A mathematical curve is called "The Witch"—but only because of a mistranslation. The woman who discovered it in 1748 was a child prodigy who spoke 7 languages by age 11, wrote the first comprehensive calculus textbook, and became only the second female university professor in history.
This is the story of Maria Gaetana Agnesi—the brilliant mathematician whose work was so advanced that a translation error gave one of her curves an ominous name it never deserved.
Maria Gaetana Agnesi was born on May 16, 1718, in Milan, Italy, into a wealthy family. Her father, Pietro Agnesi, was a mathematics professor and silk merchant who recognized his daughter's extraordinary intellect early.
By age 5, Maria was fluent in French. By age 11, she had mastered seven languages including Latin, Greek, Hebrew, Spanish, German, and French, in addition to her native Italian.
She wasn't just learning languages for social grace. She was preparing to understand the world's accumulated knowledge—because in the 18th century, most advanced texts were written in Latin or other European languages.
At age 9, she delivered a Latin speech arguing for women's right to education. At 9 years old.
Her father, unlike most men of his era, supported her intellectual development. He hired the best tutors available. He encouraged her studies in mathematics, philosophy, and the sciences.
But he also hosted elaborate salons where young Maria was displayed like a curiosity—a brilliant child performing complex mathematical demonstrations and engaging in scholarly debates for the entertainment of Milan's intellectual elite.
Maria hated it.
She was shy, deeply religious, and wanted nothing more than to join a convent and dedicate her life to God and charitable work.
Her father made her a deal: Continue your studies, participate in the salons, and you can live a more religious life at home.
Maria agreed. And she channeled her intellect into something remarkable.
Maria was the eldest of 21 children (from her father's three marriages). As the oldest, she took responsibility for educating her younger siblings, particularly after her mother's death.
This experience shaped her philosophy: mathematical knowledge should be accessible, not locked away in incomprehensible Latin texts that only elite scholars could read.
In 1748, at age 30, Maria published "Instituzioni analitiche ad uso della gioventù italiana" (Analytical Institutions for the Use of Italian Youth).
This wasn't just another math book. It was revolutionary.
The book was over 1,000 pages and covered algebra, geometry, calculus, and differential equations—essentially everything known about mathematical analysis at the time. It was comprehensive, clearly written, and methodical.
But most importantly, it was written in Italian, not Latin.
This single choice made advanced mathematics accessible to a much wider audience. Students who couldn't master Latin could now learn calculus in their native language.
The book became hugely influential across Europe. It was translated into French and English. Mathematicians praised its clarity and completeness.
And in this book, Maria described a mathematical curve with specific properties—a bell-shaped curve that she called "versiera," from the Latin "vertere" meaning "to turn."
Here's where the mistranslation happened.
When the book was translated into English in 1801, the translator, Cambridge professor John Colson, confused "versiera" with "avversiera"—an Italian word meaning "wife of the devil" or "witch."
So the curve became known in English as "The Witch of Agnesi."
The name stuck. To this day, mathematics students around the world learn about the "Witch of Agnesi"—not because there's anything sinister about it, but because of a translation error made 53 years after Maria published her work.
The curve itself is actually quite useful. It appears in probability theory, describes the Cauchy distribution in statistics, and has applications in physics.
But Maria Agnesi never called it a witch. She never intended any such association.
In 1750, Pope Benedict XIV was so impressed with Maria's work that he appointed her to the chair of mathematics and natural philosophy at the University of Bologna—making her only the second woman ever to hold a university professorship (after Laura Bassi, also at Bologna).
It was a remarkable honor.
But Maria never actually taught there. Her appointment was largely honorary, and she remained in Milan.
Why? Because by this point, Maria had achieved her real goal.
After her father's death in 1752, Maria finally withdrew from academic life entirely. She devoted the rest of her life to religious study and charitable work, particularly caring for the sick and poor.
She sold her possessions, gave the money to charity, and eventually became the director of a hospice for elderly women in Milan.
She lived simply, worked tirelessly helping others, and never published another mathematical work.
Maria Gaetana Agnesi died on January 9, 1799, at age 80, having spent the last 45 years of her life in religious service rather than mathematics.
Her mathematical legacy was largely forgotten for decades. The "Witch of Agnesi" was the only thing that kept her name alive—ironically, through a mistranslation that misrepresented her work.
But Maria Agnesi's story matters for several reasons.
First, she proved that women could master the highest levels of mathematics at a time when most believed women were intellectually inferior. Her work was so clearly excellent that even skeptics had to acknowledge her brilliance.
Second, she pioneered accessible education. By writing in Italian instead of Latin, she democratized mathematical knowledge. She believed education should serve students, not exclude them through language barriers.
Third, she lived according to her values. Despite fame, honors, and opportunities, she chose a life of service over a life of acclaim. She achieved academic greatness, then walked away to help the poor.
And finally, her story reminds us how fragile historical memory can be. One of the most important mathematicians of the 18th century became known primarily through a mistranslation, while her actual contributions were overlooked.
Today, Maria Gaetana Agnesi is finally being recognized properly. Her textbook is acknowledged as groundbreaking. Her role in making mathematics accessible is celebrated. Universities and institutions honor her contributions to education and science.
The "Witch of Agnesi" curve is still called that—the mistranslation is too embedded in mathematical tradition to change now.
But at least we know the truth: there was no witch, just a brilliant woman who mastered seven languages by age 11, wrote the first comprehensive calculus textbook in a modern language, became only the second female university professor in history, and then gave it all up to serve the poor.
Maria Gaetana Agnesi. Born 1718. Died 1799.
Child prodigy. Mathematician. Professor. Servant of the poor.
Her curve got the wrong name. But her legacy deserves to be remembered correctly.
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