TO WHILE away the last few days waiting for the new Harry Potter book, try your hand at this. The bell-shaped curve above is obtained by solving the equation y(a2 + x2) = a3. It is applied by physicists today to describe the distribution of the energy from stars at different X-ray and optical wavelengths, for example, and also the power dissipated in resonant circuits. The curve got its name from an 18th-century mathematician called Maria Gaetana Agnesi. But this doesn鈥檛 help us solve the greatest mystery about the curve: why is it called the Witch of Agnesi?
Agnesi was a child prodigy, born into a rich bourgeois Milanese family in 1718. Her publication record began at the age of 9 with a defence of education for women written in Latin (a translation of a tutor鈥檚 work).
As well as her native Italian, she mastered Greek, French, German, Spanish and Hebrew. Her forte was, however, philosophy and mathematics. She was exhibited as an intellectual curiosity in her father鈥檚 salon. At his behest, she displayed her wit, defending her 191 philosophical propositions (published in 1738) against the brains of Europe.
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How did she excel in mathematics? She brought order to an unruly field: differential calculus. Influenced by Leibniz rather than Newton, her book Instituzioni analitiche ad uso della gioventu italiana integrated methods and ideas from mathematicians throughout Europe. It was a hit. Agnesi鈥檚 world-class originality was intended to enlighten youth. It also brought her unwanted fame. The clarity of Agnesi鈥檚 work moved Pope Benedict XIV to offer her an academic post. Agnesi accepted the honour of the chair of mathematics at the University of Bologna, but seems never to have taken it up.
The city of her birth seemed a better place to be. Milan was a magnet for mathematicians: roughly contemporary with Agnesi was Paolo Frisi, who based his astronomy on Newton鈥檚 gravitational theory, and Tommaso Ceva, who worked on gravity, geometry and arithmetic.
Agnesi was notoriously shy. This could have stemmed from her dislike of being exhibited in an intellectual zoo. But it could have been a retreat from her 20 siblings. As the oldest child, she was put in charge after her father had buried his third wife. She clearly longed for peace, and is said to have lived in rooms well away from the others, where she helped out elderly impoverished women. She ended her life as one herself, having spent her wealth on charity.
None of this seems very witchy, so how did she become identified with the Witch of Agnesi? In her famous treatise, Agnesi discussed a cubic curve that was first devised by Guido Grandi in 1703. Grandi had described the curve as 鈥渧ersiera鈥� (turning), and Agnesi used the same name. The clarity of her description of this function and the bell-shaped curve it traces made it forever associated with her.
Where does the witch come in? The connection came about through a bizarre mistranslation. When translator John Colson converted Agnesi鈥檚 description into English he read 鈥渓a versiera鈥� as 鈥渓鈥檃versiera鈥�, mistaking it for l鈥檃vversiera, a witch. Thus the Witch of Agnesi was born.