Engines of Our Ingenuity

No. 217:

by John H. Lienhard

Click here for audio of Episode 217.

Today, we meet the Witch of Agnesi. The University of Houston's College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them.

Here's an old geometry book. One of its problems leads you to construct a singularly gentle and graceful curve. We're told that the curve is called the Witch of Agnesi. But why? There's nothing sinister about its flowing line.

It turns out that one person who worked with this curve was Maria Agnesi, a noted 18th-century Italian mathematician -- a woman mathematician! So she was the Witch.

Well, perhaps. But maybe we should meet the lady. Maria Agnesi was born in 1718, the daughter of an Italian mathematics professor at the University of Bologna. She was a child prodigy and the apple of her father's eye. Yet she was shy and retiring. She wanted to become a nun, but her father wouldn't have that. Still, she never married. When she was twenty, her mother died and she took responsibility for the household. She also began work on what was already her second book.

That book was a two-volume treatise on the new differential and integral calculus. It took ten years for her to complete, and it was a major step in bringing the calculus to general use. It was in this extremely important work that she showed how the calculus could be used to create the curve that would later be called the Witch of Agnesi. The work was recognized in its time. Her queen rewarded it with a gift, and the Pope arranged her appointment to the faculty of the University of Bologna.

She was made a member of the Bologna academy of science. The French Academy wrote to tell her how they admired her work, but they wouldn't take her as member because she was female.

Agnesi's father died when she was 34. After that, she put mathematics aside and got on with what she really wanted to do. She turned to charitable work among the poor and sick. She sold her belongings to raise money for the poor. She was eventually given charge over both a hospital and a retirement home. She worked steadily right up to her death at the age of 81, and after that she was labeled "an angel of consolation."

So this was our Witch of Agnesi. A woman who seized the world's attention with brilliant mathematical work and then gave it all up for a half-century of self-sacrifice. That's not the stuff most witches are made of.

It turns out that her curve was called by the Italian word versiera, which means "that which turns." But the Italians have another word, avversiera, which means "wife of the devil." When a Cambridge professor translated her book into English, he turned versiera into witch -- into avversiera. And that is how the word witch was tied to this saintly lady's name.

I'm John Lienhard, at the University of Houston, where we're interested in the way inventive minds work.

(Theme music)

This episode was written in 1989 and based upon scholarship which has been superceded. It has been substantially rewritten as Episode 1741. Please go to that episode.

Osen, L.M., Women in Mathematics. Cambridge, Mass.: MIT Press, 1974, pp. 33-48.

There are many websites which deal with the "Witch of Agnesi" as a mathematical object. See, for example,

This website provides a nice review of Maria G. Agnesi's story,

and the the following portrait:

The "versiera" curve, or the Witch of Agnesi (drawing by John Lienhard)

The Engines of Our Ingenuity is Copyright © 1988-1997 by John H. Lienhard.

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