The World of Maria Gaetana Agnesi by Massimo Mazzotti

March 18, 2022

In The World of Maria Gaetana Agnesi, Mathematician of God, Massimo Mazzotti, a historian of science, tells the fascinating story of a female mathematician in 18th century Italy.  Maria Gaetana Agnesi (1718-1799) was the daughter of a wealthy silk merchant in Milan.  Her father, who aspired to the nobility, eventually gave up his business and bought an estate.  He lived in a palazzo in Milan, where he held a salon frequented by the city’s intellectual elite.  Maria Gaetana was the oldest of his twenty-one children by three marriages.  Her younger sister, Maria Teresa (1720-1795) became a composer.  Some of Maria Teresa Agnesi’s works have recently been issued on CD.

Agnesi’s father believed in giving his daughters an education that was the equivalent of what boys and young men received at schools and universities.  He hired a series of private tutors, many of whom were associated with a movement known as the Catholic Enlightenment, for the brilliant Maria Gaetana.  Mazzotti goes into great detail on the Catholic Enlightenment, which favored religious reform and attempted to reconcile Catholic belief with modern philosophy and science.  To the philosophers and scientists of the Catholic Enlightenment, religion and science were not considered incompatible.  Agnesi herself was a devout Catholic all her life, and saw her mathematical and philosophical work as a way of glorifying God.  A key figure in the Catholic Enlightenment was the historian Lodovico Antonio Muratori.  I happened to know of him before reading Mazzotti’s book because Muratori was one of the first historians to write about Beatrice Cenci, the heroine of the novel I’m writing.  Pope Benedict XIV, who was pope for much of the time Agnesi was active, was a patron of the Catholic Enlightenment and supported Agnesi’s work.

Agnesi was a child prodigy who gave a Latin oration at the age of ten, and knew seven languages.  In addition to Italian, she knew Latin, French, Spanish, German, Greek, and Hebrew.  She did not know English, but there were a few books in English in her library, even though they may have belonged to her father.  Mazzotti includes a fascinating chapter on Agnesi’s library and what it contained.  The main focus of the collection was in theology, philosophy, and mathematics, but there were also many volumes of history, especially religious history, as well as literature.  Mazzotti mentions the fact that Agnesi owned many volumes of Latin and Italian poetry and drama, but there was only one novel in the whole collection: a French translation of Robinson Crusoe.  The collection reflected her interests and education.  Agnesi’s early education was in languages and literature, then she went on to study philosophy, theology, and mathematics.

Her father took advantage of her brilliance, and her sister’s musical talent, and made them the stars of his salon.  Visitors would come from many parts of Italy, and from France as well, to see Maria Gaetana participate in academic disputations, which was a form of entertainment in Enlightenment salons, and to see Maria Teresa play the harpsichord.  Sadly, when Maria Gaetana was fourteen, her mother died in childbirth, and her mother’s death devastated her.  Maria Gaetana suffered from a mysterious illness where she went into convulsions, and this lasted for several years.  No one knows for certain exactly what her illness was.  The stress of having to perform at her father’s salons probably contributed to it as well.  She was never comfortable with performing for guests.

After her mother’s death and her father’s remarriage, when the worst of her illness was over, Agnesi expressed the desire to become a nun, but her father rejected her plan because he wanted her to stay at home to teach her younger siblings.  She agreed, but only if her father allowed her to continue with her philosophical and mathematical studies.  Agnesi also told her father she wanted to limit the number of times she performed at his salons, and he agreed to her terms.  Mazzotti suggests that she did not really want to become a nun, and she used the possibility of joining a convent as a way to negotiate with her father.

By the time she was in her twenties, Agnesi decided that mathematics was the field she was going to study, and she learned about calculus from Ramiro Rampinelli, a monk who was one of the most prominent mathematicians of the time.  Her most significant achievement came in 1748, when she published her textbook on calculus.  It was meant to be an introduction to calculus, meant for ordinary people, not the intellectual elite, and written in Italian instead of Latin.  Her book was one of the first textbooks on calculus ever written and, of course, the first by a woman.  She wrote about both differential and integral calculus, and her book was largely based on Newton’s system, which was geometrically-based calculus, in contrast to Leibniz’s, which was algebraically-based.  She did not ignore Leibniz in her book, though, but her preference was clearly for Newton.  Agnesi’s most lasting discovery was a mathematical curve known as the “witch of Agnesi.”  As Mazzotti explains, the name came about from a mistranslation of Agnesi’s work into English, but no doubt there is some misogyny there, equating educated women with witches.  The name stuck, though, and Mazzotti says that the “witch of Agnesi” appears in just about every high school mathematics textbook.  I admit I don’t remember it, though, but it has been a long time since I took high school mathematics, so I have probably forgotten about it.

Agnesi’s book was a great success, and earned her praise from many of the prominent intellectuals of the time, as well as from the pope.  In 1750, she was appointed, at the pope’s suggestion, chair of mathematics at the University of Bologna, becoming the second woman ever to be appointed to a university professorship.  The first was Laura Bassi, a contemporary of hers, and the two of them admired each other very much.  Unfortunately, Agnesi’s illness recurred, and she was not able to accept the professorship.  She spent the rest of her life in seclusion, teaching the children of the poor.  Agnesi worked in her neighborhood hospital, and, after her father’s death, opened a branch of the hospital in her family’s palazzo.  In her later years, she helped to found a shelter for the poor and eventually moved from the palazzo to an apartment in the shelter.  She died in 1799 and was buried in a mass grave for the poor, even though there was a plaque to mark her grave site.

Mazzotti’s book is an excellent introduction to Agnesi and her world.  I have to admit that much of the discussion of 18th century philosophy and mathematics in the early chapters goes over my head, but I am sure that is because I don’t have enough knowledge in those areas to appreciate it.  The book is meant for advanced students.  It made me want to learn more about those areas.  For me, the best parts of the book were about Agnesi’s life, and the position of educated women in the society of the time.  In particular, the last chapter contains a lengthy discussion of what it meant to be an educated woman in 18th century Italy.  A university education was not strictly forbidden to women in Italy, as it was in the rest of Europe, but it was very unusual, and many scholars, including some of the key figures of the Catholic Enlightenment, thought only the daughters of noble and wealthy families should receive such an extensive education.  There was much misogynistic writing directed at educated women, but still, women had a better chance of an education in Italy at the time than they did in France or England.  Mazzotti also points out how unusual Agnesi’s position was in her time, as an unmarried, highly educated woman who was not a nun.  There were quite a few educated women in convents, particularly members of the Ursuline order, which was devoted to teaching, but, of course, they paid the price by being confined to the cloister for the rest of their lives.  Agnesi was definitely an exception in her time.  I highly recommend this introduction to a fascinating woman and mathematician.

The World of Maria Gaetana Agnesi, Mathematician of God is available from the Shapiro Science Library.