Karl Friedrich Gauss
At school he was a very good student, famously adding up the numbers 1 to 100 in seconds by treating the numbers as pairs (1+100=101, 2+99=99,... so that all the numbers added up to 50 times 101=5050). His education was encouraged by his mother and an uncle, and he was sponsored by the Duke of Brunswick to attend Caroline College. At the end of his college years, Gauss made a tremendous discovery that, up to this time, mathematicians had believed was impossible. He found that a regular polygon with 17 sides could be drawn using just a compass and straight edge.
Gauss then went to the University of Gottingen. While there he proved that every algebraic equation has at least one solution. This theorem is called "the fundamental theorem of algebra".
In 1801, he calculated the orbit of an asteroid from only three observations and worked for a while on the orbits of asteroids. Later he was among the first to treat maths as an experimental science, showing that the angles of a triangle did indeed add to 180 degrees by using measurements on mountaintops. He was appointed professor of mathematics and director of the observatory at Gottingen, remaining until his death on February 23, 1855.