Women And Mathematics
In Italy there are more women that enrol themselves in the faculty of
Mathematics in the University than men and there are more graduated women,
too. So the relation between mathematics and women seems to be excellent,
but unfortunately prejudices make reality difficult. Once again and for centuries,
the power of stereotypes has also relegated women to a subordinate and
submissive role in the scientific world. A survey which was carried out by the
American magazine "Science" shows that girls convince themselves to be
genetically disadvantaged and they feel worse than their male colleagues but in
reality there are no natural difficulties which prevent women from being
successful in mathematics.
The American researchers tested 220 women in two groups: they gave the first
group some documents where the inferiority of women in comparison to men
was well-documented, whereas the second group was given a document where
it was written that women are not disadvantaged and the problem is due to the
fact that teachers treat boys in a better way than girls.
They saw that the first group, that was discouraged, was not very good at
mathematics, while the other group was quite better. Finally, genetic
differences between men and women do not exist and we should start
changing this society that considers women as not being able to enter scientific
areas. Unfortunately the difficulties to let their own scientific merits be
recognized are still a reality for women all over the world, in fact the Fields
medal, the greatest recognition for mathematicians, has never been assigned
to any woman.
In order to face problem, an association, which called European Women in
Mathematics (EWM), was founded in 1986 and now it has its seat in
Helsinki, Finland.
EWM organization is an affiliation of women bound by a common interest in the
position of women in mathematics. Their purposes are:
9 - to encourage women to take up and continue their studies in mathematics.
9 - to support women with or desiring careers in research in mathematics or
mathematics related fields.
9 - to provide a meeting place for these women.
9 - to foster international scientific communication among women and men in
the mathematical community.
9 - to cooperate with groups and organizations, in Europe and elsewhere, with
similar goals.
History of Mathematics
The Contributions of Women
Mathematicians in general are not a well known group. However, women
mathematicians are even less well known. It is possible to read most
histories of mathematics and find little or no mention of women
mathematicians, even of the few there were. This article is therefore
intended to trace the impact some of these women have had on the
development of mathematics.
However, firstly, why were there so few women mathematicians? It appears
that the reason for this was that in almost any age women faced many
barriers, which men of far less ability did not have to face. For women,
talents alone were not sufficient criteria for success in mathematics. The
woman also needed to have drive and determination, not only to ignore role
stereotypes but also to overcome the restrictions placed on their education.
It was not until these barriers were crossed that women were able to
develop and enjoy their talents.
The women that will be discussed in this article all came from either academic
or wealthy upper-class families. Some of the women were from the French
and English aristocracy and so had the benefits of outstanding
mathematicians as teachers. This was important as education for girls was
until very recently nonexistent or very much restricted, as there was great
prejudice against women studying subjects such as mathematics or
science. These areas were considered to be male fields.
However, even when women did receive the equivalent of a secondary
education, colleges were closed to them, as it was believed that women
were made for childrearing and that "brain work" may conflict with this
function .
The other women discussed in this article are daughters of mathematicians.
Therefore, as they grew up they not only had access to mathematical texts,
which was a crucial factor because this was a time when public libraries did
not exist, but their talents were also recognised, developed and encouraged
by their fathers.
However, "even with supportive parents and teachers, the traditional roles of
wife, mother and homemaker made study at advanced levels difficult".
Husbands could also cause problems if they were opposed to their wife
studying, and even when sufficient education was obtained by women to
move to the front of their professions, gaining professional employment was
very difficult.
But despite all the obstacles women have had to face in the past, women have
still made a considerably large contribution to the development of
mathematics. Perl (1978, p.198) believes that a closer look at the history of
mathematics may also show that far more women than we realise did make
significant contributions. For example, we know that different historians
notice, select and record different events and that for a long time it was
considered improper for women to sign their own work. Therefore he
believes that when more historical research is done in this new area
surprises may emerge.
So who were those women who did succeed? The biographies that follow are a
brief overview of a few of the women who have managed successfully to
overcome the obstacles of the past. They include Germain, Hypatia,
Kovalevskaya, and Noether. However, there are many other women who
have contributed significantly to the development of mathematics.
Hypatia
Hypatia was born in 370AD, just after the Romans had invaded Greece. During
this time the Greek scholars were fighting to preserve the Greek traditions
of seeking and developing new ideas. Hypatia was not only one of the last
of the great teachers involved in this struggle, but also the last of the Greek
Mathematicians.
Hypatia was actually the first woman to have written on mathematical subjects.
So, although she was mainly a critic and commentator rather than a creator,
her place in history seems relatively secure. Often she is the only woman
mentioned in mathematical histories.
Hypatia was probably educated by her father Theon, who was a noted
mathematician and astronomer in Alexandria. He not only noticed Hypatia's
talent at an early age, but also encouraged her. Historians believe that
Theon tried to raise her to be the perfect human being .
As Hypatia grew older she developed a great interest in mathematics and
science. This interest led her to become the author of several mathematical
works. Very little is however known for certain about Hypatia's work, as
most of her works were destroyed along with the Ptolemaic libraries in
Alexandria.
Hypatia was essentially an algebraist who was inspired by Diophantus. We
know that Hypatia wrote a commentary on Diophantus' Arithmetica, as a
portion of this original work was found during the fifteenth century in the
Vatican library. Her commentaries not only included alternative solutions but
also a number of new problems that she had originated.
Additionally, Hypatia also wrote commentaries On the Conics of Apollonius,
popularising his text and developing the ideas of the hyperbolas, parabolas
and ellipses. Most of her works were actually prepared as textbooks for her
students to help make the difficult mathematical classics easier to
understand (Mueller 1987, p.76).
Hypatia lectured in her native city. She is reported to have lectured specifically
on the Arithmetica of Diophantus, including the symbolism he had devised,
the techniques he had developed and his solution of indeterminate
problems of various types. Hypatia probably also lectured on simple
mechanics, as well as philosophy and astronomy. She was one of the
University's most popular lecturers. Students came from all around the
world to hear her lectures.
However, in 415 she was brutally murdered by a Christian mob, who believed
that she would hinder the expansion of Christianity in Egypt. this act
symbolised the end of the great age of Greek mathematics and the
beginning of a new age of faith. From 641, after the Arabs had invaded and
destroyed Alexandria, Western mathematics went into a dormant period,
which was to last over a thousand years.
Sophie Germain
Sophie Germain was a revolutionary. She battled against the social prejudices
of the era and a lack of formal training in order to become a celebrated
mathematician. She is best known for her work in number theory, but her
work in the theory of elasticity is also very important to mathematics.
Sophie Germain was born in Paris on April 1, 1776,in an era of revolution,to
Ambroise-Francois and Marie Germain and she embodied the spirit of
revolution into which she was born. She was a middle class female who
went against the wishes of her family and the social prejudices of the time to
become a highly recognized mathematician. Like the member of a
revolution, her life was full of perseverance and hard work. It took a long
time for her to be recognized and appreciated for her contributions to the
field of mathematics, but she did not give up. Even today, she is not enough
appreciated for the contributions she made in number theory and
mathematical physics because she was a woman.
She spent a great deal of time in her father's library and one day she saw a
book in which was recounted the legend of Archimede's death :"during the
invasion of his city by the Romans Archimedes was so engrossed in the
study of a geometric figure in the sand that he failed to respond to the
questioning of a Roman soldier. As a result he was speared to death".
Sophie was very interessed because if someone could be so engrossed in a
problem as to ignore a soldier and then die for it, the subject must be
interesting! That's why she began her study of mathematics.
Sophie began teaching herself mathematics using the books in her father's
library. Her parents felt that her interest was inappropriate for a female and
did all that they could to discourage herbut finally they realized that Sophie's
passion for mathematics was "incurable," and they let her learn.
In 1794, when Sophie was 18, the Ecole Polytechnique (an academy founded
to "train mathematicians and scientists for the country") was founded in
Paris,where women were not allowed to enroll in the academy, but Sophie
was able to obtain the lecture notes for several of the courses and study
from them. This gave her the opportunity to learn from many of the
prominent mathematicians of the day. Sophie was particularly interested in
the teachings of J. L. Lagrange. Under the pseudonym of M. LeBlanc
Sophie submitted a paper on analysis to Lagrange at the end of the term.
He was quite impressed with the work and wanted to meet the student who
had written it. Lagrange was amazed that the author of the work was
actually a female, but he recognized her abilities and became her mentor.
With a male to introduce her, Sophie could enter the circle of scientists and
mathematicians that she never before could.
Finally in 1816 she won with her paper Memoir on the Vibrations of Elastic
Plate too and this prize was very important because it introduced her into
the ranks of the prominent mathematicians of the time.
She became the first woman who was not a wife of a member to attend the
Academy of Sciences' sessions with the help of Jean-Baptiste-Joseph
Fourier. She was praised by the Institut de France and was invited to attend
their sessions. This was "the highest honor that this famous body ever
conferred on a woman".
Sophie worked with a well-known male mathematician in the 1820s as an
"equal collaborator" to refine her proofs and work in number theory.
She died at the age of 55, on June 27, 1831, after a battle with breast cancer.
Shortly before this Gauss, one of her earliest mentors, had convinced the
University of Gottengen to give Sophie an honorary degree. She died before
she could receive it
SOFIA KOVALEVSKAJA
The Russian ingenious mathematician was one of the first women who held the
chair
of Maths at the university. She contributed in different branches of Maths.
She was born in 1850 in Saint Petersburg. From early years she showed an
excellent
talent for Maths. But she was prohibited to enter the university in
Russia, because she was a woman. In those years she was in touch with
young
people from the nihilist and revolutionary movements.
She got married and went to Austria and then to Berlin, where she
wrote some important works about the problem of the rotation of hard
bodies around a fixed point. She won an important prize, the Prix Bordin.
In 1889 the University of Stockholm proposed her to hold the chair of Maths
for life. She died in 1891 because of a heart attack.
Emmy Noether
Emmy was born in Germany in 1882. Her father, Max Noether, was a professor
of mathematics at Erlangen. During this time, women were unofficially
allowed to study at university, so she attended lectures given by her father.
In December 1907 she received her Ph.D. in mathematics. She then
worked for no salary at the University of Erlangen, doing research and
lecturing.
During WW1 (1916) Klein and Hilbert invited Emmy to help in defining one of
Einstein's theories at the University of Gottingen. She accepted and soon
afterwards began lecturing unofficially. It was not until 1919 that she
formally became an academic lecturer. She quickly accumulated a small
following of students known as Noether's boys. Many of these students
went on to become great mathematicians .
Emmy helped to alter the face of algebra. She is best known for her
contributions to a part of algebra called abstract algebra. Abstract algebra is
completely different from the early algebra of equation solving, as it deals
with the formal properties of equations, such as associativity, commutativity
and distributivity properties
Emmy did her greatest work later in life. It was not until 1920, when she was
38, that her true talents were acknowledged. This was after she coauthored
a paper on differential operators, which showed her strong interest in the
conceptual axiomatic approach.
Emmy wrote about 45 research papers. However, much of her work also
appears in papers written by her colleagues and students. She became the
inspiration for many students, who made their own contributions to
mathematics, in particular B.L. van der Waerden. In 1924 van der Waerden
wrote a book Moderne Algebra, in two volumes. The second volume
consists mainly of Emmy's work .
Noether's work was fundamental, generating many ideas which continue to
suggest research problems of great importance. She is considered to be the
most influential woman mathematician of the early twentieth century and the
greatest mathematician up to her time. Emmy died suddenly in 1935, at the
age of 53, following an operation
Eleonora Tavani
Valiantsin Tsyklaury