MacTutor
Sofia Kovalevskaya
Leigh Ellison
Professorship and Mittag-Leffler
Following his first meeting with Sofia in 1876, Gösta Mittag-Leffler said of Sofia that, I understand perfectly why Weierstrass regards her as the most talented of his students. It was the fact that he held her in such high regard which made him determined to find a suitable position for her. During his time at the University of Hilsingfors he had tried to find a place for her on the faculty yet was unsuccessful not due to the fact that she was a woman, but due to the fact that she was Russian with what those in charge of the institution regarded as radical beliefs. On taking up his place as the head of mathematics at the recently founded Stockholm University however, he was to find himself in a position where he could actually offer her a job. From the very beginning Stockholm University offered great academic freedoms to those students in attendance. Classes were open to both sexes, and there were no examinations until a student decided that they wished to sit for a degree. Mittag-Leffler was to use his considerable diplomatic and organisational skills to offer Sofia a temporary position before those who opposed such a move had the chance to gather their forces. She readily accepted this position as a sub-professor without pay or official affiliation to the university, and hoped that by doing so she would open up the profession to women throughout Europe.
Sophia wrote to Mittag-Leffler at around this time that, Weierstrass is much more anxious than I for my appointment. It is certainly true that he wanted to see her flourish in her role as a mathematician and that this was what they both felt should be the next step on her path. He did however urge her to take the time to prepare properly for her new role knowing that her work would be subject to far more rigorous scrutiny than that of her male counterparts. Her arrival in Stockholm was thus delayed until November 1883, when her appointment made the front page of the newspapers.
During the early months of her time in Sweden, Sofia stayed with Mittag-Leffler and his sister Anna Carlotta who was a fairly well-known author of feminist literature. Sofia's friendship with Anna would later lead to a literary collaboration between the two on a play which was to be called The Struggle for Happiness.
Sofia was greatly awed by this new position which she would take up on the 1stof January, 1884, although she would not teach her first lecture until the end of the month. She was greatly awed by her new post, and was determined that her example should open up work in such institutions to women across Europe. The usually confident Sofia did have moments where her confidence left her prior to beginning her work in Stockholm however, writing to Mittag-Leffler that, I begin to doubt myself . These doubts led Sofia to once again seek the council of her most trusted advisor. In a letter which saw Sofia asking Weierstrass for his opinion as to what area of mathematics she should base her lectures on she wrote,
It was decided that Sofia would begin lecturing on the theory of partial differential equations, and it was clear from the outset that she had the qualities necessary of a fine lecturer. As she did not receive a salary from the university, she had to rely on the generosity of her students who would pay her by private arrangement. During the course of her stay in Stockholm she was to teach courses which covered many of the latest topics in analysis including the theory of the theta function, the theory of elliptic functions and the application of analysis to the theory of whole numbers.
Mittag-Leffler was an impressive man who was not only intensely loyal to those he cared about, but was willing to go to great lengths to overcome any obstacles which prevented him from achieving his goals. Mathematically speaking he dedicated himself to the study of analytic functions. This meant that he and Sofia were working in different fields, yet the influence of Weierstrass on his work was just as obvious as it was on Sofia's. It was even said of their correspondence with their former teacher that, Sometimes one gets the impression that the two friends orbit Weierstrass as two planets orbiting the sun. Both allowed themselves to be guided by Weierstrass, which proved to be a wise decision as there were few people more shrewd than he when it came to the politics of academic life. Mittag-Leffler himself was also gifted in this area, and whilst he was undoubtedly a gifted mathematician, his ability to organise and compromise when necessary were his real gifts.
Further proof of the Swedish man's energy was the founding of the incredibly successful mathematical journal Acta Mathematica in 1882. Sofia immediately began collaborating with Mittag-Leffler as an editor of the journal, and in doing so set yet another precedent by becoming the first woman on the board of a major scientific journal. This work saw Sofia collaborating with the major mathematicians of both Europe and Russia in order to find articles for the journal which predominantly but not exclusively expressed the ideas of the German tendency in mathematics which of course Sofia was one of the main subscribers to. She could be relied upon to procure good papers in order to help establish the reputation of the new journal. Mittag-Leffler was also responsible for introducing Sofia to Charles Hermite who was to become a close friend, and who introduced her to the other prominent mathematicians of France at that time.
Sofia felt both lonely and stifled while in Stockholm, saying of the city that, everything about everybody is known immediately and every little incident takes on the proportions of a world event. She felt that she lacked the inspiration of other gifted people when in Sweden, yet she was to do some of her best work during this period. She could hardly have asked for a better sounding board than Mittag-Leffler, who as a fellow student of Weierstrass thought about mathematics in a very similar way to Sofia.
In 1884, despite facing a great deal of opposition due to her sex, nationality and political beliefs, Mittag-Leffler managed to obtain for Sofia a five year post as a professor in ordinary. To her delight she would receive a salary for this position which was much needed due to the fact that she was still having to pay off the debts which Vladimir had accumulated prior to his death. She was also to fill in as a professor of mechanics in 1885 when an illness meant that the position could not be filled.
Sofia was undoubtedly grateful to Mittag-Leffler for all that he had done to assist her, saying in a letter to him that, I shall never be able to express or show all the gratitude and friendship I feel for you. He risked his own reputation on numerous occasions over the years simply by being such a staunch supporter of Sofia and her work. She did not always go about showing her gratitude in the best possible way however, as she made it clear on numerous occasions during the years which followed that if she was ever offered a position of similar stature in Russia, Germany or France then she would gladly leave Sweden.
In 1883 whilst doing her work on the refraction of light in a crystalline medium, Sofia became distracted by a problem which had always intrigued her. This work would lead to her finest moment in terms of her mathematical work, and cement her place in history as the finest female mathematician of her age. The problem which distracted her was that of the motion of a rigid body about a fixed point.
Prior to the work done by Sofia on the motion of a rigid body about a fixed point, the only solutions given to the problem by Leonhard Euler and J. L. Lagrange dealt with what happened when this body was symmetric. Euler had investigated the case when the centre of mass is fixed within the body and it is subjected to no external forces, while Lagrange had investigated the case where both the fixed point and the centre of gravity lie on the axis of symmetry of the body. It was not until Sofia set her mind to it however that any real solutions were found for the much more difficult case of an unsymmetrical top.
Sophia wrote to Mittag-Leffler at around this time that, Weierstrass is much more anxious than I for my appointment. It is certainly true that he wanted to see her flourish in her role as a mathematician and that this was what they both felt should be the next step on her path. He did however urge her to take the time to prepare properly for her new role knowing that her work would be subject to far more rigorous scrutiny than that of her male counterparts. Her arrival in Stockholm was thus delayed until November 1883, when her appointment made the front page of the newspapers.
During the early months of her time in Sweden, Sofia stayed with Mittag-Leffler and his sister Anna Carlotta who was a fairly well-known author of feminist literature. Sofia's friendship with Anna would later lead to a literary collaboration between the two on a play which was to be called The Struggle for Happiness.
Sofia was greatly awed by this new position which she would take up on the 1stof January, 1884, although she would not teach her first lecture until the end of the month. She was greatly awed by her new post, and was determined that her example should open up work in such institutions to women across Europe. The usually confident Sofia did have moments where her confidence left her prior to beginning her work in Stockholm however, writing to Mittag-Leffler that, I begin to doubt myself . These doubts led Sofia to once again seek the council of her most trusted advisor. In a letter which saw Sofia asking Weierstrass for his opinion as to what area of mathematics she should base her lectures on she wrote,
You, my supreme teacher, would not let your poor little bold student
drown without extending a hand to save her.
It was decided that Sofia would begin lecturing on the theory of partial differential equations, and it was clear from the outset that she had the qualities necessary of a fine lecturer. As she did not receive a salary from the university, she had to rely on the generosity of her students who would pay her by private arrangement. During the course of her stay in Stockholm she was to teach courses which covered many of the latest topics in analysis including the theory of the theta function, the theory of elliptic functions and the application of analysis to the theory of whole numbers.
Mittag-Leffler was an impressive man who was not only intensely loyal to those he cared about, but was willing to go to great lengths to overcome any obstacles which prevented him from achieving his goals. Mathematically speaking he dedicated himself to the study of analytic functions. This meant that he and Sofia were working in different fields, yet the influence of Weierstrass on his work was just as obvious as it was on Sofia's. It was even said of their correspondence with their former teacher that, Sometimes one gets the impression that the two friends orbit Weierstrass as two planets orbiting the sun. Both allowed themselves to be guided by Weierstrass, which proved to be a wise decision as there were few people more shrewd than he when it came to the politics of academic life. Mittag-Leffler himself was also gifted in this area, and whilst he was undoubtedly a gifted mathematician, his ability to organise and compromise when necessary were his real gifts.
Further proof of the Swedish man's energy was the founding of the incredibly successful mathematical journal Acta Mathematica in 1882. Sofia immediately began collaborating with Mittag-Leffler as an editor of the journal, and in doing so set yet another precedent by becoming the first woman on the board of a major scientific journal. This work saw Sofia collaborating with the major mathematicians of both Europe and Russia in order to find articles for the journal which predominantly but not exclusively expressed the ideas of the German tendency in mathematics which of course Sofia was one of the main subscribers to. She could be relied upon to procure good papers in order to help establish the reputation of the new journal. Mittag-Leffler was also responsible for introducing Sofia to Charles Hermite who was to become a close friend, and who introduced her to the other prominent mathematicians of France at that time.
Sofia felt both lonely and stifled while in Stockholm, saying of the city that, everything about everybody is known immediately and every little incident takes on the proportions of a world event. She felt that she lacked the inspiration of other gifted people when in Sweden, yet she was to do some of her best work during this period. She could hardly have asked for a better sounding board than Mittag-Leffler, who as a fellow student of Weierstrass thought about mathematics in a very similar way to Sofia.
In 1884, despite facing a great deal of opposition due to her sex, nationality and political beliefs, Mittag-Leffler managed to obtain for Sofia a five year post as a professor in ordinary. To her delight she would receive a salary for this position which was much needed due to the fact that she was still having to pay off the debts which Vladimir had accumulated prior to his death. She was also to fill in as a professor of mechanics in 1885 when an illness meant that the position could not be filled.
Sofia was undoubtedly grateful to Mittag-Leffler for all that he had done to assist her, saying in a letter to him that, I shall never be able to express or show all the gratitude and friendship I feel for you. He risked his own reputation on numerous occasions over the years simply by being such a staunch supporter of Sofia and her work. She did not always go about showing her gratitude in the best possible way however, as she made it clear on numerous occasions during the years which followed that if she was ever offered a position of similar stature in Russia, Germany or France then she would gladly leave Sweden.
In 1883 whilst doing her work on the refraction of light in a crystalline medium, Sofia became distracted by a problem which had always intrigued her. This work would lead to her finest moment in terms of her mathematical work, and cement her place in history as the finest female mathematician of her age. The problem which distracted her was that of the motion of a rigid body about a fixed point.
Prior to the work done by Sofia on the motion of a rigid body about a fixed point, the only solutions given to the problem by Leonhard Euler and J. L. Lagrange dealt with what happened when this body was symmetric. Euler had investigated the case when the centre of mass is fixed within the body and it is subjected to no external forces, while Lagrange had investigated the case where both the fixed point and the centre of gravity lie on the axis of symmetry of the body. It was not until Sofia set her mind to it however that any real solutions were found for the much more difficult case of an unsymmetrical top.