Ivar Fredholm

Background

Ivar Fredholm was born on April 7, 1866, in Stockholm, Sweden. Fredholm was born into an upper-middle-class family. His father was a wealthy merchant and his mother, née Stenberg, was from a cultured family.

Education

In 1886 Fredholm enrolled at the University of Uppsala - the only institution in Sweden granting doctorates at that time - from which he received the Bachelor of Science in 1888 and the Doctor of Science in 1898.

Career

Fredholm was docent at Stockholm University from 1898 to 1906 and professor from 1906 until his death. He also held various other positions, becoming a civil servant in 1899 and then a Head of Department for the Swedish State Insurance Company in 1902. He was an actuary in the Skandia Insurance Company from 1904 to 1907. Fredholm also served on many government committees and he also served on the International Committee for Weights and Measures.

Fredholm's first publication came in 1890 when he published On a special class of functions in the Royal Swedish Academy of Sciences. In this paper he constructed a function which is analytic on the unit disk, is infinitely differentiable on the closed disk, but has no analytic continuation outside the disk. As was always the case with all the deep mathematical results which Fredholm produced, this result was inspired by mathematical physics, in this case by the heat equation. The result went further than earlier examples by Mittag-Leffler and Weierstrass. It so impressed Mittag-Leffler that he sent a copy of the paper to Poincaré.

Fredholm's doctoral dissertation involved a study of partial differential equations, the study of which was motivated by an equilibrium problem in elasticity. He solved his operator equation in the particular cases which arise in the study of the physical problem in his thesis, while the general case was solved by Fredholm somewhat later and not published until 1908. Fredholm is best remembered for his work on integral equations and spectral theory. In fact much of this work was accomplished during the months of 1899 which Fredholm spent in Paris. In 1900 a preliminary report on his theory of Fredholm integral equations was published as Sur une nouvelle méthode pour la résolution du problème de Dirichlet. Volterra had earlier studied some aspects of integral equations but before Fredholm little had been done. Of course Riemann, Schwarz, Carl Neumann, and Poincaré had all solved problems which now came under Fredholm's general case of an integral equation; this was an indication of how powerful his theory was.

Fredholm's contributions quickly became well known to the world of mathematics when Holmgren lectured on Fredholm's theory at Göttingen in 1901. Hilbert immediately saw the importance of Fredholm's theory, and during the first quarter of the 20th century the theory of integral equations became a major research topic. Fredholm published a fuller version of his theory of integral equations in Sur une classe d'équations fonctionelle, which appeared in Acta Mathematica in 1903. Hilbert extended Fredholm's work to include a complete eigenvalue theory for the Fredholm integral equation. This work led directly to the theory of Hilbert spaces.

Fredholm wrote papers with great care and attention so he produced work of high quality which quickly gained him a high reputation throughout Europe. However his papers required so much effort from him that he wrote only a few and in fact his Complete Works in mathematics comprises of only 160 pages. After 1910 he wrote little beyond revisiting his earlier work.

Achievements

• Ivar Fredholm was an outstanding mathematician, who introduced and analysed a class of integral equations now called Fredholm equations. His analysis included the construction of Fredholm determinants, and the proof of the Fredholm theorems. He was awarded the Poncelet Prize in 1908 and the Björkénska priset in 1910. The lunar crater Fredholm is named after him.

Works

More photos

• book

  • Oeuvres Completes 1955

Membership

Fredholm was a member of the Finnish Society of Sciences and Letters, the Accademia dei Lincei, and of the Royal Swedish Academy of Sciences.

Personality

Fredholm was also a musician and for him this was more than just a leisure activity. As a young boy he played the flute, but later took up playing the violin. He particularly loved to play Bach. Again he combined his talents, applying his mechanical skills to music as well as to mathematics. Unlikely as it sounds, he built his first violin from half a coconut, while he also used his talents at building machines to make one to solve differential equations.

Interests

• Music & Bands

  Johann Sebastian Bach

Connections

Fredholm was married to Agnes Maria Liljeblad, the secretary of Mittag-Leffler.

Father:

Ludvig Oscar Fredholm

Mother:

Catharina Paulina Stenberg Fredholm

Spouse:

Agnes Maria Fredholm

Son:

Bengt Ivar Fredholm

References

• Dictionary of Scientific Biography