AGNESI, MARIA GAETANA

(b. Milan, Italy, 16 May 1718; d. Milan, 9 January 1799)

mathematics. For the original article on Agnesi see DSB, vol. 1.

Agnesi was the first woman ever to publish a book of mathematics in her own name. The book, titled Instituzioni analitiche ad uso della gioventù italiana, appeared in Milan in 1748. In its two volumes Agnesi presented the principles and methods of algebra, Cartesian geometry, and calculus. Hers was among the first textbooks to offer such a complete introductory survey—and certainly the most accessible to beginners. The only other text published by Agnesi in her life was Propositiones philosophicae(1738), a collection of theses that, when she was twenty years old, signed the completion of her philosophical studies. This kind of publication was routinely expected from college students at the end of their course. Being a woman, Agnesi was prevented from accessing college; however, she carried out her training privately, under the supervision of eminent tutors. Agnesi also authored some writings of religious character, including a mystical treatise that remained unpublished. From 1752 onward she devoted her life to teaching young girls and to the assistance of the old and sick of her city, first at the Ospedale Maggiore and then, from 1771, at the Pio Albergo Trivulzio, a charitable institution she directed for almost thirty years.

Maria Gaetana Agnesi was born into a prominent Milanese family, which had accumulated remarkable wealth with the trade of wool and silk textiles. Pietro, her father, abandoned the trading activities of his ancestors and, by the time of Gaetana’s birth, was engaged in a difficult attempt to bring his family into the city’s aristocracy. Contrary to what was stated in the original entry, Pietro was not a university lecturer, nor had he any significant connection to the academic world. Gaetana’s exceptional education was entrusted entirely to private tutors, mainly local ecclesiastics, and should be understood within Pietro’s overall strategy of social enhancement. In the periodical gatherings at Palazzo Agnesi—or conversazioni, as these soirées were called—Gaetana performed in front of prestigious guests from all over Europe. Mainly she engaged in disputations with university lecturers over topics in natural philosophy and mathematics. On these occasions she defended the positions of the “moderns”— Isaac Newton, the Dutch experimental philosophers, and Italian natural philosophers such as Antonio Vallisneri— against the criticisms of scholastic and Cartesian philosophers. Together with her sister Maria Teresa, who was to become a renowned harpsichord player and composer, Gaetana provided Pietro with remarkable social visibility through the 1730s, just as he was pursuing a royal title and a coat of arms for his family.

Agnesi’s precocious talent for the study of languages, philosophy, and mathematics was always coupled with an intense religious piety. In fact her religiosity was nurtured by those same tutors who were supervising her philosophical and mathematical studies. These learned ecclesiastics were actively involved in an attempt to reform the theological, liturgical, and social features of contemporary Catholicism. Essentially they supported an antibaroque devotion, characterized by a more sober and rational set of practices. In opposition to contemporary Jesuit teaching, these reformers deemed necessary the introduction of the experimental sciences and modern mathematics in universities and religious institutions of higher education.

Agnesi herself would contribute importantly to this reformist current with her textbook, the first to be expressly designed to help young students to learn algebra and calculus. The distinguishing features of the book depend largely on its didactic purpose. Thus, for example, unlike the authors of other contemporary treatises and

articles on the techniques of calculus, Agnesi gave priority to the systematization of this diverse literature and to the clarification of the concepts she used, which was often achieved by relating them to the student’s most familiar intuitions. The Instituzioni were also shaped by Agnesi’s belief that the study of mathematics had particular relevance in the context of a truly Christian upbringing. The truths of geometry were exemplary in their certainty and assumed metaphysical relevance in the framework of a Malebranchian theory of knowledge of the sort she embraced. Agnesi was very clear about the priority of geometrical evidence over algebraic manipulation of symbols, hence her choice to present the most recent developments in calculus in purely geometrical terms and her emphasis on techniques such as the geometrical construction of equations. Throughout the book she keeps analytical formalism detached from mechanical and empirical considerations in order to preserve the simplicity, rigor, and evidence she held to be distinctive of the classical tradition in geometry. Unique among the texts on calculus that appeared in those years, Agnesi’s does not contain a single example of the application of its techniques to the solution of problems in experimental physics and rational mechanics. Analytic methods are presented as significant for the solution of geometrical problems and the study of curves interesting exclusively for their metric properties, such as the versiera, the curve most commonly associated with Agnesi’s name.

Following the publication of her book Agnesi reached the apex of her fame, and in 1750 she was offered a lectureship in mathematics at the University of Bologna through the personal intervention of the pontiff, Benedict XIV. Agnesi, however, never went to Bologna, convinced that her contribution to the pedagogy of mathematics was now concluded. Rather, she began devoting most of her time to teaching young girls from poor backgrounds to read, write, and count and to deepen her knowledge of religious literature. Agnesi also began volunteering at the great public hospital of Milan and soon opened the gates of her family palace to sick and infirm women who could not be assisted at the hospital. In 1752 the sudden death of her father freed her from her last commitments to the conversazione at the family palazzo. In 1771 Agnesi was nominated director of the female section of the Pio Albergo Trivulzio, a major charitable institution for the care of the sick and old in Milan. She ran it through the troubled years of the end of the century with her usual passion and determination. After bequeathing her inheritance to the city’s charitable institutions and to her relatives, Agnesi spent the last part of her life in poverty. She died in 1799 and was buried in a common grave off the city walls.

SUPPLEMENTARY BIBLIOGRAPHY

Findlen, Paula. “Maria Gaetana Agnesi.” In The Contest for Knowledge: Debates over Women’s Learning in Eighteenth-Century Italy, edited and translated by Rebecca Messbarger and Paula Findlen. Chicago: Chicago University Press, 2005.

Mazzotti, Massimo. “Maria Gaetana Agnesi: Mathematics and the Making of the Catholic Enlightenment.” Isis 92 (2001): 657–683.

Truesdell, Clifford. “Maria Gaetana Agnesi.” Archive for History of Exact Sciences40 (1989): 113–142.

Massimo Mazzotti