**Gösta Mittag-Leffler** was a Swedish mathematician who worked on the general theory of functions. His best known work concerned the analytic representation of a one-valued function.

- It was not until Gösta Leffler was a twenty year old student that he decided to add "Mittag" to his name.
- It was clear from his later life that Mittag-Leffler had many talents in addition to his mathematics and it was his upbringing that did much to foster these talents.
- Mittag-Leffler trained as an actuary but later took up mathematics.
- As a result Mittag-Leffler was appointed as a Docent at the University of Uppsala in 1872.
- In October 1873 Mittag-Leffler set off for Paris.
- Although Mittag-Leffler met many mathematicians in Paris, such as Bouquet, Briot, Chasles, Darboux, and Liouville, the main aim of the visit was to learn from Hermite.
- Mittag-Leffler attended Hermite's lectures on elliptic functions but found them hard going.
- Certainly Hermite spoke in glowing terms about Weierstrass and the contributions he and other German mathematicians were making, so Mittag-Leffler made a decision to go to Berlin in the spring of 1875.
- There he attended Weierstrass's lectures which proved to be extremely influential in setting the direction of Mittag-Leffler's subsequent mathematical work.
- We have quoted extensively from Mittag-Leffler's writing about this overseas trip and his reaction to national rivalries.
- We have done so because it is important in determining the international role which Mittag-Leffler went on to play, for his passion for international cooperation in mathematics was a direct consequence of what he saw on his three year trip abroad.
- Mittag-Leffler was appointed to a chair at the University of Helsinki in 1876 and, five years later, he returned to his home town of Stockholm to take up a chair at the University.
- Mittag-Leffler made numerous contributions to mathematical analysis particularly in areas concerned with limits and including calculus, analytic geometry and probability theory.
- His best known work concerned the analytic representation of a one-valued function, this work culminated in the Mittag-Leffler theorem.
- Mittag-Leffler tried to generalise this result to meromorphic function while he was studying in Berlin.
- Mittag-Leffler became the sole proprietor of a theorem that later became widely known and with this he took his place in the circle of internationally known mathematicians.
- Mittag-Leffler was one of the first mathematicians to support Cantor's theory of sets but, one has to remark, a consequence of this was that Kronecker refused to publish in Acta Mathematica .
- Between 1900 and 1905 Mittag-Leffler published a series of five papers which he called "Notes" on the summation of divergent series.
- The region in which he was able to do this is now called Mittag-Leffler's star.
- In 1882 Mittag-Leffler founded Acta Mathematica and served as chief editor of the journal for 45 years.
- It required an international base and certainly Mittag-Leffler fully understood this.
- Mittag-Leffler was always a good judge of the quality of the work submitted to him for publication.
- In 1884, the year Mittag-Leffler published his masterpiece, Kovalevskaya arrived in Stockholm at his invitation.
- there Mittag-Leffler appeared at his best, a most entertaining mixture of the great international mathematician and the rather naive country squire.
- However, eventually the Mittag-Leffler Institute was set up based on the house and today is a major mathematical research centre.
- Mittag-Leffler received many honours.

Born 16 March 1846, Stockholm, Sweden. Died 7 July 1927, Stockholm, Sweden.

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Origin Sweden, Set Theory

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive