Supervisor:
Dr. W. Böhm
Working title: From Hypatia to Emmy Noether and beyond:
Women in Mathematics
Keywords:
History of mathematics
Description.
On August 12, 2014 The New York Times headlined: Top Math Prize Has Its
First Female Winner, and one day later The Guardian followed with: Fields
Medal mathematics prize won by woman for first time in its history!
Indeed, these were exciting news. Maryam Mirzakhani, who was born and
raised in Iran, has been awarded the highest honor a mathematician can attain,
the Fields Medal. It is the world’s most prestigious mathematics prize and
for the first time since the award was established nearly 80 years ago it was
awarded to a woman.
The New York Times commented on this occasion: While women have reached
parity in many academic fields, mathematics is still dominated by men, who earn
about 70 percent of the doctoral degrees. The disparity is even more striking
at the highest echelons. Since 2003, the Norwegian Academy of Science and
Letters has awarded the Abel Prize, recognizing outstanding mathematicians
with a monetary award of about $ 1 million; all 14 recipients so far are men.
No woman has won the Wolf Prize in Mathematics, another prestigious award.
Emmy Noether (1882-1935) is an impressing example of the problems women
were facing when they pursued a career as academic mathematicians. Noether
was invited by Felix Klein and David Hilbert to the University of Göttingen.
But although being an outstanding and extremely prolific mathematical talent,
she was not allowed to get the venia docendi, i.e., become a docent with the
right to hold lectures at a university. Members of the faculty argued against
Noether, that being a docent she will also give examinations and it may happen,
that male students may fail such an exam. Incredible, a man failing an exam
held by a woman! It is reported that David Hilbert replied angrily: Aber meine
Herren, eine Universität ist doch keine Badeanstalt! As a result Emmy Noether
had to announce and hold her lectures under the name of David Hilbert. In
April 1933 she was expelled from Göttingen University by Nazi authorities,
emigrated to the United States and got a poorly paid teaching position at Bryn
Mawr College. Only two years later she died at an age of 53 years.
There are many other impressing examples of female mathematicians, just to
mention a few: Hilda Geiringer (1893-1973), the first woman getting a doctor’s
degree at University of Vienna in 1917. Her biography would be perfect material for a novel or a film. By the way, Hilda Geiringer spent also some time
at Bryn Mawr College. Or, Olga Taussky-Todd (1906-1995), who became a
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torchbearer for matrix theory. And there are many other extraordinary female
mathematicians. We find them though sporadically in all epochs, from ancient
times to our days. An ancient example is Hypatia of Alexandria (around 350 415 AD), an example from 18th century is Maria Gaetana Agnesi (1718 - 1799),
and a really remarkable women is certainly Sofia (Sonya) Kovalevskaya (1850 1891).
The lives of these and other women were often tragic, her achievements remarkable and outstanding even more when we recognize the difficulties and social
and academic opposition they had to overcome. But, fortunately, times are
changing and today more and more female mathematicians are fully respected
in academic and non-academic society.
Your Job.
Let me first tell you what I do not want: I will not accept an unsophisticated
collage of biographical sketches composed by cut and paste from various internet
resources.
Although the topic of this thesis is certainly located in the field of history of
mathematics, it lies at the frontier to other disciplines, in particular to sociology
of science. This is an important point regarding methodology.
So, what I want is this:
• A serious discussion of the role of women in mathematics. You should
work out clearly how the social perception of this question changed over
time, in particular since World War II.
• Find out important facts about the social backgrounds of female mathematicians. What about their families, their parents? Who discovered
their mathematical talents, who were their mentors? Find similarities
and explain them.
• Reputation of a professional mathematician is usually strongly connected to academic positions. A good indicator are renown professorships held by women. For example Alice Chang is Eugene Higgins
Professor of Mathematics at Princeton University since 1998. Another
indicator are prizes and awards like the Fields Medal ot the Abel Prize.
• And what about a very common problem women are facing when pursuing careers (not only in mathematics): how do they manage to combine
her carreer with family, with motherhood?
• Are there areas of mathematics preferred by women, like the theory of
numbers, differential geometry, statistics?
• Elaborate on the New York Times-comment above about disparity between male and female mathematicians.
• Your argumentation should also be supported by empirical analysis.
Thus you will have to collect data and analyze them.
Regarding style: this topic is in a certain sense non-mathematical which does
not mean that it is trivial from a methodological point of view. Indeed, this
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thesis does require a clear and elaborate methodological approach. So, suppose
you are a young journalist and this is your first chance at a reknown scientific
magazine. The editor-in-chief tells you: this is your topic, write a good story
about women in mathematics.
References.
Here are two books you may find interesting:
[1] Lynn M. Osen, (1975), Women in Mathematics, MIT Press.
Unfortunately this book is somewhat outdated, but still a very interesting and easyto-read text.
[2] Carl B. Boyer, Uta C. Merzbach, (2011), A History of Mathematics, John
Wiley & Sons.
This is the classical book about history of mathematics.
There are many interesting places in the internet, here are a few which I found
interesting:
• Biographies of Women Mathematicians is a webpage maintained at
Agnes Scott College, Atlanta, Georgia.
• The IAS School of Mathematics at Princeton University has a very good
page entitled Women in Mathematics.
• Smith College in Northampton, Massachusetts, is one of the biggest and
most reknown women’s collages all over the world. It has a Center for
Women in Mathematics which is part of the Department of Mathematics and Statistics.
• The Canadian Mathematical Society has a very well organized page
Resources for Women in Mathematics.
• Peter Roquette, (2008) Emmy Nother and Hermann Weyl, available at
http://www.rzuser.uni-heidelberg.de/ ci3/weyl+noether.pdf is
an interesting article. It contains also Weyl’s poignant funeral speech
for Emmy Noether on April 18, 1935.
• Last but not least: the MacTutor History of Mathematics Archive at
the University of St. Andrews.
The Procedure.
• If you are interested in this topic please contact be so that we can have
an interview.
• If, after the interview, you are still interested, the topic will be assigned
to you. From that time on I expect within 4-5 weeks an exposé of a few
pages giving a clear representation to the structure of your thesis and
the references you want to use.
• If the exposé is OK, you may start writing your thesis. Plan to finish
it within about 5-6 months. This time-line is negotiable in particular
cases.
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• Having finished a draft of your thesis, please send it to me in pdf-format.
Within 7 days you will get my feedback, comments and notes on a hard
copy of your thesis.
• Within 4 weeks you should take care of my comments (or not) and finish
the final version of the thesis. This will be the basis of assessment.
Assessment.
The result of assessment will be:
• Sehr Gut, if
– the thesis is comprehensive,
– the thesis is methodologically correct,
– the material is presented nicely,
– the presentation is original and interesting to read,
– you have elaborated and included own nontrivial ideas,
• Gut, if
– the thesis is methodologically correct,
– the material is presented nicely,
– the presentation is interesting to read.
• Befriedigend, if
– the presentation is somewhat sloppy and not very original.
• Genügend, if
– there are severe errors in the draft which have been taken care of
in the final version,
– the theses missed the major points of the topic,
– the presentation is sloppy and boring.
• Nicht Genügend in all other cases.
Technical Note.
The manuscript may be written in English or German language, in any case, it
has to be typeset in LATEX.