Niels Henrik Abel (1802-29), Norwegian mathematician, who was the first to demonstrate conclusively the impossibility of solving by the elementary processes of algebra general equations of any degree higher than the fourth. Abel was born on Finnøya Island, Rogaland County. After study at the University of Christiania (now Oslo), he spent two years in Paris and Berlin and in 1828 was made instructor at the university and military school in Christiania. His chief contributions were to the theory of functions, of which he was a founder. An important class of transcendental functions is known as Abelian, after their discoverer, as are Abelian equations, groups, and bodies. The binomial theorem had been formulated by Sir Isaac Newton and the Swiss mathematician Leonhard Euler, but Abel gave it a more comprehensive generalization, including the cases of irrational and imaginary exponents.