|Sofia Kovalevskaya||MacTutor Index|
(The Lamé Equations)
It was during this period when her life was lacking any real focus that she and Vladimir, took the momentous decision to end the charade of their fictitious marriage by consummating it.40 It has been suggested by Don H. Kennedy that this decision was due to the fact that, She no longer needed to fear pregnancy as a hindrance to study or a career.41 It is also possible that she realised that she was wasting her intellectual gifts and was seeking some sort of distraction from this thought in the form of attempting to have a more normal life. She nevertheless did become bored by the frivolity of her life, as well as, appalled at her mental stagnation.42
In August of 1878, Sofia contacted Weierstrass for the first time in three years, and he was thrilled to hear from her. He had tried to engage her in mathematical activity on numerous occasions during her hiatus by posing problems for her, and by sending one of his pupils by the name of Gösta Mittag-Leffler to check on her in 1876, but it had all been to no avail. He even wrote to her somewhat pleadingly his opinion that, we should never have been separated. 43 It was not until she herself became convinced that, only a life of productive mathematical work could [satisfy her], 44 that she could be lured out of her mathematical slumber. Weierstrass had been deeply hurt by her neglect of their relationship, but said to Sofia that his only regret was that, her long silence has deprived him of the opportunity of helping her.45 The full resumption of their correspondence was delayed until 1880 however, with Sofia having discovered that at the age of twenty-eight she was pregnant. He had managed to bring her up to date with his work on periodic functions and the theory of partial differential equations.
In October of 1878 Sofia gave birth to a daughter who was named Sofia but nicknamed Fufa to prevent any confusion with her mother. Sofia would later say that,
her daughter was the only good thing to come out of her five-year hiatus in mathematical activity.46
Following Fufa's birth relations between Sofia and Vladimir were never again close. The death of Sofia's mother in 1879 was quickly followed by the collapse of the construction empire which the couple had invested much of their money in. This did not deter Vladimir from borrowing more money though, and it is clear that from this time onwards his mental health began to deteriorate quite rapidly. These financial worries made Sofia even more determined than ever to reintegrate herself into the mathematical community. This return was greatly encouraged when Sofia was asked by Chebyshev to present a paper at the Congress of Russian Naturalists and Physicians. She translated her unpublished dissertation on Abelian integrals, and her talk was met with a great deal of praise. Amongst those in attendance was Mittag-Leffler, who was even more impressed with Sofia than when he had first met her four years earlier. It was on this day that he vowed to find a suitable teaching position for her at a European university.
With no suitable academic positions open to her, Sofia made a decision to prepare as many mathematical papers as possible so that if a viable position ever did come up for her, she would be in a stronger position. As a result she went to see the man whose guidance she knew she could rely upon. Weierstrass felt that having just had such a long break from intense mathematical work, she should ease herself back in by working on a concrete problem. He suggested that she investigate the refraction of light in a crystalline medium. This investigation was to become almost a fourth dissertation, and in mid-1881 she settled down to working on the set of equations derived by Lamé to describe the displacement of a particle in an elastic medium. Her work on this topic shall be looked at later, but was not of huge interest to Sofia. It was to emerge years later that her work was flawed, but it served its purpose by once again allowing Sofia to immerse herself in the world of mathematics.
(The Lamé Equations)