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**Science Discussion Forum / Maria GaÃ«tana Agnesi and her witch**

« **on:**May 30, 2012, 12:38:12 PM »

**Maria GaÃ«tana Agnesi (1718â€“1799)**

Italian Mathematician and Philosopher

Agnesi (pronounced ahn-YAY-zee or anyesi) was born in Milan, Italy. By the time she was 5 years old, she could speak both Italian and French. Her father was a professor of mathematics in Bologna, and Agnesi enjoyed a childhood of wealth and privilege. Her father provided her with tutors, and she participated in evening seminars, speaking to the guests in languages as varied as Latin, Greek, Hebrew, and Spanish.

In her teens, Agnesi mastered mathematics. She became a prolific writer and an advocate for the education of women. After her mother died, Agnesi managed the household of eight children, and educated her brothers. Her father remarried and after her stepmother died, Maria became housekeeper for twenty siblings.

Agnesi continued studying mathematics, mostly at night, and often to the point of exhaustion. In 1748 her mathematical compendium, Instituzioni analitiche ad uso della gioventÃ¹ italiana (Analytical Institutions), derived from teaching materials she wrote for her brothers, was published in two volumes. In this work, Agnesi had not only written clearly about algebra, precalculus mathematics, differential calculus, and integral calculus, but she had also added her conclusions and her own methods. Analytical Institutions remains the first surviving mathematical work written by a woman.

So successful was Agnesiâ€™s textbook that it became the standard text on the subject for the next 100 years. Her book was studied and admired not only in Agnesiâ€™s native Italy but also in France and Germany, and was translated into a number of other languages.

In his 1801 English translation of Agnesiâ€™s work, John Colson, the Cambridge (England) Lucasian Professor of Mathematics, made the mistake of confusing the Italian word for a versed sine curve, aversiera, with another Italian word for witch or wife of the devil, avversiere. Although 200 years have passed, the curve Colson misnamed the â€œWitch of Agnesiâ€ still bears that name in many calculus texts as an illustration of an â€œevenâ€ function with a â€œmaximumâ€ value. For a = 2, for example, the maximum value of y will be 2. The curve illustrates many basic concepts in calculus.

Witch of Agnesi

**Recognition**

Agnesi was recognized during her lifetime with election to the Bologna Academy of Science. The Pope at the time was interested in mathematics and in 1750 made certain that Agnesi was invited to be an honorary lecturer in mathematics at the University of Bologna. However, Agnesi turned down the appointment and instead adopted a religious life, spending much of her time working among the elderly poor and sick women of Milan.

Although a hospice Agnesi founded has become famous throughout Italy, and Italian streets, a school, and scholarships have been named in her honor, Agnesi is perhaps best known today for her contributions to mathematics.

**References**

**Maor, E.**

*Trigonometric Delights*, Princeton University Press, 1998

**Brandenberger, Barry M. Jr.**(editor in chief)

*Mathematics The Macmillan Science Library Volume 1-4*, Macmillan Reference USA, Thomson/Gale, 2002.

**Bradley, M. J.**

*Pioneers in Mathematics The Age of Genius 1300 to 1800 Vol. 2*, Facts on File, 2006.