Maria Gaetana Agnesi  16 May 1718 – 9 January 1799 was an Italian mathematician, philosopher, theologian and humanitarian.

Born in Milan, to a wealthy and literate family Maria Gaetana was the third of 21 children. Her father, Pietro Agnesi, was not a professor, or even a mathematician as many sources suggest. He was born into a family of wealthy silk merchants. Evidence from family wills show that he was so wealthy he may never have worked in the family business at all. Pietro Agnesi enjoyed socializing with scholars and noblemen.  Her mother was the daughter of a prosperous silk manufacturer as were his two later wives. Each brought a substantial marriage portion with them an between them produced 21 children, 13 of whom survived to adulthood.

Maria’s father supported her learning but in keeping with tradition, he gave priority to the education of his sons. Soon Maria outstripped her brothers. When she was 10 she was recognised as a child prodigy along with her sister Theresa the musician. Maria could speak both Italian and French when she was five years old. When she was nine years old, she composed and delivered an hour-long speech in Latin to some of the most distinguished intellectuals of the day; and the subject was, of course, a women’s right to be educated.  By her eleventh birthday, she had added Greek, Hebrew, Spanish, German, and Latin to her arsenal of knowledge. With such a flair for languages, she was often referred to as the “Seven-Tongued Orator”. At the age of 12, she was found to be suffering from some undefined malaise, which may, of course, have been grief for her dead mother. Her ill health was automatically attributed to her excessive studying. Her doctors prescribed vigorous dancing and horseback riding as a remedy. However, this treatment did not work. Maria began to experience extreme convulsions, and on doctor’s orders, the vigorous exercise was curtailed. Henceforth Maria was encouraged to be moderate in all her pursuits.

There was no stopping Gaetana, though. By the age of fourteen she was studying ballistics and geometry and a year after that her father began to regularly include her in his gatherings which included some of the most learned men in Milan. Some believe he educated Maria, and her younger sister, Theresa, to increase his popularity among the upper classes of the town and get the family a coat of arms. He dearly wanted entry into the town senate, which had been dominated by a few key families for more than 400 years. His talented daughters were one of the town’s social and intellectual elite’s main sources of free entertainment, but they did not get him what he wanted.

At her father’s soirees, Maria would read papers on the most abstruse philosophical questions of the day. Records of these meetings are given in Charles de Brosses’ Lettres sur l’Italie and in the Propositiones Philosophicae, which her father published in 1738. In 1739 two Burgundian gentlemen who were passing through Milan on their ‘Grand Tour’ were invited to join Signore Agnesi and his family. They were Charles De Brosses, conseiller, at the parliament of Dijon and its future president and Germain Ann Loppin de Montmort, conseiller at the parliament of Bourgogne, who was also a mathematician. While touring the churches and libraries of Milan in July 1739 they met a friend of Agnesi, Count Belloni and were invited to attend a salon or conversazione at the Agnesi Palazzo. The evening was that of the 16th of July.

The travellers arrived tired and thirsty. Their first thoughts were that the palazzo’s exterior was disappointingly plain. Everything changed however when they got inside. They were then led through a large room decorated with gold and silver threaded tapestries that glistened in the candlelight. A grand portrait of the Holy Roman Emperor Charles VI and his consort for Elizabeth Christine gazed down on them from on high.  When the entered the salon they found it was the music room. The guests were an usual collection of aristocrats, clerics, city notables, and learned gentlemen and ladies. The travellers were treated to a gala evening spent amidst the elegant people and the Agnesi art collection which included a work by Titian and some drawings by Leonardo. As the travellers noted in their diaries (the precious source for this history), the evening centred on musical performances by Maria Gaetana’s two sisters and a series of Latin orations and debates on questions of natural philosophy by Gaetana herself. Agnesi was all of nine years old at the time of this performance.  The conversation began when Count Belloni rose and asked Gaetana a question in Latin. The question concerned the nature of tides. She began the discourse in the form an academic disputation first putting forward ideas then dismissing them. An hour later Brosses was invited to ask a question. He decided to ask her two questions. One on the subject of the nature of the soul and the body and one on the nature of light and colours. De Montmort’s question concerned the nature of circles and curves. When the discussion was over they were served fruit flavoured ices and her sister Theresa played the harpsichord to entertain the guests.

As urbane and worldly as the Palazzo Agnesi was it was also a proper Catholic home with a strong respect for traditional religion. Gaetana was well-schooled in the Catholic catechism, languages, mathematics and philosophy with no distinction made between religion and science. Her father’s intellectual sensibilities leaned toward those wings of the Catholic church that emphasized the harmonies between secular and religious life, and engaged teachers for his daughters who shared his values. This was not difficult in Milan as the city had a long history of independent thinking within the Roman Catholic world. ‘The Catholic Enlightenment’ that took place in Milan in Gaetana’s lifetime brought those Catholics devoted to progressive social and political reform and those devoted to certain progressive theological currents together. This religious and cultural background would shape Gartana’s intellectual and emotional life. Her unconventional scientific education gave her room to think outside the usual conventions of the age.

In 1740, aged twenty-two, Gaetana began a period of studies with Father Ramiro Rampinelli, professor of physics and mathematics at the monastery of Olivetani of San Vittore. Rampinelli was an Olivetan monk and chair of mathematics and physics at ‘ University of Pavia. With Rampinelli Maria started to study other notable mathematicians and to develop her mathematical skill by learning differential and integral calculus. Differential Calculus cuts things into small pieces to find how it changes. Integral Calculus joins (integrates) the small pieces together to find how much there is. These skills led to her main contribution to the world of mathematics, the formula for a curve called ‘versiera’ a term derived from Latin vertere, to turn. The name ‘versiera’ is from Guido Grandi (Quadratura circuli et hyperbolae, Pisa, 1703) and is a type 63 in Newton’s classification. Its principal use today is in astronomy and to show the distribution of energy in objects such as ocean waves.


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With the help of fellow mathematician and astronomer Jacopo Riccati, she drafted her first book, Institutions Analytical for use by the Italian Youth which was published in two volumes in 1748 and 1749. Dedicated it to Empress Maria Teresa, the Empress sent her a gift of jewels in return. In the book, she argues for women to be able to access the ‘sublime sciences’ yet she seems to have had no desire to enter the 18th-century world of female scholars who were generating some Europe’s best science and literature.  Her books were well received and translated into French in 1755 and English in 1801. Its two volumes were written in Italian not Latin, as was the custom for great mathematicians such as Newton and Euler. The vernacular made it more accessible to students. In 1750, she began teaching mathematics at ‘ University of Bologna and she remained a tutor there until she died in 1752. Pope Benedict XIV gave her a special dispensation to hold the rank of Professor but she did not take it up. Instead, she dedicated herself to charitable works. She opened a small hospital and worked there herself nursing the poor at the end of their lives. Gaetana was a devout Catholic and wrote extensively on the marriage between intellectual pursuit and mystical contemplation, most notably in her essay Il Cielo Mistico (The Mystic Heaven). She saw the rational contemplation of God as a complement to prayer.

Gaetana was caught at a unique point in time, between two contrasting and seemingly irreconcilable elements of the Catholic Enlightenment. Her heart’s desire was to maintain the traditions of the Catholic Church with its philosophy of verbal disputation and logic, but her intellect drew her towards the experimentation of physics and disputation based on mathematical reasoning. After suffering bouts of ‘unexplained’ illness for periods of her life that have been interpreted as epilepsy or neurosis, which may have been depression Gaetana reconciled herself to the study of algebra because it did not concern enquiry into the physical nature of reality. Thus she was able to save her sanity, maintain her Catholic view of a world and continue to work on her beloved mathematics.

Gaetana undoubtedly benefited from a brief opening of opportunity for a few talented women at the top of the church during the pontificate of Benedict XIV (1740-1758). She was the first woman to write a book on mathematics and the first to teach mathematics at a university. She was the first female professor of mathematics too although she never took up the post. Her lasting legacy is her wave, known as The Witch of Agnesi. Other honours included the dedication of one of the largest craters on the planet Venus, and a metal model of a versiera is embedded in the square outside the town hall of the city of Varedo as a tribute to their most famous inhabitant. The house she lived in until she died in 1799 is now a music academy. As a tribute to her genius, several Italian cities have dedicated a street in her honour. In Merate ( LC ) there is a high school specialising in science and languages named after her.

How this deeply religious woman became known as a witch is down to an error in translation. The name “Witch of Agnesi” was invented by Cambridge University mathematics professor John Colson when he translated Maria’s textbook from Italian into English. Colson gave the book it’s English title: Analytical Institutions. Unfortunately, when Colson translated Maria’s description of the curve, he apparently confused “la versiera” with “l’avversiera,” which means “wife of the devil.” Because of this mistake, Colson named the curve the “Witch of Agnesi” and the silly pun is still preserved in most English textbooks. Her curve appeared in the writings of Fermat (Oeuvres, I, 279–280; III, 233–234) and in the work of other prominent mathematicians.



The World of Maria Gaetana Agnesi, Mathematician of God By Massimo Mazzotti, JHU Press, 2012

Carmela Martino

Julia Herdman writes historical fiction that puts women to the fore. Her latest book Sinclair, Tales of Tooley Street Vol. 1. is  Available on Amazon 

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