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Magic circle

Jo Gatoff looks at the life of Maria Agnesi, the 18th-century developer of the 'Witch's Curve'

Today our image of a woman mathematician is Carol Vorderman. There were, however, many women who contributed to mathematics before the present era of equal opportunities and Girl Power. Maria Agnesi, who died 200 years ago in 1799, produced original work in algebra, analytical geometry and calculus. In addition to speaking her native Italian, Maria was fluent in French by the age of five.

By the age of nine, she had also mastered Latin, Greek and Hebrew. She became an important mathematician who gave up her privileged life to devote herself to the care of the needy. Having donated all her wealth to good causes, Maria died in poverty aged 81.

Maria's father was a professor of maths, who frequently held gatherings for prominent intellectuals at his home. At one of these meetings, when she was only nine years old, Maria delivered a speech entirely in Latin, defending higher education for women. She regularly took part in debates concerning philosophical and scientific issues.

Maria decided that she would like to become a nun in 1739. Her father refused to allow this, but he did agree to three wishes: she would be allowed to dress simply and modestly, she could go to church whenever she wanted, and she would not have to attend balls or similar social occasions.

When Maria was only 21, her mother died, leaving her to look after her father and 20 brothers and sisters. She devoted the next 20 years to her own development in maths.

Maria's book, Instituzioni Analitiche (Foundations of Analysis), was published in 1748 and made her famous in the world of maths. It is a two-volume study of algebra, analytical geometry, calculus and differential equations. The book was dedicated to the Empress Maria Theresa of Austria, who sent her, in response, a crystal box set with diamonds, and a crystal ring. Maria was recognised by Pope Benedict XIV, who rewarded her with a gold wreath et with precious stones, and a gold medal. He also made her an honorary professor at the university of Bologna in 1750.

Her book is usually remembered for the development of a curve that, after 1801, was called the Witch of Agnesi. When this curve is plotted on a graph, it resembles a symmetrical wave which fits around the top of a circle. It was originally called a versiera - a word derived from the Latin word vertere, to turn - but versiera was also an abbreviation for the Italian word avversiera, or wife of the devil.

When John Colson, a professor of maths at Cambridge, translated Maria's book into English, he incorrectly translated the word versiera as witch. Which is how, from then on, the curve was known as the Witch of Agnesi.

After her father's death in 1752, Maria gave up maths and studied theology. She continued to live with her family but in a separate apartment, where she cared for a few poor sick people. When she needed money for her charitable work, Maria sold her gifts from Empress Maria Theresa, to a rich Englishman, and Pope Benedict.

In 1771 Prince Antonio Tolemeo Trivulzio gave his palace to be used as a home for the aged. Maria's duties included visiting and supporting the women there. Eventually, in 1783, she moved into the home as a residential care worker, devoting her last 28 years to this cause.

Maria died in 1799 and she was buried in a common grave for the poor with no elaborate tombstone.

Maria Agnesi has been honoured both as a mathematician and for her devotion to the poor. It is ironic that a woman so pious and devoted to the care of the impoverished should be remembered as the witch of Agnesi. Streets have been named after her in Milan (where she was born), and Monza in Italy. A school in Milan bears her name. Scholarships for underprivileged girls have been donated in her honour. Even 200 years after her death, Maria's life story is an inspiration.

Jo Gatoff teaches maths at Parrs Wood high school, Manchester

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