Maria Gaetana Agnesi (1718–1799) is mentioned in most histories of mathematics. The main reason for that is simply that she was one of first women to be active in mathematics in Early Modern Europe. She wrote what we would now describe as the first mathematics text book, which covers much of mathematics, from elementary material up through what was then the very new subject of calculus. One of the curves she discusses in her book, “la versiera,” is often called “The Witch of Agnesi” as a result of a misreading: “l’aversiera” would have meant “the witch.”
I was very happy to hear that there was finally going to be a full-length biography of Agnesi in English. (In fact, there are now two: a much longer scholarly work on Agnesi by Antonella Cupillari was published April 2008.) The treatment of Agnesi in the history books is usually quite brief. Most of them mention that she was the oldest of a wealthy and extremely large Italian family (21 children). Unfortunately, some of these books go on to state and that she wrote her text, Instituzioni Analitiche ad Uso della Gioventù Italiana (1748) to help her younger brothers learn mathematics. Nothing could be further from the truth.
A child prodigy, Agnesi was a star of the “conversazioni” of Milan, which were staged scholarly discussions attended by the upper class. Her prowess encompassed languages, especially Latin, the classical authors and philosophers, natural history, and religion, and her performances at the “conversazioni” were popular.
Agnesi's interest in what we would now term pure mathematics, particularly the new field of differential and integral calculus, led her to read l'Hospital’s 1707 account of the differential calculus. She felt it was an important work, but not accessible nor clear enough for those just learning the subject. So she endeavored to write an introduction to the work for young readers. This project grew into a commentary on the work that would clarify and elaborate certain sections. Eventually her commentary on l'Hospital grew into a full length book that provided a systematic introduction to algebra, analytic geometry and calculus. Thus her Instituzioni Analitiche became the first mathematics text book in the modern sense.
While today Agnesi is known mostly for her mathematics, in her time she was known even more for her religious devotion. After her father’s death, she left the salons and went into a convent; dying in poverty at the Catholic charitable hospital she directed and lived at for the second half of her life.
Mazzotti’s book on Agnesi is very well written and I enjoyed it and learned quite a lot from it. However, it is not primarily a biography of Agnesi, and especially not of Agnesi the mathematician. Rather, it is a study of the role of the Catholic enlightenment and the Counter Reformation on education and pedagogy in late 17th and early 18th century northern Catholic Italy, in which Agnesi is used as a case in point. To be frank with the reader of this review, I know little of the Catholic enlightenment, the Counter Reformation, history of 17th century northern Italy, nor the philosophers and religious thinkers pertinent to this work. Therein lies the reason why I learned so much by reading this book. After reading it, I feel that I have a much clearer picture of Agnesi, the child prodigy, but not of Agnesi the mathematician.
As noted above, this book focuses on effects of the Catholic enlightenment on education, both in the colleges and in private schools, focusing on Angesi’s era and locality. Her mathematics is not discussed, only the motivation for the writing of her text. Mathematics in general is discussed briefly to put the significance of her text in context.
I would recommend this book to any reader, not for the insight into the history of mathematics it might provide, but for the portrait of a person who personified a religious and philosophical outlook particular to a specific time and place in history. Though localized, her story sheds light on the shifting stage of politics, religion and education of the 17th century.
Agnesi represents a moment of progress in the enfranchisement of women in the sciences and society in general. Though that step forward was later withdrawn, we are the inheritors of the progress that she inspired.
Amy Shell-Gellasch is a Faculty Fellow at Pacific Lutheran University in Tacoma, WA. She is actively involved with the MAA and its History of Mathematics SIGMAA as chairperson to several committees. She enjoys researching and promoting the use of history in the teaching of mathematics through editing books and organizing meetings. She received her bachelor’s degree from the University of Michigan in 1989, her master’s degree from Oakland University in Rochester, Michigan in 1995, and her doctor of arts degree from the University of Illinois at Chicago in 2000.