematics. Much of Euler's work resulted in discoveries which are the basis of modern mathematics. Indeed, modern high school math courses (which, by and large, cover 'old' mathematics), demonstrate many theorems and ideas that originated with Euler. High school students learn Euler's Rule v - e + f = 2 relating the number of verticies, edges, and faces of a closed polyhedron. Students studying number theory discover Euler's Theorem. College students learn Euler's method for solving quartic equations, and are shown the Euler Line of a triangle in geometry. Euler published papers in differential and integral calculus, differential geometry, and recreational mathematics (he solved the Königsberg Bridge problem). He also produced many works in the area of applied mathematics, notably in the areas of ship building, the three-body problem in celestial mechanics, hydraulics, artillery, and music. Euler was a good textbook writer; his material was presented clearly, with great detail and completeness, and the books were widely used in his era. Many later mathematicians have written that their work owed a great debt to the fundamental strides made by Euler in an earlier time. |
for the summation sign