The Witch of Agnesi

A mistranslation led to the unusual name of this mathematical concept

A posthumous engraving of Maria Agnesi from 1836. Wikimedia Commons

Eighteenth-century mathematician Maria Gaetana Agnesi’s talent for languages let her see math in a new way.

“The Witch of Agnesi” isn’t her, though. It’s a curve, described in her book Analytical Institutions, published in 1748. Besides being the first text to unite many different mathematical theories written in a number of languages, the book is the oldest surviving mathematical text authored by a woman.

Agnesi, who was born on this day in 1718, was a prodigy who found scope for her many talents in 1700s Milan, writes the American Physical Society. Her family called her “the Walking Polyglot” because she spoke seven languages by the time she was 13. “By her late teens, she had also mastered mathematics,” the Society writes. Her family was wealthy, if new money, and her father supported her studies—maybe even a little too much.

Her father “had ambitious plans” for her, writes historian Massimo Mazzotti. During her childhood and teen years, he hosted intellectual parties, called salons, at which she was the star attraction. “He began using his salon to attract prestigious foreign visitors,” writes Mazzotti. Encouraging his daughter’s studies beyond what was normal for a woman gave him an attraction worth coming to see. “By 1739,” Mazzotti writes, “the twenty-year-old could argue on philosophical and mathematical matters and had mastered the typically masculine technique of academic disputation.”

But “there is evidence from contemporary accounts that Agnesi loathed being put on display, even though her erudition earned her much admiration,” the Society writes. Shy and interested in becoming a nun, Agnesi was able to retire from the salon culture somewhat when her mother died and she took over running the house.

It was during this period that Agnesi wrote Analytical Institutions, which was at first intended to be nothing more than a text for her younger brothers to study. But the volume quickly grew: the final groundbreaking book was over one thousand pages long and took up two volumes.

Written with the support of leading mathematicians, the book brought together mathematical ideas from around the globe that Agnesi was able to read because of her gift for languages. For instance, the book “was the first tome discussing calculus that included the very different methods developed by co-inventors Isaac Newton and Gottfried Von Leibniz,” the Society writes.

The book also contained a description of a curve that had first been studied by groundbreaking mathematicians Pierre de Fermat and Guido Grandi in 1703. In Agnesi’s book, the curve has nothing to do with witches. Mathematics resource Wolfram Alpha explains the name change: "The name 'witch' derives from a mistranslation of the term averisera ('versed sine curve,' from the Latin vertere, 'to turn') in the original work as avversiera ('witch' or 'wife of the devil') in an 1801 translation of the work by Cambridge Lucasian Professor of Mathematics John Colson.

It’s particularly ironic that the work of Agnesi, who was so talented with languages, would suffer from a mistranslation that’s carried on into mathematics textbooks today: the curve is still used as a modeling and statistical tool 250 years later.

But in the public memory of Milan, writes Mazzotti in a separate article, her book has little to do with how she's remembered. Agnesi, whose shyness was pathological, wanted to retire from the world and was kept from doing so by her father, he writes. Four years after her book was finished, her father died and Agnesi did turn to doing "good works" rather than mathematics. She spent the rest of her life working to aid the poor and elderly, particularly women, and died in chosen poverty.

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