The History of Mathematics: A Brief Course

3. MODERN EUROPEAN WOMEN 89

philosopher-mathematician Alfred North Whitehead (1861-1947), who paid trib-

ute to her work in promoting a community of scholars, saying, "A life's work such

as that of Professor Charlotte Angas Scott is worth more to the world than many

anxious efforts of diplomatists. She is a great example of the universal brotherhood

of civilisations."

Charlotte Angas Scott retired from Bryn Mawr in 1924. The following year she

returned to Cambridge, where she lived the rest of her life. She died in 1931.

Sof 'ya Kovalevskaya. Most of the women discussed up to now came from a leisured

class of people with independent incomes. Only such people can afford both to defy

convention and to spend most of their time pursuing what interests them. However,

merely having an independent income was not in itself sufficient to draw a young

woman into a scientific career. In most cases, some contact with intellectual circles

was present as well. Hypatia was the daughter of a distinguished scholar, and Maria

Gaetana Agnesi's father encouraged her by hiring tutors to instruct her in classical

languages. In the case of Sof'ya Kovalevskaya, the urge to study mathematics and

science fused with her participation in the radical political and social movements

of her time, which looked to science as the engine of material progress and aimed

to establish a society in accordance with the ideals of democracy and socialism.

She was born Sof'ya Vasil'evna Kryukovskaya in Moscow, where her father was

an officer in the army, on January 15, 1850 (January 3 on the Julian calendar in

effect in the Russia of her day). As a child she looked with admiration on her older

sister Anna (1843-1887) and followed Anna's lead into radical political and social

activism. According to her Polish tutor, she showed talent for mathematics when

still in her early teens. She also showed great sympathy for the cause of Polish

independence during the rebellion of 1863, which was crushed by the Tsar's troops.

When she was 15, one of her neighbors, a physicist, was impressed upon discovering

that she had invented the rudiments of trigonometry all by herself in order to read

a book on optics; he urged her father to allow her to study more science. She

was allowed to study up through the beginnings of calculus with a private tutor

in Saint Petersburg, but matriculation at a Russian university did not appear to

be an option. Thinking that Western Europe was more enlightened in this regard,

many young Russian women used a variety of methods to travel abroad. Some were

able to persuade their parents to let them go. Others had to adopt more radical

means, either running away or arranging a fictitious marriage, in Sof'ya's case to

a young radical publisher named Vladimir Onufrevich Kovalevskii (1842-1883).

They were married in 1868 and soon after left for Vienna and Heidelberg, where

Kovalevskaya studied science and mathematics for a year without being allowed

to enroll in the university, before moving on to Berlin with recommendations from

her Heidelberg professors to meet the dominant influence on her professional life,

Karl Weierstrass (1815-1897). At Berlin also, the university would not accept her

as a regular student, but Weierstrass agreed to tutor her privately. (Comparisons

with the relationship between Charlotte Angas Scott and Arthur Cayley inevitably

come to mind here.)

Although the next four years were extremely stressful for a number of personal

reasons, her regular meetings with Weierstrass brought her knowledge of math-

ematical analysis up to the level of the very best students in the world (those

attending Weierstrass' lectures). By 1874, Weierstrass thought she had done more

than enough work for a degree and proposed throe of her papers as dissertations.