Erik Ivar Fredholm | Biography

Erik Ivar Fredholm developed the modern theory of integral equations. His work served as the foundation for later critical research performed by David Hilbert, and several concepts and theorems are attributed to him. Fredholm was born on April 7, 1866, in Stockholm, Sweden. His family was upper-middle-class; his father was a well-to-do merchant, and his mother came from a cultured background. He was privy to the highest quality education available in his country and proved gifted. In 1885 he began studies at the Polytechnic Institute in Stockholm, where he developed what turned out to be a lifelong interest in problems of practical mechanics. He remained at the Institute for only one year and enrolled in the University of Uppsala in 1886, receiving his bachelor's degree in 1888.

Fredholm received his doctorate from Uppsala in 1898, although he conducted the bulk of his studies under Mittag-Leffler at the University of Stockholm. At that time, Uppsala was the only university in Sweden that offered a doctoral degree. Fredholm conducted his doctoral thesis on partial differential equations, and his work became significant to the study of deformation of anisotropic media, such as crystals.

After receiving his doctoral degree Fredholm accepted a position as lecturer in mathematical physics at the University of Stockholm and in 1906 became a professor of rational mechanics and mathematical physics. The research he conducted during this time yielded a fundamental integral equation that now bears his name. The equation, which is highly relevant in physics, was contained in a seminal research paper for which Fredholm was honored with the Wallmark Prize of the Swedish Academy of Sciences and the Poncelet Prize of the Academie des Sciences.

Much of Fredholm's research on integral equations was based on the work of American astronomer George William Hill. Fredholm laid the foundation for this renowned research in a 1900 paper, Sur une nouvelle methode pour la resolution du problèm de Dirichlet. It was in this paper that Fredholm developed the essential component of the theory that led to what is now called Fredholm's Integral Equation. Fredholm then went on to develop what came to be known as the Fredholm Equation of the Second Type, which involved a definite integral. He also discovered the algebraic analog of his theory of integral equations. While Fredholm's contributions to mathematics and physics were significant, his research resume is sparse. Biographers attribute his small output to the mathematician's strict attention to detail, a characteristic that earned Fredholm an excellent reputation throughout Europe.

Fredholm's work was carried on by David Hilbert, who learned of Fredholm's work through Erik Holmgren, a colleague of Fredholm's whom Hilbert met in Göttingen. Hilbert incorporated Fredholm's ideas into his own theories, including the theory of eigen-values and the theory of spaces involving an infinite number of dimensions. These theories, in turn, laid the foundation for the study of quantum theory and the discovery of what are now termed Hilbert spaces.

Fredholm remained at the University of Stockholm until his death on August 17, 1927.