The History of Mathematics: A Brief Course

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  1. INDIVIDUAL ACHIEVEMENTS AND OBSTACLES TO ACHIEVEMENT 77


(^2) Kowalewski believed himself to be distantly related to Vladimir Kovalevskii, husband of Sof'ya
Kovalevskaya, but this connection has never been verified.
(^3) The kind of behavior exhibited by Roethe eventually disappeared, thanks in large part to the
efforts of the Prussian Kultusminister Friedrich Althoff (1839-1908), who had asked Felix Klein
(1854-1925) to be on the lookout for promising women students. In 1894, with AlthofT's approval,
Klein took Grace Chisholm Young as his student, and the doors of Gottingen University were
thereafter open to women. One of Althoff's last acts as Kultusminister was to unify the education
of boys and girls. Klein can be described as a liberal but not a radical, one who believed in equal
opportunity for women and even affirmative action to recruit women; but he insisted that only
women with demonstrated talent and background should be admitted to universities.


for conversation. The Marquise du Chatelet defied convention and went to cafes

anyway, dressed as a man. In the nineteenth century women were not allowed into

laboratories at some universities, so that Christine Ladd-Franklin (1847-1930) be-

came a mathematics major even though she would have preferred physics. After

writing a brilliant dissertation but being unable to obtain a degree, she turned to

the new profession of psychology, but even there was shut out of professional life. In

the twentieth century, when his colleagues were objecting to hiring Emmy Noether

at Gottingen, Hilbert is reported (Dick, 1981, p. 168; Mackay, 1991, p. 117) to have

ridiculed their objections, saying, "The Senate is not a locker room; why shouldn't

a woman go there?" As our narrative proceeds, the same three institutions the

University of London, Bryn Mawr College, and the University of Gottingen will

appear repeatedly, showing how few opportunities there were for women to pursue

advanced studies in mathematics until quite recently.

The situation in the early twentieth century was described by the mathemati-

cian Gerhard Kowalewski (1876-1950) in his memoirs:^2

At that time [1905] the first women students began to appear at

the University of Bonn. They were still being met with harsh rejec-

tion on the part of distinguished professors at other universities,

for example, Berlin, where Gustav Roethe, if he caught sight of

women in the auditorium, simply refused to begin his lecture until

they left the room.^3 People were not so narrow-minded at Bonn.

The women students formed a Society and arranged balls to which

they invited their professors. There was a whole series of talented

women mathematicians. Many of them took the state examina-

tion under my supervision: [among them was] Maria Vaerting, who

later became a famous novelist and whose first novel.. .was based

on her student days... At the same time she was working on a very

difficult topic for a doctoral dissertation under my direction. In

the end, however, she didn't receive the doctorate as my student,

since I was called to Prague. She then moved to Giessen, where

her work was accepted by Professor Pasch. [Kowalewski, 1950, pp.

206-207]

Discouragement from family, friends, and society in general. We do not know what

attitudes were faced by the very earliest women mathematicians, but from the eigh-

teenth century on there are many documented cases of family opposition to such a

career; particularly good examples are Sophie Germain and Sof'ya Kovalevskaya,

both of whom had to go to extraordinary lengths to participate in the mathemat-

ical community. (Kovalevskaya was fortunate in being able eventually to win her
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