The French mathematician Augustin Louis Cauchy (1789-1857) provided the foundation for the modern period of rigor in analysis. He launched the theory of functions of a complex variable and was its authoritative pioneer developer.
Niels Henrik Abel (1802-1829) was a Norwegian mathematician who proved that fifth and higher order equations have no algebraic solution. Had he not died prematurely, it is speculated that he might have become one of the most prominent mathematicians of the 19th century. He provided the first general proof of the binomial theorem and made significant discoveries concerning elliptic functions