92 4. WOMEN MATHEMATICIANS
(1804 1851). All she had to do was reduce the equations of motion to integrals;
evaluating them was within her power, she knew. Unfortunately, it turns out that
the completely general set of such equations cannot be reduced to integrals. But
Kovalevskaya found a new case, much more general than the cases already known,
in which this reduction was possible. The algebraic changes of variable by which
she made this reduction are quite impressive, spread over some 16 pages of one of
the papers she eventually published on this subject. Still more impressive is the
80-page argument that follows to evaluate these integrals, which turn out to be
hyperelliptic, involving the square root of a fifth-degree polynomial. This work so
impressed the leading mathematicians of Paris that they decided the time had come
to propose a contest for work in this area. When the contest was held in 1888, Ko-
valevskaya submitted a paper and was awarded the prize. She had finally reached
the top of her profession and was rewarded with a tenured position in Stockholm.
Sadly, she was not to be in that lofty position for long. In January 1891 she con-
tracted pneumonia while returning to Stockholm from a winter vacation in Italy
and died on February 10.
Bronze bust of Sof'ya Kovalevskaya, placed outside the Institut
Mittag-Leffler in Djursholm, Sweden on January 15, 2000, the
150th anniversary of her birth.
