Fredholm, Erik Ivar (1866–1927)

Swedish mathematician and mathematical physicist. He founded the modern theory of integral equations (see integral calculus) and his work provided the foundations for much of the research later carried out by German mathematician David Hilbert.

Fredholm founded much of his theory on work carried out by US astronomer George Hill (1838–1914), who used linear equations involving determinants of an infinite number of rows and columns. In Fredholm's paper ‘Sur une nouvelle méthode pour la résolution du problème de Dirichlet’ (1900), he first developed the essential part of the theory of what is now known as Fredholm's integral equation; further, he went on to define and solve the Fredholm equation of the second type, involving a definite integral. Fredholm discovered in 1900–03 the algebraic analogue of his own theory of integral equations. His results were used by Hilbert, who extended them in deriving his own theories, which contributed fundamentally towards quantum theory.

Fredholm was born in Stockholm and studied at the Polytechnic Institute there, and at the University of Uppsala. He became professor at Stockholm University in 1906.