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The reluctant mathematician

Name: Maria Gaetana Agnesi
Nationality: Italian
Lived: 1718-1799
Fields: Mathematics
Claim to fame: Published the first book to discuss both differential and integral calculus

Shy and retiring from early childhood, Maria Gaetana Agnesi (1718-1799) sought the quiet life offered by religious devotion. But her father had other ideas for her and encouraged the development of her skills as a linguist, mathematician and philosopher. Agnesi devoted herself to the study of mathematics and, having set out to write a textbook to help teach the subject to her younger siblings, she published a work that was to make her famous across Europe.

Devoted daughter and sister

Maria Gaetana Agnesi was born on 16 May 1718, the eldest of the 21 children born to her father Pietro by his three wives. As she grew up, Agnesi was to play the combined role of housekeeper and tutor to her brothers and sisters and Pietro depended upon her steadying influence. The family was a wealthy one, having made its fortune in the silk trade, and Pietro was able to provide tutors of the highest calibre – young men of learning from the church – for Maria Gaetana and her siblings.
Agnesi excelled as a linguist from a young age; at only nine years old she published a translation into Latin of an elaborate discourse defending the right of women to access higher education and, by the age of 13, she had also mastered Greek, Hebrew, French, Spanish and German.

Neither ugly nor pretty

When Agnesi was around 15 years old, her father began to host gatherings in their home of the most learned men of the day. Although naturally reticent, Agnesi addressed these audiences, expounding on difficult philosophical questions. These meetings were recorded by the French writer, Charles de Brosses, in his Lettres sur l’Italie, describing Agnesi as “a girl of about 20 years of age, neither ugly nor pretty, with a very simple and sweet manner”. He went on to state that she expressed a particular interest in the work of Isaac Newton, but that she did not enjoy public discussion of this nature, “where for every one that was amused, 20 were bored to death”.
At about this time, Agnesi made it clear to her horrified father that she wished to enter a convent. He refused and begged her to stay at home. She eventually agreed to continue living in his house and care for him on three conditions: that she be allowed to go to church whenever she wished, that she could dress simply and humbly, and that she no longer had to attend balls, theatres and other “profane amusements”.

A publishing success

Although Agnesi’s wish to join a convent was not granted, from the age of 20 she began to live as if it had been. She shut herself away, avoiding society and devoting herself entirely to the study of mathematics and religious books.
In the field of mathematics, she was fortunate to benefit from the advice and teaching of a monk named Ramiro Rampinelli, a mathematician who had been a professor at the universities of Rome and Bologna. He encouraged Agnesi to write a book on differential calculus. She was enthusiastic about the idea and thought that such a work could be used as a textbook by her younger siblings. However, the resulting work would develop into much more. Instituzioni analitiche ad uso della gioventù italiana was published in Milan in 1748; it went on to be translated into French and English and brought Agnesi widespread fame.

Papal recognition

In 1750, Pope Benedict XIV read Agnesi’s work and was prompted to write to its author, saying that such a work would bring credit to Italy. Soon after this, the Pope went further, appointing her to the position of honorary reader at the University of Bologna. It is likely that Agnesi neither accepted nor rejected this offer – her name was added to the statutes of the university and remained there for 45 years, but it is thought that she never visited the city, or university, of Bologna.

The role she craved

The death of Pietro Agnesi in 1752 allowed his daughter to abandon her mathematical work and to live the life that she had longed for from a young age. Agnesi became the director of the Hospice Trivulzio and was able to devote herself to the study of theology and to charitable acts. Later, she would achieve her dream of joining the sisterhood of the ‘Azure’ nuns. By the time of her death in the sisterhood’s poorhouse on 9 January 1799, she had spent all of her wealth on charitable works.

Scientific achievements

Maria Gaetana Agnesi’s book Instituzioni analitiche ad uso della gioventù italiana was unique for a number of reasons. The work is considered to be the first  book to discuss both differential and integral calculus. It gave a clear summary of the state of knowledge at the time in mathematical analysis, bringing together examples from the works of a number of mathematicians in a systematic manner with Agnesi’s own analysis. Agnesi’s work gained popularity for its clarity of style and it was translated into French (1778) and English (1810). In the book, she discussed the cubic curve that has come to be known as the “witch of Agnesi”. Although this curve had been discussed before her time, it bears her name to this day, albeit, as a result of a mistake in the English translation, with this rather curious title.