Mittag-Leffler avait fait la connaissance de Kovalevskaia en 1876 lors d’un voyage en Russie. Dans leur correspondance, Weierstrass et lui échangent souvent de ses nouvelles. Dans son article sur la carrière de Kovalevskaia à Stockholm, Hörmander évoque les débuts de l’amitié entre elle et Mittag-Leffler :
After receiving his doctorate in Uppsala in 1872, Gösta Mittag-Leffler spent the years 1873–1876 studying in Germany and France. He made many lasting friendships during this period, and in particular he became a devoted student and admirer of Karl Weierstrass in Berlin. It made a great impression on him to hear Weierstrass talk about Sonja Kovalevsky as his best student ever. After four years of study with Weierstrass, she had returned to Russia in 1874 and it was there that Mittag-Leffler met her in 1876. In a letter […], he described this encounter: “Ce qui m’a le plus vivement intéressé à St. Petersbourg, a été de faire la connaissance de Madame Kowalewsky. Aujourd’hui (10 février 1876), j’ai passé quelques heures chez elle. Comme femme, elle est délicieuse. Elle est belle et, quand elle parle, son visage s’éclaire d’une expression de bonté féminine et d’intelligence supérieure qu’on ne soutient pas sans éblouissement. Ses manières sont simples et naturelles, sans aucune trace de pédantisme ou de savoir affecté. Du reste, en tous points ‘dame du monde’. Comme savante, elle se distingue par une clarté et par une précision d’expression peu commune, ainsi que par une conception singulièrement prompte. On s’aperçoit aisément aussi du degré de profondeur où elle a poussé ses études, et je comprends parfaitement que Weierstrass la regarde comme le mieux doué de ses disciples.” Shortly afterwards Mittag-Leffler became a professor at Helsingfors University. He tried to arrange a position for Sonja Kovalevsky there but ran into opposition. The Finns were worried that as a Russian nihilist she would foment revolutionary ideas and so provoke the Russians controlling Finland at that time. However, Mittag-Leffler did not give up. After moving to Stockholm in 1881 as the first professor at the new university there, he renewed his efforts on her behalf. Already in June 1881, he wrote in a letter […]: “As far I am concerned, I shall be extremely happy if I have a chance to invite you to Stockholm as a colleague, and I do no doubt that with you in Stockholm our faculty will be one of the most advanced in the mathematical world.” After the death of Sonja Kovalevsky’s husband Vladimir in 1883, it was finally arranged that Sonja would come to Stockholm as docent. (Hörmander (1991, 196))
Gösta Mittag-Leffler à Henri Poincaré - 28 août 1884