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.

I have this neat old book on
analytical geometry. The solution to one of its
problems is a singularly gentle and graceful curve.
It's called *The Witch of Agnesi*. But why?
There's nothing sinister about this flowing line.

It turns out that one person who worked
with this curve was a noted eighteenth-century
Italian mathematician named Maria Agnesi. So,
problem solved: she was the Witch. Well, wait a
minute. Let's meet the woman herself. Maria Agnesi
was born in Milan in 1718. Her father was a
gentleman intellectual. She was a child prodigy and
the apple of his eye.

Yet Maria was shy and retiring, and, when she was
twenty, her mother died, leaving the household in
her care. She wanted to become a nun, but her
father wouldn't hear of that. So they struck a
deal. She would stay at home if she could attend
church whenever she chose, dress simply, and avoid
secular socializing.

In that same year she published her first book -- a
set of 191 well-organized philosophical
propositions, what we would call a physics text.
She defended it (as one might a thesis) in an open
meeting. One observer said, "She spoke like an
angel."

Her major contribution was a two-volume treatise on
the new differential and integral calculus, which
she finished at the age of thirty. It was a major
step in organizing the calculus and bringing it
into general use. In this extremely important work,
she showed how the calculus could be used to create
the curve that would later be called *The Witch
of Agnesi*.

Her queen rewarded the treatise with a gift, and
the Pope arranged for her appointment to the
faculty of the University of Bologna. She remained
on their rolls for forty-five years, although she
never took up the appointment. Instead, she did
charitable works and taught mathematics in one wing
of her father's house.

When Agnesi was 34, her father died. Then she put
mathematics aside and got on with her real
business. She turned to charitable work among the
poor and sick. She sold her belongings to raise
money to create a retirement home for the poor. She
worked steadily until she herself died in that
poorhouse at the age of 81. After that, our "witch"
was labeled "an *angel* of consolation."

Here was 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
is not the stuff we usually take witches to be made
of. So where did the term *Witch of Agnesi*
come from?

Well, that curve was called a *versiera*, or
*that-which-turns*. But the Italians have
another word, *l'aversiera*, which means
*she-devil* or *witch*. When a
Cambridge professor translated her book into
English, he turned *versiera* into
*witch* -- into *l'aversiera*.

And that is how this saintly mathematician became a
witch.

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

(Theme music)

Years ago, I originally did this in a version
(Episode 217) based upon
Lynn Osen's very accessible book, *Women in
Mathematics*. Cambridge, Mass.: MIT Press,
1974, pp. 33-48. More recent scholarship greatly
expands upon that and corrects some errors of fact.

For details, see an excellent web site with many
good sources:

Maria Gaëtana Agnesi

The following two web sites deal with the "Witch of
Agnesi" as a mathematical object:

The Witch of Agnesi, first site

The Witch of Agnesi, second site