Magnus Gustaf (Gösta) Mittag-Leffler was a famous Swedish mathematician, one of the best of his era. He was born in Stockholm on 16 March 1846. He studied at Uppsala University, where he completed his PhD in 1872. He became a docent at the University the same year. In 1873 Mittag-Leffler went to Paris to learn from Hermite, and where he met many mathematicians (Bouquet, Briot, Chasles, Darboux, Liouville). In 1875 he went to Berlin where he attended Weierstrass's lectures. The mathematical work of Mittag-Leffler was much influenced by the work of Weierstrasse. He took a position of professor of mathematics at the University of Helsinki 1877–1881, and then a first professor of mathematics at the University College of Stockholm (Stockholm University). He was a member of the Royal Swedish Academy of Sciences (1883), the Finnish Society of Sciences and Letters (1878, later honorary member), the Royal Swedish Society of Sciences in Uppsala, the Royal Physiographic Society in Lund (1906) and others (the Royal Society of London,   Académie des sciences in Paris). He held honorary doctorates from the University of Oxford and several other universities. He attracted many students which became famous mathematicians, such as Edvard Phragmén, Ivar Bendixson, Helge von Koch, Ivar Fredholm. Mittag-Leffler founded the famous mathematical journal Acta Mathematica (1882), which is still one of the most prestigious mathematical journals in the world, serving as chief editor of the journal for 45 years. The famous Russian female mathematician Sofia Kovalevskaya became a full professor of mathematics in Stockholm much by help of Mittag-Leffler, becoming the first woman anywhere in the world to hold that position. Mittag-Leffler died at 7 July 1927.

There is a legend which is not supported by historical evidence that Alfred Nobel did not set up a prize in Mathematics because Mittag-Leffler had ran off with Nobel’s wife.

Mittag-Leffler made numerous contributions to mathematical analysis, analytic geometry and probability theory. His best known work concerned the analytic representation of a one-valued function culminated in the Mittag-Leffler theorem. He generalized Weierstrass's theorem to meromorphic functions, proposing a series of general topological notions on infinite point sets based on Cantor's new set theory.

In the period from 1900 to 1905 Mittag-Leffler published a series of five papers ("Notes") on the summation of divergent series. The aim of these notes was to construct the analytical continuation of a power series outside its circle of convergence. The region in which he was able to do this is now called Mittag-Leffler's star.

He introduced the following function (today known as the Mittag-Leffler function):

which is a generalization of the exponential function; E₁(z)=e^z. This function and its generalizations (which are introduced later) appear as solutions of fractional differential equations, becoming a very useful tool for modeling anomalous diffusive processes.

Trifce Sandev

Radiation Safety Directorate, Republic of Macedonia

This e-mail address is being protected from spambots. You need JavaScript enabled to view it