Carl Friedrich Gauss, born in 1777, was a German prodigy, and he began his mathematical career with an investigation of imaginary numbers. His doctoral thesis was a proof of the fundamental theorem of algebra—proving that a polynomial of degree n (a quadratic has degree 2, a cubic has degree 3, a quartic has degree 4, and so on) has n roots. This is only true if you accept imaginary numbers as well as real numbers.
