A Mathematician, a Catholic - and a Witch

Recently I have been posting on the ACS blogg about GKC and mathematics. If today were Thursday, I might have posted the following discussion over there - as GKC has very interesting things to say about Catholicism and mathematics, and about witches. But the Witch I am referring to is not the Hogwarts type of witch, nor the "double-double" kind, nor the evil and dark kind. It is not even a human being! Ah, my title has mislead you? I will show you a picture of this Witch:


[image from the CRC Handbook of Standard Mathematical Tables]

This curve is called "witch" by transliteration from an Italian term versiera (which means the above curve). Fermat had written an equation for it in 1665, but the name "Agnesi" has come to be associated with it.

Who was this Agnesi?

According to the Dictionary of Scientific Biography, Maria Gaetana Agnesi (1718-1799) is "the first woman in the Western world who can accurately be called a mathematician." She was the oldest of 21 children; her father was a professor of mathematics at the University of Bologna, and encouraged her interest in scientific matters. She was brilliant at languages: "By age eleven, she was thoroughly familiar with Greek, German, Spanish, and Hebrew." In 1748, she wrote a massive work (over 1000 pages) on teaching mathematics to the young - it was in Italian but "won acclaim in academic circles all over Europe" and was translated into English.

It was she who gave this definition for the above "witch" curve:

If C is a circle of diameter a with center at (0, 1/2 a), and if the variable line OA through the origin O intersects the line y = a at point A and the circle at point B, then the versiera is the locus of point P, which is the intersection of lines through A and B parallel to the Y axis and X axis, respectively. The curve, generated as the line OA turns (Latin vertere, hence the name versiera), is bell-shaped with the X axis as asymptote.
[Ibid.; cf. the CRC reference. This explanation matches the above CRC diagram. The diagram shows the equation given in the usual cubic form, and also as a parametric in f by which it is easier to plot if you're all excited to make your own...]

But Maria was not simply a brilliant writer, linguist, and mathematician. She was also a very serious Catholic:

The recognition of greatest significance to Agnesi was provided in two letters from Pope Benedict XIV. The first, dated June 1749, a congratulatory note on the occasion of the publication of her book, was accompanied by a gold medal and a gold wreath adorned with precious stones. In his second letter, dated September 1750, the pope appointed her to the chair of mathematics and natural philosophy at Bologna. [Ibid.]

After her father's death in 1752, she retired from all scientific work, and devoted herself to religious work and study, making great material sacrifices to help the poor in her parish. Finally, a long-held desire for the religious life was satisfied: "after acting for some years as the director of the Hospice Trivalzio of the Blue Nuns in Milan, she joined the order and died a member of it, in her 81st year." [The Catholic Encyclopedia, 1907 ed.]

What an exemplary woman! I do not know if her Cause has been started, but given tomorrow's feast, it is not unreasonable to request her intercession for us: dear Maria of the witch-that-turns, intercede with our Lord for linguists, for mathematicians, for the sick, and for the young who are learning mathematics!