“Maria Gaetana Agnesi was born in Milan on May 16, 1718, to a wealthy and literate family” [Osen, 39]. She was the oldest of the 21 children that her father, a rich merchant, had with his three wives. “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 mother’s death provided her the excuse to retire from public life. She took over management of the household. 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. [See cover page]
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 yx2=a2(a-y) or y = a3/(x2 + a2). 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.