Agnesi, Maria Gaetana (1718–1799)

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Agnesi, Maria Gaetana (1718–1799)

Italian mathematician credited with calculating the bell-shaped curve known as the "Witch of Agnesi" and the first woman in Europe to distinguish herself in the field of mathematics. Name variations: Agnese. Born Maria Gaetana Agnesi on May 16, 1718, in Milan, Italy; died on January 9, 1799, in Milan, Italy; daughter of Pietro Agnesi (a wealthy merchant with ties to the University of Bologna) and Anna Fortunata (Brivio) Agnesi ; sister of Italian composer Maria Teresa Agnesi (1720–1795); tutored privately; no formal education; never married; no children.


Gold medal and a gold wreath adorned with precious stones presented by Pope Benedict XIV in honor of her publication of Instituzioni Analitiche(1749); Crystal box with diamonds and a diamond ring given by Empress Maria Theresa of Austria to whom Instituzioni Analitiche was dedicated (1749).

Participated in debates at her father's house with learned guests from the age of nine until 1739, when she withdrew from public life to concentrate on the study of mathematics; member of Academia della Scienze (Bologna); published Instituzioni Analitiche (Foundations of Analysis), a systematic compilation of developments in algebra, calculus, differential equations and analytic geometry (1748); appointed by Pope Benedict XIV as honorary chair of Mathematics and Natural Philosophy at the University of Bologna (1750–52); devoted herself to the study of theology and to charity work (after 1752); made director of women at Pio Instituto Trivulzio (1771), where she took up residence (1783) and lived until her death (1799).

Maria Gaetana Agnesi, one of the earliest pioneers in the field of mathematics, was the oldest of 21 children of Pietro Agnesi, a wealthy merchant who prized culture and learning and moved among the highest circle of the Milanese intelligentsia. Maria's mother, Anna Fortunata Brivio, died in 1732 after giving birth to eight children; Pietro remarried twice.

Maria Gaetana exhibited great potential for learning from early childhood. By the age of five, she spoke French fluently, and by the age of eleven she could converse in Latin, Greek, German, Spanish, and Hebrew. Pietro Agnesi used his wealth and influence to secure for Maria the finest tutors available in Italy, including Carlo Belloni and two future university professors, Francesco Manara (in Pavia) and Michele Casati (in Turin). After 1740, Maria studied almost exclusively with Ramiro Rampinelli, a professor of mathematics at the University of Pavia.

From the time Maria was nine years old, Pietro put her on display at his "academic evenings," during which he hosted a gathering of local celebrities and learned men from all over Europe. At age nine, Maria presented, in Latin, a scholarly address defending the study of liberal arts by women. Typically, at these gatherings Maria would recite a series of theses in Latin and engage distinguished guests in debates on mathematics, logic, mechanics, chemistry, botany, and a variety of other scientific topics. Visitors to Pietro Agnesi's home were deeply impressed by Maria's linguistic fluency and the breadth of her knowledge. Monsieur De Brosses, first president of the parliament of Dijon and a member of the Royal Academy of Inscriptions and Belles Lettres of Paris, called her facility with languages "prodigious" and described her usage of Latin as "with such purity, ease and accuracy that I do not recollect to have ever read any book in modern Latin that was written in so classical style as that in which she pronounced these discourses." He recalled that later in the evening "the conversation be came more general, every one speaking to her in the language of his own country, and she an swering him in the same language."

Maria Gaetana's sister, Maria Teresa Agnesi , showed an early predilection for music and was given lessons in the harpsichord by her father. In between Maria Gaetana's discourses, Maria Teresa often entertained the assembly by playing her own compositions. In 1738, Maria Gaetana compiled 190 of her defended theses in a work entitled Propositiones Philosophicae.

As Maria Gaetana neared adulthood, she expressed a strong preference for studies in mathematics, geometry, and ballistics. Always shy and retiring, she began to express displeasure at being put on display in her father's soirees. When she was 20, she declared her desire to enter a convent, preferably that of the Blue Nuns, an Augustinian order that earned their nickname because of the color of their habits. When her father objected to her desire to take the veil, Maria struck a compromise wherein Pietro agreed to excuse her from public display, to allow her to dress simply and modestly, and to attend mass whenever she desired. Maria thereafter remained at home and dedicated the next decade of her life to the study of mathematics.

The result of Agnesi's systematic study of the new mathematical discoveries of the 17th and 18th centuries was the publication of the Instituzioni Analitiche (Foundations of Analysis). A two-volume work of over 1,000 pages, the Instituzioni Analitiche was a compilation of the most recent developments in the study of algebra, analytic geometry, calculus, and differential equations. The first volume dealt with finite processes, while the second concentrated on infinitesimal analysis. Agnesi supervised the publication of the Instituzioni Analitiche, which was printed in late 1748 on presses installed in the Agnesi house. It was published in Italian, instead of the more traditional Latin, in an effort to encourage its study by the gioventu (youth) and to avoid the necessity of translation.

Although Agnesi intended the Instituzioni Analitiche to be a compilation of previous discoveries rather than a presentation of new theories, the process of weeding through and organizing such a large mass of material prompted her to include some of her own theories and developments. She described her attempts to put the material into its "natural order," although much of it was "scattered here and there in the works of many authors, and principally in the Acta of Leipzig, in the Memoires of the Academy of Paris and in other journals." She modestly admitted that "in the act of handling the various methods, there occurred to me several extensions and a number of things, which by chance are not without novelty and originality."

Despite the publication of several of her own discoveries, the "discovery" with which Agnesi has been popularly accredited was actually developed earlier by both Pierre de Fermat and Isaac Newton. It is the curve known in English as the Witch of Agnesi, so called because of a mistranslation of the word versiera, derived from the Latin word versoria (a rope that guides a sail), which was translated by the English scholar John Colson as the Italian word for "female goblin or witch." The Witch of Agnesi is a bell-shaped curve, which she described using the equation x(a2+y2)=a3, where the x-axis is vertical and the y-axis is horizontal:

In the Instituzioni Analitiche, Agnesi used the curve as an exercise in analytic geometry, and she utilized algebraic formulae to illustrate the method of deriving points of inflection on the curve.

Agnesi's Instituzioni Analitiche won immediate acclaim within the academic community. The French Academy of Sciences proclaimed: "The work is characterized by its careful organization, its clarity, and its precision. There is no other book, in any language, which would enable a reader to penetrate as deeply, or as rapidly, into the fundamental concepts of analysis. We consider this treatise the most complete and best written work of its kind." The Academy subsidized the translation of the second volume into French in 1749. The entire work was later translated into English by John Colson, Lucasian professor of mathematics at Cambridge University, who "found her work to be so excellent that he was at the pains of learning the Italian language at an advanced age for the sole purpose of translating her book into English, that the British Youth might have the benefit of it as well as the Youth of Italy." The English edition was published in 1801.

Agnesi dedicated the Instituzioni Analitiche to Empress Maria Theresa (1717–1780) of Austria, who had a reputation for enlightenment and patronage of scholarship. In her dedication, Agnesi noted, "For, if at any time there can be an excuse for the rashness of a woman who ventures to aspire to the sublimities of a science which knows no bounds, not even those of infinity itself, it certainly should be at this glorious period." Maria Theresa acknowledged the dedication with a crystal box with diamonds and a diamond ring. Pope Benedict XIV recognized Agnesi's achievement with a gold wreath set with precious stones and a gold medal. In 1750, he also named Agnesi an honorary professor of mathematics and natural philosophy at the University of Bologna, a position she held until 1752.

Although Agnesi was often entreated by her contemporaries to lecture publicly, she always declined, and after her father's death in 1752 she withdrew from the scholarly world and dedicated herself to charity work, the study of theology, and supervising the education of her many brothers and sisters. Her withdrawal from the outside world was noticeable enough to encourage rumors that she had finally entered the order of the Blue Nuns. Although there is no evidence to that effect, the rumor was strong enough to survive in accounts of Agnesi's life into modern times.

For a while after 1752, Agnesi resided in separate apartments in her family home, where she took in the poor and the sick. In 1759, she secured a house for herself and her wards. Despite her great wealth, Agnesi lived in the simplest quarters, spending the money set aside for her food, clothing, and books on the poor of her parish of San Nazaro. When she was in need of money to finance her charitable activities, she sold the gifts sent to her by Maria Theresa to a rich Englishman and later even sold the crown given by Benedict XIV. Her earliest biographer, Luisa Anzoletti , wrote: "To her it is not enough to make the daily pilgrimage as a nurse inside and outside the poorest huts, so that she asked from her father for some rooms to live in, separate from the rest of the family and little by little she transformed them into something like a private hospital."

In 1771, Archbishop Pozzobonelli opened the Pio Albergo Trivulzio in the palace given for this purpose by Prince Antonio Trivulzio. It became a home for the elderly, sick, and poor. He persuaded Agnesi to take the position as director of women there, and within a few years the number of inhabitants had increased to over 450, forcing her to close her own little hospital to concentrate exclusively on this institution. In 1783, she took up residence in two of the rooms at the Pio Albergo Trivulzio, where she insisted on paying rent in order to avoid diminishing the resources available for the poor. Agnesi was described by her colleagues there as "an angel of consolation to the sick and dying women until her death at the age of 81 years on January 9, 1799." In Agnesi's later years, she grew blind and deaf, and developed hydrothorax, which eventually caused her death.

At her request, Maria Agnesi's body was buried in a common grave, without a monument. In 1833, Lorenzo Prinetti, honorary director of the Pio Albergo Trivulzio, placed a small monument on the stairway of the institute to which was later added a marble bust of Agnesi, which he inscribed:

To Maria Gaetana Agnesi
Treasure of knowledge
Most pure flower of virtue
Well known all over Europe
In the serious sciences of computation
Here where, having repudiated the comforts and honours of
the world she lived XV years with the poor of Jesus
happy till her last day
for the joys of charity.

At the centennial of her death in 1899, a street in each of three towns—Milan, Monza, and Masciago—was named in her honor and a cornerstone was placed in the facade of the Luogo Pio with the inscription:

Maria Gaetana Agnesi
erudite in Mathematics
glory of Italy and of her century
most acknowledged in asylums of poor and old
humble servant of charity
died in the year 1799.

Two scholarships were set up in Agnesi's honor, which have served to keep her name as an inspiration for future generations.

The curve known as the Witch of Agnesi was studied merely as a curiosity by the scientific community until the 20th century, when physicists discovered that the curve could be used to represent the spectral energy distribution of xray lines, optical lines, and the power dissipation in sharply tuned resonant circuits. The discovery of practical applications for the Witch of Agnesi has served to bring the work of this remarkable woman back to light. As a personification of the best ideals of the Enlightenment period, and as an example to women of their capacity to equal men in academic endeavor, Agnesi still provides a stunning example of brilliance, determination, and uncommon devotion to the cause of those less fortunate than herself.


Jur, Barbara A. "An Abnormal Witch," in Mathematics Teacher. Vol. 85. October 1992, pp. 584–87.

Kennedy, Hubert. "Maria Gaetana Agnesi (1718–1799)," in Women in Mathematics. Edited by Louis S. Grinstein and Paul J. Campbell. NY: Greenwood Press, 1987.

——. "The Witch of Agnesi—Exorcised," in Mathematics Teacher. Vol. 62, 1969, pp. 480–82.

Lowe, Roger. "The Witch of Agnesi," in Historical Topics for the Mathematics Classroom. Washington, DC: National Council of Teachers of Mathematics, 1969.

Spencer, Roy C. "Properties of the Witch of Agnesi: Application to Fitting the Shapes of Spectral Lines," in Journal of the Optical Society of America. Vol. 30, 1940, pp. 415–19.

Thomas a Kempis, Sister Mary. "The Walking Polyglot," in Scripta Mathematica. Vol. 6, 1939, pp. 211–17.

Kimberly Estep Spangler , Assistant Professor of History, Friends University, Wichita, Kansas

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Agnesi, Maria Gaetana (1718–1799)

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