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.

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