Maria Gaetana Agnesi

Maria Gaetana Agnesi
Portrait from “LIVES AND PORTRAITS OF ILLUSTRIOUS ITALIANS”, LONGHI GIUSEPPE, BOSSI GIUSEPPE, VOLUME I, PADUA, 1812 / WIKIMEDIA PUBLIC DOMAIN
This month’s essay deals with one of the most important mathematicians and philosophers/theologians of the 18th century. It is important to note that this person was a woman who was competing in the very male-dominated sphere of mathematics, science, philosophy, and theology. These disciplines were certainly not supposed to be areas of concern for women, and many men practicing in these fields were hard-pressed to accept such an outstanding mathematical and philosophical mind of the opposite sex. However, they had to accept her and give her ideas an important place in the development of mathematical and philosophical/theological thinking.

She is considered the first woman in the Western world to have achieved a reputation in mathematics. This reputation is because she was the first to write a mathematics handbook discussing the new mathematical tools of differential and integral calculus. She was also the first woman appointed as a mathematics professor at a university (Bologna), although she never served in that position.

She devoted the last 40 years of her life to studying theology (especially patristics). She was a devout Catholic and she wrote extensively on the connection between the intellectual pursuit of science/math and mystical contemplation, most notably in her essay Il Cielo Mistico (The Mystic Heaven). She saw the rational contemplation of God’s order and work in the universe as a complement to prayer and contemplation of the life, death and resurrection of Jesus Christ. In addition to her intellectual studies and work, she was also an important humanitarian, helping the poor and downtrodden of 18th-century Italy.
ASSOCIATIONS: Mathematics
ADDITIONAL KEY INFO: Theology
Lived 1718-1799
COUNTRY OF ORIGIN: Italy

Early Years

Maria Gaetana Agnesi was born on May 16, 1718, in Milan, Italy (then part of the Habsburg empire) to a wealthy and literate family. Her father, Pietro Agnesi, was a silk merchant and ambitiously wanted to elevate his family into the Milanese nobility. In order to do so, he married Anna Fortunato Brivio of the Brivius de Brokles family in 1717. (This family was a Milanese/Hungarian family that was a branch of the noble Brivio family of Milan). Maria was born to this couple the following year. Pietro would eventually marry three times, and Maria thus became the oldest of 21 children.
Pietro Agnesi could afford high-quality tutors for Maria, and he provided her with the best available tutors, who were all young men learning from the Church. Maria was recognized early as a child prodigy; she could speak both Italian (the Tuscan dialect) and French at 5 years of age. By her 11th birthday, she had also learned Greek, Hebrew, Spanish, German, and Latin and was referred to as the “Seven-Tongued Orator.”
When she was 9, she published a Latin discourse in defense of higher education for women. However, it was not this composition that displayed her precocious talents to the world, as some biographers have claimed, but rather it was another article written in Italian by one of her tutors which Maria translated into Latin and delivered from memory to an academic gathering that was arranged by her father in his garden to display her intellectual talents.
At the age of 12, Maria suffered a mysterious illness that was attributed to her excessive studying and reading. To counter the effects of the intellectual rigor, she was prescribed vigorous dancing and horseback riding. This treatment did not work, and she began to experience extreme convulsions. So, the decision was made that she should pursue both her intellectual work and her physical exertions with moderation. By the time she was 14, she was studying ballistics and geometry.

Management of a Nimble Mind

When Maria was 15, her father began hosting regular gatherings of a circle of the most learned men from Bologna and from other countries. In these meetings, Maria spoke on various subjects, from logic and ontology to hydromechanics and universal gravitation. However, philosophy was one of her favorite subjects and she spoke at great length on it. These topics were usually addressed in fluent Latin, but when a foreign scholar would ask her complicated questions in his native tongue, she always answered and debated him in the same language he had used if she could speak that language.
Records of these meetings are recorded in Charles de Brosses’ Lettres sur l’Italie (Letters on Italy) and in the Propositiones Philosophicae (Philosophical Propositions) that her father had published in 1738, which recorded her final performance. This latter work consisted of a series of essays on philosophy and natural science containing 190 philosophical theses that Maria defended in disputes with the invited guests at that final meeting. De Brosses described a presentation that he attended:

“I was brought into a large fine room, where I found about thirty people from all countries of Europe, arranged in a circle and Mlle. Agnesi, all alone with her little sister, seated on a sofa. She is a girl of about twenty years of age, neither ugly nor pretty, with a very simple and very sweet manner. … Count Belloni, who took me, wanted to make a public show. He began with a fine discourse in Latin to this young girl, that it might be understood by all. She answered him well, after which they entered into a dispute, in the same language, on the origin of fountains and on the causes of the ebb and flow which is seen in some of them, similar to tides at sea. She spoke like an angel on this topic; I have never heard anything so pleasurable. … She is much attached to the philosophy of Newton, and it is marvelous to see a person of her age so conversant with such abstract subjects. Yet however much I was amazed at her learning, I was perhaps more amazed to hear her speak Latin with such purity, ease and accuracy…” (quoted in Famous Scientists.org, op.cit.)

It might look as if this were an extremely distasteful affair, with Maria’s father showing off his daughter’s intellectual brilliance like a stage act. To some extent, this probably was the case, but it is fair to say that shows of this type were relatively common at the time. (Consider Mozart’s father showing off the composing and performing talents of his very young son, Wolfgang Amadeus). Although Maria always obeyed her father’s wishes, she was also very shy and did not really relish being put on display or asked to talk in front of a group.

A Mentor

Besides doing her own lessons and performing, she was also saddled with the tasks of educating her numerous siblings and helping care for the household. These tasks kept her from doing what she longed to do which was to enter a convent and become a nun. When she asked her father to send her to the convent, he refused. Horrified that his special child should want to leave him, he begged her to change her mind. She agreed to continue living in his house and caring for him on 3 conditions: that she be able to go to church whenever she wanted, that she be able to dress simply and humbly, and that she be able to abandon theaters, balls, and profane amusements. Thus, she was allowed to live in semi-retirement in an almost convent-like setting and devote herself entirely to the study of mathematics.
In 1739, after she had read the Traité Analytique des Sections Coniques (Analytical Treatment of Conic Sections) by the Marquis Guillaume de l’Hôpital, she wrote a commentary on it that was never published. Those who saw it in manuscript form were greatly impressed by it and highly praised her quality of analysis. Learning mathematics, especially higher mathematics, without proper instruction is an almost impossible task, and only a few mathematicians have ever achieved great things without some tutoring in the subject. Maria was fortunate in her bid to learn mathematics when she was introduced to Ramiro Rampinelli, an Olivetan monk who was one of the most notable Italian mathematicians of the time. He had been a professor at both Rome and Bologna, and, after he arrived in Milan, he became a frequent visitor to the Agnesi house. After reading her commentary on de l’Hôpital’s work, he became impressed by her knowledge and excitement about mathematics. He became Maria’s tutor, and she studied the new mathematics of both differential and integral calculus with him.
Maria understood the debt she owed to Rampinelli, and in the preface to her book <strong>Instituzioni Analitiche ad Uso della Gioventù Italiana</strong> (Analytical Institutions—or Foundations– for the Use of Italian Youth) she wrote: “With all the study, sustained by the strongest inclination towards mathematics, that I forced myself to devote to it on my own, I should have become altogether tangled in the great labyrinth of insuperable difficulty, had not [Rampinelli’s] secure guidance and wise direction led me forth from it …; to him I owe deeply all advances (whatever they might be) that my small talent has sufficed to make.”

Her Contributions to Mathematics

This was Maria’s most famous work, published in 1748, in two lengthy volumes. It provided a remarkably comprehensive and systematic treatment of algebra (volume 1), and analysis needed to understand the new developments in mathematics, such as integral and differential calculus (volume 2). It is in this work that one can find a discussion of the Agnesi curve, a cubic curve that had been studied and constructed earlier by Pierre de Fermat and Guido Grandi.
In 1718 Grandi had given the curve the Latin name versoria (turning in every direction), which the curve does do. Since it was also a name given a rope that turns a sail on a boat, he named the curve because its shape reminded him of this rope. Grandi called the curve in Italian versiera, translating the Latin term versoria. In fact, Maria quite correctly states in her book that the curve was called in Italian la versiera. The problem with the name arises from the fact that the term la versiera began to refer to a “she-devil” or “witch.” It was taken from the Latin adversarius, which was an alias for “devil” (i.e. adversary of God). Future translations and publications of the Instituzioni Analitiche from the Italian carried forward the latter meaning either as a translation error or possibly as a pun. The curve has thus become known as the “Witch of Agnesi.” (Read more about this mathematical concept on Wikipedia)
The work was written and published in Italian rather than in Latin, which one would have expected for a scholarly work such as this. However, by writing in Italian, Maria showed that she was truly interested in demonstrating algebra and calculus to Italian youth who might not have been fluent in Latin (for example, her younger siblings). Another distinction about this work that separates Maria from other mathematics writers: at that time, most people considered calculus to be important because of its utility to solving physics problems (it was the “language” of physics), and most contemporary calculus books were more or less collections of physics problems solved by applied mathematics. Maria was interested in calculus as an intellectual pursuit for its own sake, as a way to hone the logical faculties of the mind. Her book was one of the first that did not focus on the physics applications of calculus. Despite all of these differences, and despite the fact that it was written by a woman, the work gained the respect of mathematicians around Europe as an unusually clear treatment of the subject.

 

maria gaetana agnesi elder
The elder Maria Gaetana Agnesi (public domain)

Her Elder Years

After the publication of Analytical Institutions, Maria gradually retreated from the study of mathematics. However, Pope Benedict XIV wrote to Maria saying that he had studied mathematics when he was young man and was very impressed with her work, seeing that it would bring credit to Italy and to the University of Bologna. So, in 1750 he offered her an appointment as Professor of Mathematics, Natural Philosophy, and Physics at the University of Bologna. However, she never “professed”, nor did she ever visit Bologna during her lifetime, although she held the position there until her death. She was the second woman ever to be granted a professorship at a university, Laura Bassi (see my essay on Bassi in a previous Bulletin) being the first. Benedict XIV also appointed Bassi to her position at Bologna.
Pietro Agnesi died in 1752, and with that, Maria became free to carry out her long-cherished goal: to study her favorite subject, theology, especially a study of the Fathers of the Church. She also devoted herself for the next 47 years to the service of the poor, the homeless, and the sick. She used her father’s house for a while, turning it into a hospital for the sick. She gave away the gifts she had received over the years from her work in mathematics. And when this was gone, she begged for money to continue her work with the poor. Eventually, she established several houses throughout Milan, and she became the director of the women’s section of the Pio Albergo Trivulzio, (Pious Hotel Trivulzio, commonly known as Baggina) which was a shelter for the poor and sick that she founded in 1783.
Maria Gaetana Agnesi died in total poverty in Pio Albergo Trivulzio in Milan on January 9, 1799, at the age of 80. She had long suffered from dropsy (known today as edema); she finally succumbed to the underlying cause of the disease, most probably congestive heart failure. She was buried in Cimitero Monumentale di Milano (Monumental Cemetery of Milan) in a pauper’s common grave with 15 others who tended the poor and the sick.

Assessment

Maria Gaetana Agnesi is considered the first woman to attain fame as a mathematician, although that role ended fairly early and was replaced for the bulk of her life doing her charitable works. Her religious fervor can seem strange to our modern sensibilities since we often think of science and religion as conflicting. However, many of the important figures in European science history, especially before the 19th century, were Jesuits or members of other religious orders. Newton himself, in between inventing calculus and revolutionizing physics, wrote treatises on alchemy and religious topics, including hidden messages in the Bible. In Maria’s day, it was thought that intellectual pursuits could be a form of devotion to God. She certainly espoused this idea. She felt that deeply studying a subject like calculus was a form of prayer.
In later life, her religious writing turned mystical. However, when she was most active in mathematics, her approach to religion was more intellectual and rational. As her religious practice became more mystical, she still saw intellect and passion as two complementary parts of a religious life. “The human mind contemplates [the virtues of Christ] with marvel,” she wrote in an unpublished mystical essay, “the heart imitates them with love.”
Reading her story, one gets the sense that Maria was straining against the limitations of a society that still could not accept female scholarship and agency. But within the rigid confines of her position in the world, she was able to carve out her own path. She was neither a nun, nor a wife and mother. She was respected by society for both her mathematical skills and her charitable work as a lay Catholic woman. She both acquiesced in and rebelled against her father’s wishes for her. As Prof. Paula Findlen has written: “To us she seems so conservative, so not modern, and certainly not radical, but maybe that’s just the limits of our own understanding of her world.” (Quoted in Lamb, op.cit.)

Adapted by James J. Botiano, PhD from:

“Maria Gaetana Agnesi: Italian Mathematician.” Encyclopedia Britannica website
“Maria Gaetana Agnesi.” Famous Scientists.org website
“Maria Gaetana Agnesi Biography: First Woman to Write a Mathematics Handbook and the First Woman Appointed as a University Mathematics Professor.” The Famous People.com website
Lamb, Evelyn. “The 18th-Century Lady Mathematician Who Loved Calculus and God.” Smithsonian Magazine website, May 16, 2018
Mazzoti, Massimo. “Maria Gaetana Agnesi: The Unusual Life and Mathematical Work of an Eighteenth-Century Woman.” Isis, Vol 92 (2001), pp. 657-683
O’Connor, J.J. and Robertson, E. F. “Maria Agnesi.” University of St. Andrews (Scotland) School of Mathematics & Statistics website
Wikipedia.com website
Picture of James J. Boitano, PhD

James J. Boitano, PhD

​James J. Boitano, PhD, is the author of our history and culture feature "Il Professore". He taught for 36 years at Dominican College/University in San Rafael, California and retired as Professor Emeritus of Political Science and Humanities and Dean Emeritus of Arts and Sciences. Jim also served on the Marin Symphony Board of Directors for 15 years, including two years as President.

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