(1718 - 1799)

Even though her contribution to
mathematics are very important, Maria Gaetana Agnesi was not a
typical famous mathematician. She led a quite simple life and
she gave up mathematics very early. At first glance her life may
seem to be boring, however, considering the circumstances in
which she was raised, her accomplishments to mathematics are
glorious. Enjoy!

During the Middle Ages, under the
influence of Christendom, many European countries were opposed
to any form of higher education for females. Women were mostly
deprived from the fundamental elements of education, such as
reading and writing, claiming that these were a source of
temptation and sin. For the most part, learning was confined to
monasteries and nunneries which constituted the only opportunity
for education open to girls during the Middle Ages. After the
fall of Constantinople (today Istanbul), many scholars migrated
to Rome, bringing Europe knowledge and critical thinking, which
in turn gave rise to the Renaissance. However, except in Italy,
the status of women throughout Europe changed very slowly.

In Italy, however, where the
Renaissance had its origin, women made their mark on the
academic world. Intellectual women were admired by men, they
were never ridiculed for being intellectual and educated. This
attitude enabled Italian women to participate in arts, medicine,
literature, and mathematics. Among many others, Maria Gaetana
Agnesi was by far the most important and extraordinary figure in
mathematics during the 18th century.

"Maria Gaetana Agnesi was born in
Milan on May 16, 1718, to a wealthy and literate family" [Osen,
39]. She was the oldest of 21 children. Her father was a
professor of mathematics and provided her a profound education.
"She was recognized as a child prodigy very early; spoke French
by the age of five; and had mastered Latin, Greek, Hebrew, and
several modern languages by the age of nine. At her teens, Maria
mastered mathematics" [Osen, 40]. The Agnesi home was a
gathering place of the most distinguished intellectuals of the
day. Maria participated in most of the seminars, engaging with
the guests in abstract philosophical and mathematical
discussions. Maria was very shy in nature and did not like these
meetings. She continued participating in the home gatherings to
please her father until the death of her mother. Her mothers
death provided her the excuse to retire from public life. She
took over management of the household. Her father did not oppose
this, because it was difficult and expensive to find a
housekeeper to take care of 21 children and a lonely man. It is
possible that this heavy duty job was one of the reasons why she
never married.

However, she did not give up
mathematics yet. In 1738 she published a collection of complex
essays on natural science and philosophy called *Propositiones
Philosophicae*, based on the discussions of the intellectuals
who gathered at her father's home. In many of these essays, she
expressed her conviction that women should be educated.

By the age of twenty, she began
working on her most important work, *Analytical Institutions*,
dealing with differential and integral calculus. "It is said
that she started writing *Analytical Institutions* as a
textbook for her brothers, which then grew into a more serious
effort" [Osen, 41]. When her work was published in 1748, it
caused a sensation in the academic world. It was one of the
first and most complete works on finite and infinitesimal
analysis. Maria's great contribution to mathematics with this
book was that it brought the works of various mathematicians
together in a very systematic way with her own interpretations.
The book became a model of clarity, it was widely translated and
used as a textbook.

*Analytical Institutions* gave
a clear summary of the state of knowledge in mathematical
analysis. The first section of *Analytical Institutions*
deals with the analysis of finite quantities. It also deals with
elementary problems of maxima, minima, tangents, and inflection
points. The second section discusses the analysis of infinitely
small quantities. The third section is about integral calculus
and gives a general discussion of the state of the knowledge.
The last section deals with the inverse method of tangents and
differential equations.

Maria Gaetana Agnesi is best known
from the curve called the
"Witch of Agnesi" (see illustration from her text *
Analytical Institutions*). Agnesi wrote the equation of this
curve in the form y = a*sqrt(a*x-x*x)/x because she considered
the x-axis to be the vertical axis and the y-axis to be the
horizontal axis [Kennedy]. Reference frames today use x
horizontal and y vertical, so the modern form of the curve is
given by the Cartesian equation y*x^2=a^2(a-y) or y = a^3/(x^2 +
a^2). It is a versed sine curve, originally studied by Fermat. "It
was called a versiera, a word derived from the Latin vertere,
meaning 'to turn', but it was also an abbreviation for the
Italian word avversiera, meaning 'the wife of the devil'" [Osen,
45]. However, when Maria's text was translated into English the
word versiera was confused with "witch", and the curve came to
be known as the
witch of Agnesi.

After the success of her book,
Maria was elected to the Bologna Academy of Sciences. The
university sent her a diploma and her name was added to the
faculty. However, there is a debate over whether or not Maria
accepted this appointment. The consensus is that she accepted
the position and served at the university until the death of her
father. It seems that her father was the inspiration for her
interest in mathematics. When he died, Maria gave up any further
work in mathematics. "When, in 1762, the University of Turin
asked her for her opinion of the young Lagrange's recent
articles on the calculus of variations, her response was that
she was no longer concerned with such interests" [Osen, 47].

Maria was a very religious woman.
She devoted the rest of her life to the poor and homeless sick
people, especially women. When the Pio Instituto Trivulzo, a
home for the ill and infirm, was opened, Maria was given an
appointment as the director of the institute. She took care of
ill and dying women until her own death.

It seems to me
that even though she was a genius, mathematics was only a
temporary hobby of hers. It may be that she was only dealing
with mathematics to please her father who apparently was
expecting his prodigy child to be involved in mathematics. Of
course, this is only a personal observation. However, her
behavior implies that she was not dedicated to mathematics which
I think explains why she gave up mathematics altogether as soon
as her father died. She was a very shy and decent person. She
was not ambitious to become a well-known mathematician. Her most
famous work, *Analytical Institutions*, was intended to be
a textbook for her brothers. Her intelligence and talent made it
possible to integrate all the state of the art knowledge about
calculus in a very clear way. Religious life and helping the
needy seem to have interested her more than mathematics.

*http://www.agnesscott.edu/lriddle/women/agnesi.htm *