One of the great figures of Italian science, Maria Gaëtana Agnesi (1718-1799) was born and died in the city of Milan. Her principal work, Analytical Institutions, introduces the reader to algebra and analysis, providing elucidations of integral and differential calculus. Among the prominent features of Agnesi's work is her discussion of a curve, subsequently named the "Witch of Agnesi."

# Maria Agnesi

In early childhood, Agnesi demonstrated extraordinary intellectual abilities, learning several languages, including Greek, Latin, and Hebrew. Her father, who taught mathematics at the University of Bologna, hired a university professor to tutor her in mathematics. While still a child, Agnesi took part in learned discussions with noted intellectuals who visited her parents' home. Her knowledge encompassed various fields of science, and to any foreign visitor, she spoke fluently in his language.

Her brilliance as a multilingual and erudite conversationalist was matched by her fluency as a writer. When she was 17 years old, Agnesi wrote a memoir about the Marquis
de l'Hospital's 1687 article on conic sections. Her *Propositiones Philosophicae,* a book of essays published in 1738, examines a variety of scientific topics, including philosophy, logic, and physics. Among the subjects discussed is Isaac Newton's theory of universal gravitation.

Following her mother's death, Agnesi wished to enter a convent, but her father decided that she should supervise the education of her numerous younger siblings. As an educator, Agnesi recognized the educational needs of young people, and eloquently advocated the education of women.

## Witch of Agnesi

Agnesi's principal work, *Instituzione analitiche ad uso della gioventu' italiana* (1748), known in English as her *Analytical Institutions,* is a veritable compendium of mathematics, written for the edification of Italian youth. The work introduces the reader to algebra and analysis, providing elucidations of integral and differential calculus. Praised for its lucid style, Agnesi's book was translated into English by John Colson, Lucasian Professor of Mathematics at Cambridge University. Colson, who learned Italian for the express purpose of translating Agnesi's book, had already translated Newton's *Principia mathematica* into English. Among the prominent features of Agnesi's work is her discussion of a curve, subsequently named the "Witch of Agnesi," due in part to an unfortunate confusion of terms. (The Italian word *versiera,* derived from the Latin *vertere,* meaning "to turn," became associated with *avversiera,* which in Italian means "devil's wife," or "witch.") Studied
previously by Pierre de Fermat and by Guido Grandi, the "Witch of Agnesi" is a cubic curve represented by the Cartesian equation y (x2 + a2) = a3, where "a" represents a parameter, or constant. For "a" = 2, as an example, the maximum value of y will be 2. As y tends toward 0, x will tend, asymptotically, toward ± ∞.

## Received Papal Recognition

In 1750, Pope Benedict XIV named Agnesi professor of mathematics and natural philosophy at the University of Bologna. As David M. Burton explained, it is not quite clear whether she accepted the appointment. Considering the fact that her father was gravely ill by 1750, there is speculation that she would have found the appointment difficult to accept. At any rate, after her father's death in 1752, Agnesi apparently lost all interest in scientific work, devoting herself to a religious life. She directed charitable projects, taking charge of a home for the poor and infirm in 1771, a task to which she devoted the rest of her life.

## Further Reading on Maria Agnesi

Alic, Margaret, *Hypatia's Heritage: A History of Women in Science from Antiquity through the Nineteenth Century,* Beacon Press, 1986.

Burton, David M., *Burton's History of Mathematics: An Introduction,* Wm. C. Brown, 1995.

*Dictionary of Scientific Biography.* edited by Charles Coulston Gillispie, Charles Scribner's Sons, 1970.

Olsen, Lynn M., *Women in Mathematics,* MIT Press, 1974.