Womens Contributions to Mathematics
Women in the world of mathematics is a subject that people rarely hear about. The only
time people do is if it's a female math teacher. But what many do not know is that
women have made extremely important contributions to the world of mathematics.
Women have been documented to be involved in mathematics, since as early as the fifth
century A.D. Women such as Hypatia, Maria Gaetana Agnesi, Sophie Germain, Emmy
Noether, Ruth Moufang and Sun-Yung Alice Chang. These women have lived through
difficult times such as women's oppression, the French Revolution, World War I and II,
which included Hitler's administration over women's schooling, and social prejudices.
This did not stop their yearning for math though. These women combined have earned
many different awards, specifically ones usually given to men. They have conquered the
biases people have had towards them and made what they do best count. Many of their
theorems and equations are still used today, and some are even being perfected by others.
It is important that the reader realizes that educating children about women in
mathematics is important. Many children think of mathematicians as men, and that is
totally untrue. That thought could possibly contribute to the fact that women are less
likely to enter the mathematics field compared to men. This is because they are not
educated properly on the subject, and are not given the opportunity to excel. There are
many more women in mathematics then mentioned above, but the ones named are very
important to the field and children need to know that. By taking these 6 women's
contributions and focusing on how they apply to the middle school curriculum would be
very useful to any teacher. The children could each pick a female mathematician, and
make a poster and do a presentation about their findings. It could also be done as a
group project. As long as the topic gets discussed and that the girls come out feeling like
they could also get involved in mathematics.





Women's Contributions to Mathematics

In the world of mathematics, you rarely hear anything about women
mathematicians. Although not much is said about women and math, there are many
women mathematicians who have made significant contributions to the field. From as
early as 370 AD, women have been contributing to the study of equations, theorems, and
even solving problems that have deemed themselves in the mathematical world as
impossible. Because of the time period that these women lived, many were not
recognized for their achievement; some were even banished or killed. Names such as
Hypatia, Maria Gaetana Agnesi, Sophie Germain, Emmy Noether, Ruth Moufang, and
Julia Bowman Robinson may not be common to the everyday person. But to
mathematicians around the world, especially women, they are a sign of achievement and
determination in a field dominated by men. In order to make women recognized in the
field of mathematics, educators need to spend time teaching their students that math is not
just for males. Because of the contributions of the women named above, math
exploration has been furthered and many questions have been answered, although some
are still to this day unresolved.
Hypatia
370?-415 AD
Hypatia is the first, truly documented woman mathematician. Her works have
given way to famous male mathematicians such as Newton, Descartes, and Leibniz.
Raised in ancient Egypt during the time that Christianity started to take over many other
religions, it was hard for Hypatia to study anything in an age where males dominated
many fields of study. Hypatia was looked at, though, as a woman of strong character, and
as a strong orator, astrologist, astronomist, and mathematician. Raised mostly by her
father, Theon, a known mathematician of the times, Hypathia gained a lot of knowledge
at a young age. She studied under her father's supervision, which gave her the wanting to
know the unknown in mathematics.
Hyapthia made many contributions to the study of mathematics, her most famous
being her work on conic sections. A conic section is when a person divides cones into
different parts using planes. Because she edited a book written by Apollpnius so well, her
work survived all the way up until today. Her concepts later developed into what is today
called, hyperbolas, parabolas, and ellipses.
Hypatia died a very tragic death in 415 AD. Because she was a woman in the
field of mathematics and science, many rumors were spread about her. One of the
Christian leaders named Cyril heard of these rumors and because he did not like the civil
governor of Alexandria, where Hypatia lived, he made Hypatia a target. She was very
respected and he knew that killing her would definitely hurt the city. On her way home
one night, she was attacked by a mob and literally skinned with oyster shells. Some say
she died for the love of mathematics(Adair, 1995).
Maria Gaetana Agnesi
1718-1799
Maria Gaetana Agnesi was not really considered a mathematician in her time. But
now that some people look back, she made a very significant contribution to the world of
mathematics. She practiced mathematics during the Renaissance in Italy. During this
time, it was considered an honor to be an educated woman. So Maria was both looked up
to and considered a prodigy by the time she was very young. This could be attributed to
the fact that her father was an upstanding mathematician and professor in Milan, Italy.
He often had lectures and seminars at his house for people to come and hear about math.
She liked to listen to these lectures which may have sparked her interest in mathematics.
There are two accomplishments that Maria is accredited with. Her first is her
book that she got published called Analytical Institutions, which was about integral
calculus. Some say that it was originally written for her younger brothers, to aide them in
math. Now that the book has been translated, many mathematicians are using her work
and it is used as a textbook.
Her second accomplishment is a curve called the Witch of Agnesi. Maria came
up with the equation for this well known curve: y= a*sqrt(a*x-x*x)/x . The way to
generate the curve is xy2=a2(a-x)(Golden & Hanzsek-Brill, no date) The reason why it
is called the Witch of Agnesi is because the man who translated the name of the curve
may have mistranslated the Latin word versiera. It can either mean "to turn" or "the wife
of the devil." This curve is very useful in the field of mathematics; even Fermat studied
this curve. Fermat also made the famous problem called Fermat's Last Theorem, which
famous female mathematician Sophie Germain studied (Unlu, 1995).
Sophie Germain
April 1, 1776-June 27,1831
Sophie Germain, was born right before the French Revolution. She was born into
the middle class, and this meant that she had to hide her identity in order to practice math.
The middle class was not supportive of women studying math, therefor much of her work
is done under her pseudonym M. Leblanc. Because of the Revolution, Sophie had to
spend many days in her house, for fear of being killed in a revolt. She was intrigued by
the story of Archimedes and how he got killed because he would not respond to a soldier
while looking at a math problem. Some people think this is why Sophie choose to study
mathematics.
Sophie Germain studied under famous mathematician of the time, Carl Friedrich
Gauss. Gauss was really into number theory and Fermat's Last Theorem. Fermat's Last
Theorem is closely related to the Pythagorean theorem. Instead of using x2+y2=z2,
Pierre de Fermat used x,y,and z raised to powers of 3, 4, 5,etc. Many think that this
problem was unsolvable, but Fermat said that he had proof it could work. The mystery is
though, that Fermat never wrote down his solution. It was up to future mathematicians to
find the solution that Fermat claimed.
Sophie was up to the challenge, and in a letter to Gauss, written in 1808 she came
up with a calculation that said something about several solutions. Fermat's theory says
there are no positive integers such that for n*2. But Sophie proved in her theorem that if
x, y, and z are to the fifth power than n has to be divisible by five. Sophie said that this
would work only with what are now called Germain primes. Germain primes are primes
such that when you take a prime, multiply it by two, and then add one, your answer will
be prime. Some Germain primes are 2, 3, 5, 11, 23 and 29 (Singh, no date). In 1825,
she proved, that for the first part of Format' Last theorem, these primes would work.
There are many other mathematicians that have followed up on Sophie's work on
Fermat's Last Theorem. Number theorist ,Euler and Legrange, proved that if p=3 is
prime, 2p+1 is also prime if and only if 2p+1 divides 2p-1. In 2000, famous number
theorist, Henri Lifchitz, found an easier way to determine a Germain prime. He says that
if p*=5 is prime, q=2p+1 is also prime if and only if q divides 3p-1. It turns out though in
1994, Andrew Wiles, a researcher at Princeton, claimed to have proof of the theorem.
His manuscripts have been reviewed and it is among the majority that he has proved it
(Swift, 1997)
Emmy Noether
March 23, 1882-April 14, 1935
Still in the late 1800s, it was not proper or allowed for a woman to go to college.
Emmy Noether became one of these women, when she was denied enrollment at the
University of Erlangen. They did allow her, though, to sit in on two years of math
classes and take the exam that would let her be a doctoral student in math. She passed the
test and after going for five more years, she was given a diploma. After graduation,
Emmy decided to take up teaching, but the university would not hire her because she was
a woman. So she decided to work along side her father, who at the time was a professor
at the university. Emmy Noether's first piece of work was finished in 1915. It is work in
theoretical physics, sometimes called the Noether's Theorem, which proves a relationship
between symmetries in physics and conservation principles. This basic result in the
general theory of relativity was praised by Einstein, where he commended Noether on her
achievement.
During the 1920s Noether did foundational work on abstract algebra, working in
group theory, ring theory, group representations, and number theory. During the time that
she was a teacher, Germany was involved in WWI and WWII. Because of the war, and
since Noether was a Jew, she was forced out of Germany and went to live in the United
States ( "Emmy Noether", no date).
While in the United States, Noether taught at an all girls college. Her students
loved her and many followed her teachings. Some say that they way she taught was
phenomenal. She was clear and used many different methods of teaching so that her
students could understand math easier. She was praised by Einstein constantly on her
theory of relativity. Albert Einstein paid her a great tribute in 1935: "In the judgement of
the most competent living mathematicians, (Emmy) Noether was the most significant
creative mathematical genius thus far produced since the higher education of women
began." Throughout her career she worked with many mathematicians such as Emanuel
Lasker, Bartel van der Waerden, Helmut Hasse and Richard Brauer. Twice Noether was
invited to address the International Mathematical Congress (1928, 1932). In 1932 she
received the Alfred Ackermann-Teubner Memorial Prize for the Advancement of
Mathematical Knowledge. It is said that her greatest work was that of abstract algebra
(Taylor, 1995).
Ruth Moufang
January 10, 1905-November 26, 1977
Like the Nazis refused Emmy Noether the right to teach, Ruth Moufang was also
denied the right. Because of this, Ruth Moufang decided to enter the field of industrial
mathematics, and work on the elasticity theory. She was the first German woman to have
a doctorate in this field. Ruth Moufang published one famous paper on group theory.
This paper was first written based on the writings of Hilbert. Ruth's most famous
teachings were on number theory, knot theory, and the foundations of geometry. She also
is famous for what we call today, Moufang planes and Moufang loops. Moufang loops
are a class of loops which arise naturally in many other fields such as finite group theory
and algebraic geometry (O'Conner & Robertson, 1996).
Sun-Yung Alice Chang
March 24, 1948-present
Sun-Yung was born in Ci-an, China. During research, no information was found
on the time period when she was born. What was found though is an abundance of
information on her college life and what her contributions to mathematics were.
Sun_Yung Chang received her doctorate in mathematics from University of
California. She then went to teach college math at UCLA. Currently, she still teaches at
UCLA, but since she started many things have happened to her.
Her greatest accomplishment is when she received the Ruth Lyttle Satter prize for
her contributions to mathematics over the last five years. She was awarded the prize for
her contributions to partial differential equations and on Riemannian manifolds. The
study of manifolds having a complete Reimannian Metric is called Reimannian geometry
(Weinsstein, 1996-2000). This is a topic that Sun-Yung studied a lot. Sun-Yang says, in
her speech at the American Mathematical Society, "Following the early work of J Moser
and influenced by the work of T Aubin and R Schoen on the Yamabe problem, P. Yang
and I have solved the partial differential equation of Gaussian/scalar curvatures on the
sphere by studying the extremal functions for certain variation functionals. We have also
applied this approach in conformal geometry to the isospectral compactness problem on
3-manifolds when the metrics are restricted in any given conformal class. More recently
we have been studying the extremal metrics for these functionals. We are working to
derive further geometric consequences. This latter piece of work is a natural extension of
the earlier work by Osgood-Phillips-Sarnak on the log-determinant functional on compact
surfaces."(O'Conner & Robertson,1998, p. 2) Sung-Yung is already considered to be a
great mathematician, even though she says there is still work to be done.

Women in Mathematics connected to the Middle School Curriculum
In Sun-Yung's speech, given at the acceptance of her award in 1995 she states,
"Since the Satter Prize is an award for women mathematicians, one cannot help but to
reflect on the status of women in our profession now. Compared to the situation when I
was a student, it is clear that there are now many more active women research
mathematicians. I can personally testify to the importance of having role models and the
companionship of other women colleagues. However, I think we need even more women
mathematicians to prove good theorems and to contribute to the profession." (O'Conner
& Robertson, 1998, p. 2)
This is exactly why this topic needs to be discussed in the middle grades. Girls
need to know that mathematics is not only for men. Young girls may be less apt to go
into the field of mathematics based on the biases that have been going for years.
Teachers need to tell about the importance of mathematical skills for both boys and girls,
and also need to plan activities centered around women in mathematics. By talking to
young girls in middle school about female mathematicians, educators could possibly
ignite a flame, under possibly, another great female mathematician.

Although many do not think of women as mathematicians, there are many women
who have proved themselves in the mathematical world. Through their theorems and
problem solving, these women have furthered the world of mathematics, for others to
someday conquer.



References
Adair, G. (1995). Hypatia. Agnes Scott College [Online]. Available:
http://www.agnesscott.edu/lriddle/women/agnesi.htm [1 March 2000].
Emmy Noether (no date). [Online].
Available:http://www.coastal.edu/academics/science/jump/biography/enoether.ht
ml [5 March,2000].
Golden & Hanzsek-Brill. (no date). Investigation of the Witch Curve. [Online].
Available: http://jwilson.coe.uga.edu/Texts.Folder/Agnesi/witch.html [1 March,
2000].
O'Conner, J.J., & Robertson, E.F. (1996). Ruth Moufang. [Online]. Available:
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Moufang.html [24
February 2000].
O'Conner, J.J., & Robertson, E.F. (1998). Sun-Yung Alice Chang. [Online]. Available:
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Chang.html [6
March 2000].
Singh, Simon. (no date). Math's Hidden Women. [Online]. Available:
http://www.pbs.org/wgbh/nova/proof/germain.html [1 March 2000].
Swift, Amanda. (revised in 1997). Sophie Germain. Agnes Scott College [Online].
Available: http://www.agnesscott.edu/lriddle/women/germain.htm [1 March
2000].
Taylor, Mandie. (1995). Emmy Noether. Agnes Scott College [Online]. Available:
http://www.agnesscott.edu/lriddle/women/noether.htm [2 February 2000].
Unlu, Elif. (1995). Maria Gaetana Agnesi. Agnes Scott College [Online]. Available:
http://www.agnesscott.edu/lriddle/women/agnesi.htm [1 March 2000].
Weisstein, Eric. (1996-2000). Riemannian Geometry. Wolfram Research Inc. [Online].
Available: http://www.mathworld.wolfram.com/RiemannianGeometry/html [7
March 2000].











 
Bibliography:
References Adair, G. (1995). Hypatia. Agnes Scott College [Online]. Available: http://www.agnesscott.edu/lriddle/women/agnesi.htm [1 March 2000]. Emmy Noether (no date). [Online]. Available:http://www.coastal.edu/academics/science/jump/biography/enoether.ht ml [5 March,2000]. Golden & Hanzsek-Brill. (no date). Investigation of the Witch Curve. [Online]. Available: http://jwilson.coe.uga.edu/Texts.Folder/Agnesi/witch.html [1 March, 2000]. O’Conner, J.J., & Robertson, E.F. (1996). Ruth Moufang. [Online]. Available: http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Moufang.html [24 February 2000]. O’Conner, J.J., & Robertson, E.F. (1998). Sun-Yung Alice Chang. [Online]. Available: http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Chang.html [6 March 2000]. Singh, Simon. (no date). Math’s Hidden Women. [Online]. Available: http://www.pbs.org/wgbh/nova/proof/germain.html [1 March 2000]. Swift, Amanda. (revised in 1997). Sophie Germain. Agnes Scott College [Online]. Available: http://www.agnesscott.edu/lriddle/women/germain.htm [1 March 2000]. Taylor, Mandie. (1995). Emmy Noether. Agnes Scott College [Online]. Available: http://www.agnesscott.edu/lriddle/women/noether.htm [2 February 2000]. Unlu, Elif. (1995). Maria Gaetana Agnesi. Agnes Scott College [Online]. Available: http://www.agnesscott.edu/lriddle/women/agnesi.htm [1 March 2000]. Weisstein, Eric. (1996-2000). Riemannian Geometry. Wolfram Research Inc. [Online]. Available: http://www.mathworld.wolfram.com/RiemannianGeometry/html [7 March 2000].
 
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