The witch of Agnesi, you may be disappointed to know, is a curve that math students generally learn about in calculus class. It doesn’t look much like a witch, or a hat or even a broomstick. It’s nothing more than a gentle, sloping curve.
If a modern math textbook says anything about the Agnesi for whom it is named, it will probably note that Maria Gaetana Agnesi was an 18th-century mathematician who became the first woman to write a major calculus textbook. It may also note that the name is a mistranslation of the Italian versiera, a term the mathematician Guido Grandi had coined based on the Latin for “turning curve,” which translator John Colson mistook for “avversiera,” which means she-devil—or, more succinctly, witch.
That a devout Catholic woman who dedicated decades of her life to serving the poor should be perpetually associated with a witch via a curve she didn’t even invent is ironic to say the least. But in some ways it feels fitting. “It really is like a Freudian slip of the mathematical imagination to make the Italian word ‘curve’ into the Italian word for a diabolically possessed woman,” says Stanford University science historian Paula Findlen. “It’s a great mathematical joke.” Whether he was being deliberately punny or not, Colson’s mistranslation has cemented Agnesi’s place in calculus classes.
Reading Agnesi’s biography, one gets the feeling that she was constantly living in the shadow of society’s and her family’s expectations and desires for her. Yet if we avoid the temptation to interpret her through our own lenses, we can begin to understand her on her own terms.
Born in 1718, Agnesi was the oldest child of Pietro Agnesi, a wealthy Milanese silk merchant. Her education probably began accidentally when tutors came by to instruct her younger brothers. She was a precocious student, particularly in the study of languages, and Pietro quickly recognized her talent. Eager to elevate his family’s social status, he would have her and her musical prodigy sister Maria Teresa perform for guests at salons in the Palazzo Agnesi. Gaetana would speak about topics in science and philosophy in several different languages, and her sister would play music, often of her own composition. Pietro used his talented daughters to make his house an important stop in Milanese social circles.
The Agnesi sisters were two of several girl prodigies from northern Italy from around the same time. Laura Bassi (1711-1778), a physicist from Bologna who became the first woman university professor in Europe, had been a child prodigy as well. Massimo Mazzotti, a science historian at the University of California at Berkeley who wrote the book The World of Maria Gaetana Agnesi, Mathematician of God, calls it a strategy “of fashioning and controlling this phenomenon of the learned woman.” Wealthy families would provide their daughters with a limited education—literature, French, religion—but women could not attend school outside the home.
The phenomenon of the girl prodigy “was one way of signaling talent and exceptional capacity and giving it