Maria Gaetana Agnesi

                                                                        (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.