Season of the Witch

First Witch
When shall we three meet again?
In thunder, lightning, or in rain?

Second Witch
When the hurlyburly’s done,
When the battle’s lost and won.

Third Witch
That will be ere the set of sun.

First Witch
Where the place?

Second Witch
Upon the heath.

Third Witch
There to meet with Macbeth.

The above is of course the three witches in the opening scene of Shakespeare’s Macbeth, which inspired the wonderful joke from I’m Sorry I’ll Read That Again

Three Witches

Yes we can.


I hear you can foretell the future.

Shakespeare is of course so called highbrow culture and for those who prefer their entertainment somewhat more lowbrow there is the wonderful scene in the film of the Wizard of Oz where the Wicked Witch of the West dissolves as she gets sprayed with water.

For those of a theological bent The Bible offers us the Witch of Endor and the most recent addition to that strange British literary genre the boarding school novel gives us that by now world famous academy for all things magical Hogwarts.

But can you locate the Witch of Agnesi? No! In fact this witch has nothing to do with mastery of the occult powers but is a geometrical curve named, incorrectly, after the 18th century Italian mathematician Maria Gaetana Agnesi who was born on the 16th May 1718 in Milano.


Maria Gaetana Agnesi Source: Wikimedia Commons

Now the expression 18th century female mathematician is almost an oxymoron; the Agnes Scott College website, Biographies of Women Mathematicians, lists only five of whom three, although born in the 18th, gained most of their fame in the 19th century leaving a grand total of two, one of whom is today’s birthday girl Maria.

The eldest of twenty-one children born to the rich Milanese silk merchant Pietro Agnesi (c.1692 – 1752) Maria was a child prodigy who was a fluent multi-linguist with a talent for mathematics and philosophy. Educated at home, at her fathers wish, by a series of private tutors she had already produced an impressive Latin translation, from the original Italian, of a long discourse by one of her tutors advocating advanced education for ladies at the age of nine. She went on to produce equally impressive linguistic achievements in Greek and a handful of modern European languages. At the age of twenty, her father published a list of 191 philosophical theses that she was prepared to defend ex tempore against all comers. This might appear to be a bit like presenting a trained ape who could jump through hoops but such semi-public displays of intellectual or cultural erudition were fairly common practice in the salons of the rich and powerful in 18th century Italy.

There are numerous eyewitness accounts of Signorina Agnesi’s extraordinary intellectual talents so it came as quite a shock when she announced that she wished to enter a convent and become a nun. Her father persuaded her not to take this step but her conditions were that she could continue to live at home, not marry, attend church as often as she wished, wear plain drab clothes and abandon the frivolous social life of her contemporaries.

She devoted the next ten years of her life, actively supported by he father and his acquaintances, studying philosophy, theology and mathematics and during this time wrote a commentary on l’Hôpital’s posthumous treatise on conic sections, which however was not published. She now started to receive tuition in mathematics from the mathematician Ramiro Rampinelli (1697 – 1759) and under his guidance she wrote her only mathematical work, Instituzioni Analitiche ad Uso della Gioventù Italiana, which is best translated in English as Textbook of Analysis for the Use of Young Italian, which was published in 1748.


First page of Instituzioni analitiche (1748) Source: Wikimedia Commons

This was a clear and well written textbook on analysis that received praise throughout Europe and was translated into a number of other languages. Agnesi did no original mathematics and her reputation is unfortunately somewhat inflated but in an age that discriminated against education for women her contribution to emancipation cannot and should not be ignored.

After the publication of her textbook Maria turned to theology and charitable work which she continued until her death at the age of 81.

Coming back to the curve that gave this post its introduction and is the thing most frequently connected with the name Agnesi, the Witch of Agnesi was neither invented nor named by her. The name witch is actually the result of an error in translation, the curve, which she discusses in her book, was originally called Versoria in Latin meaning “rope that turns a sail” this was rendered correctly in Italian by Agnesi as la versiera. Her English translator John Colson mistook la versiera for the word l’aversiera, which means witch or she-devil and so the curve came to be known as the Witch of Agnesi.



Filed under History of Mathematics

7 responses to “Season of the Witch

  1. But can you locate the Witch of Agnesi? No!

    Ah, but the median is easy to fine. And don’t we all like to strike a happy median?

    I have a professional like of the Witch of Agnesi – she’s a wonderful source of counter-examples in statistics.

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  4. I recall the Witch of Agnesi being mentioned in my (high school) algebra textbook, in a footnote, with no context explaining it, or what Agnesi meant in this context, or why it was called the witch. It was one of the nagging little irritants of that textbook.

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