106 4. WOMEN MATHEMATICIANS4.5. What were the advantages and disadvantages of marriage for a woman seeking
an academic career before the twentieth century? How much of this depended on
the particular choice of a husband at each stage of the career? The cases of Mary
Somerville, Sof'ya Kovalevskaya, and Grace Chisholm Young will be illuminating,
but it will be useful to seek more detailed sources than the narratives above.4.6. How big a part did chance play in the careers of the early women mathemati-
cians? (The word chance is used advisedly, rather than luck, since the opportunities
that came for Sof'ya Kovalevskaya and Anna Johnson Pell Wheeler were the result
of tragic misfortunes to their husbands.)4.7. How important is (or was) encouragement from family and friends in the
decision to study science? How important is it to have a mentor, an established
professional in the same field, to help orient early career decisions? How important
is it for a young woman to have an older woman as a role model? Try to answer these
questions along a scale from "not at all important" through "somewhat important"
and "very important" to "essential." Use the examples of the women whose careers
are sketched above to support your rankings.4.8. Why were most of the women who received the first doctoral degrees in math-
ematics at German universities foreigners? Why were there no Germans among
them? In his lectures on the development of nineteenth-century mathematics (1926,
Vol. 1, p. 284), Klein mentions that a 17-year-old woman named Dorothea Schlozer
(apparently German, to judge by the name) had received a doctorate in economics
at Gottingen a full century earlier.4.9. How strong are the "facts" that Loria adduces in his argument against admit-
ting women to universities? Were all the women discussed here encouraged by their
families when they were young? Is it really true that it is impossible to "fix with
precision" the original contributions of Sophie Germain and Sof'ya Kovalevskaya?
You may wish to consult biographies of these women in which their correspondence
is discussed. Would collaboration with other mathematicians make it impossible
to "fix with precision" the work of any male mathematicians? Consider also the
case of Charlotte Angas Scott and others. Is it true that they were exhausted after
finishing their education?
Next, consider what we may call the "honor student" fallacy. Universities select
the top students in high school classes for admission, so that a student who excelled
the other students in high school might be able at best to equal the other students
at a university. Further selections for graduate school, then for hiring at universities
of various levels of prestige, then for academic honors, provide layer after layer of
filtering. Except for an extremely tiny elite, those who were at the top at one stage
find themselves in the middle at the next and eventually reach (what is ideally) a
level commensurate with their talent. What conclusions could be justified in regard
to any gender link in this universal process, based on a sample of fewer than five
women? And how can Loria be sure he knows their proper level when all the women
up to the time of writing were systematically locked out of the best opportunities
for professional advancement? Look at the twentieth century and see what becomes
of Loria's argument that women never reach the top.
Finally, examine Loria's logic in the light of the cold facts of society: A woman
who wished to have a career in mathematics would naturally be well advised to find
a mentor with a well-established reputation, as Charlotte Angas Scott and Sof'ya