Women play a significant role in life as well as men.
Due to customs and traditions, we see that many women are not mentioned
in historical events. This may be for two reasons. First, females did not
have the same rights as most males at one time. Schools were mainly institutions
for boys. The woman's main role in life was as a homemaker. The second reason
women may not have been documented in history is that they were documented
as men. Often we hear of publications that were written by the wife and
published under the husbands name. The following is a brief collections
of stories which were found that show the role women played in building
the foundation of mathematics.

First, we should begin with Theano. An actual account
of all Theano's work may not be available since it possibly could be credited
to her husband, Pythagoras. After his death, Theano and their two daughters
carried on the Pythagorean School. Theano's work included treatise on child
psychology, medicine, physics, and mathematics. Her most important work
was the principle of the "Golden Mean."

Hypatia was the daughter of Theon, a noted Greek mathematician
and astrologer. Before his daughter's birth around 400 B.C., Theon had bragged that he could create the perfect human.
Being the subject of his experiment, Hypatia was schooled in art, literature,
philosophy, science, and speech. Theon also supervised the development of
her body as well as her mind. Since her beauty and talents were legendary,
it appears that Theon succeeded in creating the perfect human.

At a young age, Hypatia surpassed her father's mathematical
knowledge. He then sent her to Athens to begin studies in astronomy and
astrology as well as mathematics. Her work in mathematics includes writing
commentaries on Apollonius, Diophantus, and Euclid. She was intrigued with
Apollonius's conic sections and the new mathematics of the day, Algebra.
Hypatia was also known at the time as a great instructor in Alexandria.
Here she taught geometry and astronomy, and was one of the university's
most popular lecturers.

Hypatia's death was tragic for two reasons. First,
she was caught in a struggle between the Christians and the Neoplatonists.
Her bodied was dragged through the streets and her flesh was scraped off
the bones with oyster shells. The second reason her death was tragic is
that it marks the end of the great Greek mathematicians.

The next woman that helped lay the foundation of mathematics
is Elena Lucreziao Cornaro Piscopia. Elena was born June 5, 1646. She was
the first female in the world to receive a doctorate degree. Elena became
a lecturer of mathematics in 1678 at
the University of Padua, six years before her death. Elena's father spent
his life trying to establish the Cornaro name. He was a highly esteemed
Venetian serving as the Procurator of San Marco, but what has kept this
family's name remembered is Elena's intellect.

The most versatile female mathematician may very well
have been Emilie du Châtelet. Emilie was born in 1706 on December
17th. Emilie was born into a wealthy French aristocratic family. Her father
provided Emilie with the best academic education possible because he feared
that she would never marry based on her appearance.

Emilie's life was one to dream about. Half of her
life was spent at glamorous balls, vacationing at one of the many estates
of her husband, or with one of her lovers. At this time in France, it was
popular for men to have more than one lover, but not women. Emilie's philosophy
of life must have been similar to "what is good for the goose is good
for the gander." She did not allow her gender to stop her from doing
anything. For example, she once was not admitted to a restaurant because
it was for males. She wanted to attend this restaurant for the academic
discussions being held. She went home, dressed like a man, and returned
with no problems entering the restaurant.

The other half of Emilie's life was spent involved
with her true passion. Emilie spent numerous hours studying mathematics
and science. The most productive time of Emilie's life was the work that
she completed at Cirey. She spent ten years at this estate of her husband.
She was not here alone, instead her two children were with her as well as
her lover the French poet Voltaire. A servant said her days were filled
with her work in the morning and societal gaieties only after finishing
her studies.

Emilie died working on one of her greatest works.
While translating Newton's *Principia*, Emilie gave birth to her second
daughter. Some stories say that the child was laid temporarily on a quarto
volume of geometry. Emilie became deathly ill and died from childbed fever.
The baby died a few days later.

Emilie du Châtelt had many significance accomplishments
in mathematics. What is ironic about Emilie's life is that one of her books,
*Institutions de physique*, was written as a text for her son when
she found no suitable science text. This text is considered one of her greatest
achievements.

Maria Gaetana Agnesi was a timid lady. At a very young
age her father realized that she was a child prodigy. Born in Milan, Italy
on May 16, 1718, Maria spoke French by the age of five and Latin, Greek,
Hebrew and several other languages by the age of nine. Maria became interested
and mastered mathematics during her teen years.

Her father was a professor of mathematics and this led to two advantages
for Maria. First, she was provided an intense education. Second, Maria had
the opportunity to participate in numerous seminars that were gatherings
of the intellectuals of the time at the Agnesi home. Being very shy and
timid, Maria did not enjoy these seminars, but participated for the sake
of her father.

At the time of her mother's death, Maria took over
the household. This allowed her to retire from public life. There was no
objection from her father this time since it was difficult to find a housekeeper
to care for 21 children. Maria continued her work in mathematics until the
death of her father.

One of Maria Gaetana Agnesi's greatest works is *Analytical
Institutions*. Published in 1748, this work began as a textbook for her
younger brothers. When published it became a sensation in the academic world
since it was one of the first works on finite and infinitesimal analysis.
The book became a popular textbook and a model of clarity.

Maria is best known for the curve called the "Witch of Agnesi."
The modern form of the curve is given by the following Cartesian equation:

The Canadian composer Elma Miler wrote a musical work
by the same name, "Witch of Agnesi." Since its premier performance
was so near Halloween many misunderstood that the piece was indeed for the
curve of Maria G. Agnesi.

It seems that mathematics was only a hobby for Maria. Her true passions
came in serving others, including her twenty siblings, as well as the elderly,
poor, and ill. She died at the age of eighty-one, blind, deaf, and suffering
from dropsy, the accumulation of body fluid.

Today astrologists use the *New General Catalogue*
for the recording and identifying of celestial objects. Caroline Herschel
wrote the foundation of this information when she catalogued the observations
made by her brother William and herself. What is remarkable about Caroline
is the hard road she traveled before this accomplishment.

Caroline was born into a working class family in Hanover,
Germany. Her father, a musician, encouraged all of his six children to study
mathematics, French, and music, while he tended gardens to support the family.
Her mother disagreed and thought Caroline should become the house servant.
At a very young age Caroline became ill and stunted her growth. Her father
predicted that she would live her life as an old maid. After her father's
death, Caroline became her mother's housekeeper and indeed it appeared she
would become an old maid.

At the age of twenty-two, Caroline was rescued by
her brother William. He requested that she come and live with him. In exchange
for Caroline, William had to provide the funds for his mother and brother
to have a housekeeper. Once Caroline moved to England, William arranged
for her to receive lessons in English, music, arithmetic, accounting, and
shopping. The later two were to help her manage the household.

William was a musician who became interested in astrology.
He built the first reflecting telescope. Funded by the monarchy, William
began sweeping the heavens in search of new celestial objects. Caroline
was by his side recording data. Caroline downplayed her involvement although
she did all the numerical calculations and reductions. This is impressive
since Caroline never learned her multiplication tables. She carried multiplication
tables on a sheet of paper in her pocket while she worked. Caroline never
got a grasp of them because she studied them so late in her life. Caroline
Herschel died January 9, 1848, about two months shy of her ninety-eighth
birthday.

In 1776, the American Revolution began and Sophie
Germain was born in France. Sophie Germain influenced the change in the
role of women in mathematics as much as the American Revolution influenced
the rights of the citizens of the United States. At that time in France,
the only females that were educated were those from well-to-do families.
Fortunately, Sophie was born to a wealthy family, her father was a merchant
and later became a director of the Bank of Finance.

Although Sophie's family was well off, her parents
were not overly excited to encourage her studies in mathematics. Late at
night, Sophie's parents would take the candles and clothes from her room.
They would then also put the fire out trying to force Sophie to stay in
the bed and sleep. This did not work. Sophie was so determined to work on
the mathematics problems that she hid candles and wrapped herself in quilts
to work at her desk. It was not until her parents found her asleep one night
at her desk and the ink in the inkwell frozen that her parents decided to
allow her to study mathematics, yet did not support her in any way.

What makes a young lady become so intrigued in the
study of mathematics? For Sophie Germain, the story of Archimedes' death
sparked an interest. While a young child, Sophie read many of the books
found in her fathers library. When she read of how involved Archimedes was
in mathematics that it ultimately caused his death, she decided then that
she wanted to know more about this mathematics.

When Sophie was 18, the *Ecole Polytechnic* was
founded. Sophie was not permitted to enroll in this technical academy established
to train mathematicians and scientists due to her gender. Sophie did not
let this stop her from learning what was being taught at this academy. She
got friends' lecture notes and studied them in great detail. Under the name
M. LeBlanc, Sophie submitted a paper on analysis to Lagrange. He was so
impressed that he insisted on meeting this wonderful young mathematician.
When Lagrange found out that M. LeBlanc was female, he continued to recognize
her abilities and became her mentor.

This was the big break that Sophie needed to advance
in the male dominated world of mathematics. Sophie soon started communicating
with Gauss by letters. Some of her most important work in number theory
would be described in these letters. This includes her major step toward
proving Fermat's last theorem. Here she shows that there are solutions for
the following:

Gauss began lobbying for Sophie Germain to become
a professor at the University of Göttingen. Unfortunately Sophie began
a battle with breast cancer that she lost. A few months after her death,
Karl Gauss's loyalty for the friend he never met face-to-face paid off.
The University of Göttingen was willing to award Sophie an honorary
doctorate.

When one hears the name Florence Nightingale, we usually think of a wonderful
nurse. What is remarkable is that although Florence was a nurse she was
also one of the first female statisticians. For five years, Florence visited
every health-care facility that she could find in Egypt, France, and Greece.
While at these facilities she noted anything that affected the patients,
such as buildings, care, diet, personnel, procedures, and sanitation. Florence
returned to England collecting the same data at institutions for the poor.
She organized her findings and compiled the statistics. These statistics
helped lead to improvement in sanitary conditions of health care facilities.

Florence was born into a wealthy family in 1820.
It was not easy for her to obtain an education since it was not common for
Victorian women at that time to be educated. If it was not for her father
wanting his daughters to be educated, she may not have had the opportunity
for schooling. Even still, it was not easy for her. One story says that
when Florence was twenty, she begged her parents to let her study mathematics
instead of practicing quadrilles.

A great mathematician, scholar, and teacher is how
Emmy Noether is remembered. Emmy had challenges in her way that were unlike
others. Fortunately she came from a family who did support her education.
Her father was a professor of mathematics. Emmy was born into a Jewish family
living in Erlangen, Germany in 1882 Emmy faced the same problem that most
of the female mathematicians did. She was not allowed to enroll into a university
to study mathematics. Emmy fortunately was granted permission to audit classes
at the University of Erlangen, where her father was a professor and her
brother was a student. After two years of auditing classes, Emmy passed
the exam that allowed her to begin doctoral studies in mathematics. Five
years later, Emmy was granted the second mathematics degree to a female.
The first was awarded a year earlier.

The next challenge that Emmy faced was an actual teaching
job. She had trouble finding a job since most universities had a strict
policy against female professors. Emmy spent the next ten years doing research
with her father at the Mathematics Institute in Erlangen. Klein and Hilbert
then asked Emmy to come help them in their research of Einstein's theories
at the University of Göttingen. She worked with the staff for three
years before receiving a small salary.

In 1933, Hitler and the Nazis came to power and ordered all Jews out of
universities. Emmy moved to the United States to accept a teaching position
at Bryn Mawr College. This was the first time that Emmy had female colleagues.
All of these women understood how Emmy had to struggle to have a career
in mathematics. To this day, she is still known for her mathematical contributions
and her teaching style. She published over 40 papers specializing in the
field of abstract algebra. Her pupils were inspired to make their own contributions
to the field of mathematics and appeared to teach with a modern day constructivists
approach.

In conclusion, a foundation has been laid for future
mathematicians. The women discussed not only helped open doors for others,
but also discovered significant mathematics. These women have had to overcome
obstacles that we do not see in our life today. Many of the women were forbidden
a formal education. All needed to go against society to accomplish their
achievements. One thing is important, these women and others such as Sonya
Kovalevskaya and Ada Byron Lovelace laid the foundation by accepting challenges
to do the one thing that they loved: mathematics.

Resources

Brewer, J., & Smith M. (Ed.). (1981). *Emmy Noether A Tribute to her
Life and Work*. New York: Marcel Dekker, Inc.

National Council of Teachers of Mathematics (Ed.). (1996). *Celebrating
Women in Mathematics and Science*. United States of America: NCTM.

Perl, T. (1978). *Math Equals: Biographies of Women Mathematicians and
Related Activities*. United States of America: Addison-Wesley.

Perl T. (1993). *Women and Numbers*. San Carlos, CA: Wide World Publishing.

http://www.scottlan.edu/lriddle/women/women.html