Maria Gaetana Agnesi

Italian mathematician and charity worker

• Born: May 16, 1718
• Birthplace: Milan (now in Italy)
• Died: January 9, 1799
• Place of death: Milan (now in Italy)

In her youth, Maria Agnesi advocated education for young women, in part by demonstrating her own impressive intellectual abilities. Her two-volume textbook on the calculus provided a complete synthesis of the mathematical methods developed during the Scientific Revolution. In her later years, she devoted herself to charitable work for the sick, poor, and aged.

Early Life

Maria Gaetana Agnesi (mah-REE-ah gah-ay-TAHN-ah ahn-YAY-zee) was born to a wealthy and literate Italian family, the oldest of twenty-one children. According to most accounts, her father, Pietro Agnesi Mariami, became a mathematics professor at the University of Bologna, but there is no record of this. He and her mother, Anna Brivia, recognized Maria’s abilities early and encouraged her to develop her intellect. Her special gift for languages was evident, as she could speak French fluently by the age of five. Impressively, at age nine she wrote a lengthy discourse in Latin on the importance of higher education for women entitled Oratio qua ostenditur artium liberalium studia femineo sexu neutiquam abhorreri (1727; an oration by which it is shown that the study of the liberal arts should not at all be abhorred by the female sex), which was printed at Milan. By the age of eleven, Maria was known as the Walking Polyglot and the Seven-Tongued Orator for her competence in Italian, French, German, Spanish, Latin, Greek, and Hebrew.

Maria’s father engaged leading university professors to be her tutors. Their home became a gathering place for the most distinguished intellectuals of the time, both Italian and foreign. Maria participated in most of these meetings, engaging the guests in abstract academic discussions. Her younger sister, Maria Teresa (b. 1720), was a composer, singer, and harpsichordist who often performed her music at these meetings while Maria Gaetana presented theses in Latin on a wide variety of scientific and philosophical topics and defended them in the native language of her questioners. By the age of fourteen, Agnesi was solving difficult problems in ballistics and geometry. At seventeen, she circulated a critical commentary on the Traité analytique des sections coniques (1696; analytical treatise on conic sections) by the French mathematician Guillaume de L’Hôpital.

Life’s Work

Although Agnesi had an attractive and agreeable manner, she was not eager to continue the public displays of her extraordinary learning. At the age of twenty, she expressed a desire to enter a convent. However, the death of Pietro Agnesi’s second wife gave her another opportunity to retire from public life by assuming responsibility for her father’s household and care for her twenty younger siblings. For the next two decades, she devoted herself to these duties along with the study of mathematics and the education of her younger brothers.

After her father’s meetings were discontinued, Maria published a collection in Latin of 190 of the theses she had defended as a girl in a book called Propositiones philosophicae (pb. 1738; philosophical propositions). The topics covered in this book indicate the breadth of her knowledge in the sciences and philosophy of her day, including mechanics, hydromechanics, elasticity, celestial mechanics, universal gravitation, chemistry, mineralogy, botany, zoology, logic, and ontology. The theses on these topics appear together with a plea for the education of women.

For the next decade, Maria concentrated on mathematics, culminating in the publication of her most important mathematical work as a text for her younger brothers. Instituzioni analitiche ad uso della gioventù italiana (1748; Analytical Institutions, 1801) consisted of two volumes of 1,020 pages plus 59 pages of figures engraved by Marc’ Antonio Dal Rè. Agnesi wrote the book in Italian rather than Latin to make it more accessible to young students. Her facility with languages enabled her to draw from a wide range of authors, producing the most complete synthesis of eighteenth century mathematics for at least the next fifty years. The second volume was later translated into French by Pierre d’Antelmy as Traités élémentaires de calculus (1775; elementary treatise on calculus), and the entire book was translated into English by the Cambridge mathematics professor John Colson and published in London in 1801 as Analytical Institutions.

The first volume of Analytical Institutions deals with the analysis of finite quantities, using algebra and geometry to construct and analyze geometric curves. The second volume develops differential and integral calculus and gives an introduction to the emerging topic of differential equations. It was the first text to give a systematic presentation of both differential and integral calculus, establishing the modern differential notation of Gottfried Wilhelm Leibniz over the more archaic “fluxions” of Isaac Newton. The English translation of 1801 introduced England to modern calculus notation.

One geometric curve discussed by Agnesi in Analytical Institutions has come to be uniquely associated with her name in an unusual but confusing way. She called this bell-shaped curve a versed sine or “versiera” (from the Latin vertere, meaning “to turn”). John Colson in his 1801 English translation confused this term with the Italian word avversiera, which means “witch.” Hence, this curve came to be known as the “Witch of Agnesi” in the English-speaking world.

Agnesi dedicated Analytical Institutions to Empress Maria Theresa of Austria, who rewarded her with a diamond ring and a letter in a diamond-encrusted crystal case. Pope Benedict XIV sent her a congratulatory letter with a gold medal and a wreath made of gold and precious stones. She was elected to the Bologna Academy of Sciences and commended by the French Academy of Sciences for producing the best book of its kind. Pope Benedict named Agnesi an honorary professor of mathematics at the University of Bologna in 1750, although there is no record of her teaching there.

After her father’s death in 1752, Agnesi turned increasingly to religious studies and charitable work. For the rest of her life, she devoted herself to the needs of the poor, starting with a small hospital in her home. During nearly forty years of charitable work, Agnesi gave away her inheritance to the poor, beginning with her diamond ring and crystal box from Maria Theresa, and even begged for money from others to provide for those in need. In 1771, she founded a charitable home for the aged with the Blue Nuns in Milan called Pio Albergo Trivulzio, acting as director of this hospice for several years. According to some sources, she took the blue habit of the Augustinian nuns before she died at the age of eighty.

Significance

Maria Gaetana Agnesi was the first woman to publish a book on mathematics in modern Europe. Her most important contribution was the publication of Analytical Institutions in 1748. This was the first comprehensive and systematic textbook covering both differential and integral calculus with a unified notation. It is the first surviving mathematical work written by a woman and the most valuable work in establishing the calculus for at least the next fifty years. It unified the ideas and methods of the greatest mathematicians of the Scientific Revolution, including the analytic geometry of René Descartes and the newly developed calculus of Newton and Leibniz, establishing the superior notation of Leibniz. She also led the way in applying the calculus to many original problems in geometry and physics.

In addition to her mathematical work, Agnesi lived an exemplary life of service. Although science had faltered to some extent after the condemnation of Galileo a century earlier, Agnesi contributed to the revival of scientific work in Italy and the associated Catholic Enlightenment. She was an early advocate of education for women and a champion of this cause in several publications. Her devotion to duty and her lifelong service to the poor and needy set a worthy example of Christian charity.

Bibliography

Alic, Margaret. Hypatia’s Heritage. Boston: Beacon Press, 1986. Focuses on the historical contributions of women in science, including a discussion of the work of Maria Agnesi.

Gray, S. I. B., and Tagui Malakyan. “The Witch of Agnesi: A Lasting Contribution from the First Surviving Mathematical Work Written by a Woman.” College Mathematical Journal 30, no. 4 (September, 1999): 258-268. This commemorative article on the two hundredth anniversary of Agnesi’s death discusses her life and the geometric curve named for her.

Mazzotti, Massimo. “Maria Gaetana Agnesi: Mathematics and the Making of the Catholic Enlightenment.” Isis 92, no. 4 (December, 2001): 657-683. Places Agnesi’s work in the context of the Italian enlightenment of the mid-eighteenth century.

Osen, Lynn M. Women in Mathematics. Cambridge, Mass.: MIT Press, 1974, 1995. Includes a chapter on Agnesi and her mathematical contributions.

Smith, Sanderson. Agnesi to Zeno: Over One Hundred Vignettes from the History of Math. Emeryville, Calif.: Key Curriculum Press, 1996. This book on historical developments in mathematics includes a one-page introduction to the life and work of Agnesi followed by questions and projects for math students.