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
Alberto Calderón's (born 1920) revolutionary influence turned the 1950s trend toward abstract mathematics back to the study of mathematics for practical applications in physics, geometry, calculus, and many other branches of this field. His award-winning research in the area of integral operators is an example of his impact on contemporary mathematical analysis.