Maria Gaëtana Agnesi

1718-1799

Italian Mathematician

The daughter of a mathematics professor at the University of Bologna, Maria Gaëtana Agnesi grew up possessing an enormous command of mathematics, languages, and the sciences. She later dedicated herself to the education of her many younger siblings, a project that resulted in her most important work, Instituzione analitiche. This work includes discussion of the curve referred to as the "Witch of Agnesi."

Agnesi spent her entire life in the northern Italian city of Milan. Her father taught mathematics at the University of Bologna, and appreciation for learning permeated the family's home life. Recognizing his daughter's promise as a scholar, the father hired a tutor for her; meanwhile, she excelled in languages all on her own. The many visitors to her parents' home carried on their conversations in Latin, still the language of learned discourse. Not only did young Maria master that tongue, but for guests who did not speak it, she could also converse and translate into a variety of other languages, including Greek and Hebrew.

At the age of 17, Agnesi wrote a commentary on a study of conic sections by an earlier mathematician, the marquis de l'Hospital. Three years later, in 1738, she published a book of essays entitled Propositiones philosophicae, in which she discussed a number of subjects, including the theory of universal gravitation put forth in the previous century by Sir Isaac Newton (1642-1727). Yet, when her mother died, Agnesi expressed a desire to enter a convent and put an end to her intellectual pursuits. Her father, however, requested that she devote herself to the education of her younger siblings, of which she had many (Agnesi was the eldest), and this became her life's work.

As part of her effort to teach mathematics to her younger brothers and sisters, Agnesi wrote and in 1748 published Instituzione analitiche ad uso della gioventu' italiana. This mathematics textbook for youngsters provided an introduction to algebra, analysis, and both differential and integral calculus. Among the topics it discusses is the curve incorrectly identified as the "Witch of Agnesi," so named due to a mistranslation; the Italian word for curve, versiera, looked like versicra, or "witch." The "Witch of Agnesi," studied earlier by Pierre de Fermat (1601-1665) and Guido Grandi (1671-1742), was represented by the equation y (x² + a²) = a³, where a is a constant. As y tends toward 0, x will tend toward ∞. In 1801, John Colson of Cambridge, who learned Italian specifically for the purpose, translated Agnesi's book as Analytical Institutions.

Recognizing the contributions to learning made by the 32-year-old Agnesi, Pope Benedict XIV named her professor of mathematics and natural philosophy at Bologna—her father's old school. Her father, however, had become seriously ill, and Agnesi devoted herself to caring for him. Two years later, he died, and rather than accept the appointment at Bologna, Agnesi threw herself into religious work. In 1771 she opened a home for the poor and infirm, and devoted herself to this project for the remaining 18 years of her life.

JUDSON KNIGHT