We may bemoan the dearth of women in mathematics these days, but throughout history, they were actively discouraged from such intellectual pursuits. Still, occasionally a woman would defy social mores and eagerly embrace the world of numbers. It helped if they had a privileged upbringing, like Maria Gaetana Agnesi, born to a wealthy 18th century Italian family whose fortune came from the silk trade.
Agnesi was known in her family as “the Walking Polyglot” because she could speak French, Italian, Greek, Hebrew, Spanish, German and Latin by the time she was 13. Her father hired the very best tutors for his talented elder daughter. Unfortunately for the shy, retiring Agnesi, he also insisted she participate in the intellectual “salons” he hosted for great thinkers hailing from all over Europe. The young Maria delivered an oration in defense of higher education for women in Latin at the age of 9 (she had translated it from the Italian herself and memorized the text).
There is evidence from contemporary accounts that Agnesi hated being put on display. One contemporary, Charles de Brosseslde Brosses, recalled, “she told me that she was very sorry that the visit had taken the form of a thesis defence, and that she did not like to speak publicly of such things, where for every one that was amused, twenty were bored to death.”
De Brosses admired her intellectual prowess greatly, and expressed horror upon learning that she wished to become a nun. “What a waste!” was the implied sentiment. But maybe she was just too intelligent for her own good. Perhaps she realized that she would always be proving herself, and that her accomplishments, no matter how impressive, would always be treated with some degree of patronizing amazement. (“Look at the smart woman discoursing in Latin!”)
Agnesi did, eventually, become a nun, but not before spending 10 years writing a seminal mathematics textbook, Analytical Institutions, which was published in 1748. One of the curves featured in Analytical Institutions is the Witch of Agnesi. Agnesi dubbed it la versiera, meaning “a rope which turns a sail” – an allusion to the motion by which the curve is drawn. At some point, a harried English translator misinterpreted the word as l’avversiera: “she-devil” or “witch.”
Curves are geometry in motion, and this curve describes a swinging pendulum that is being poked or prodded to keep it in motion, like someone pushing a child on a swing. When the rate of prodding matches the rate of the pendulum’s swing, it is said to be in resonance. If the rate of prodding is very, very close to the rate of the swing, the amplitude (height) of the swing, plotted as a function of frequency, forms the Witch of Agnesi.
Agnesi died a pauper in 1799, having given away everything she owned. But her work continues to resonate today, hopefully inspiring other young women to follow in her mathematical footsteps.