Maria Gaetana Agnesi

Maria Gaetana Agnesi (Italian pronunciation: [maˈriːa ɡaeˈtaːna aɲˈɲeːzi; -ɛːzi];[1] 16 May 1718 – 9 January 1799) was an Italian mathematician, philosopher, theologian, and humanitarian. She was the first woman to write a mathematics handbook and the first woman appointed as a mathematics professor at a university.[2]

She is credited with writing the first book discussing both differential and integral calculus and was a member of the faculty at the University of Bologna, although she never served.

She devoted the last four decades of her life to studying theology (especially patristics) and to charitable work and serving the poor. She 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 and contemplation of the life, death and resurrection of Jesus Christ.[3]

Maria Teresa Agnesi Pinottini, clavicembalist and composer, was her sister.

Maria Gaetana Agnesi
Maria Gaetana Agnesi
Born16 May 1718
Died9 January 1799 (aged 80)
Known forAuthor of Instituzioni Analitiche ad uso della gioventù italiana (English: Analytical Institutions for the use of Italian youth)
Scientific career
InstitutionsUniversity of Bologna

Early life

Maria Gaetana Agnesi was born in Milan, to a wealthy and literate family.[4][5][6] Her father Pietro Agnesi, a wealthy silk merchant,[7] wanted to elevate his family into the Milanese nobility. In order to achieve his goal, he had married Anna Fortunato Brivio of the Brivius de Brokles family in 1717. Her mother's death provided her the excuse to retire from public life. She took over management of the household. She was one of 21 children.[8]

Il diploma di nomina dell' Agnesi all' Università di Bologna
Agnesi's diploma from Università di Bologna

Maria was recognized early on as a child prodigy; she could speak both Italian and French at five years of age. By her eleventh birthday, she had also learned Greek, Hebrew, Spanish, German, and Latin, and was referred to as the "Seven-Tongued Orator".[9]

Agnesi suffered a mysterious illness at the age of twelve that was attributed to her excessive studying and was prescribed vigorous dancing and horseback riding. This treatment did not work; she began to experience extreme convulsions, after which she was encouraged to pursue moderation. By age fourteen, she was studying ballistics and geometry.[9] When she was fifteen, her father began to regularly gather in his house a circle of the most learned men in Bologna, before whom she read and maintained a series of theses on the most abstruse philosophical questions. Records of these meetings are given in Charles de Brosses' Lettres sur l'Italie and in the Propositiones Philosophicae, which her father had published in 1738 as an account of her final performance, where she defended 190 philosophical theses.[9]

Her father remarried twice after Maria's mother died, and Maria Agnesi ended up the eldest of 21 children, including her half-siblings. Her father agreed with her that if she were to continue her research into mathematics, then she would be permitted to do all the charity work she wanted.[10] In addition to her performances and lessons, her responsibility was to teach her siblings. This task kept her from her own goal of entering a convent, as she had become strongly religious. Although her father refused to grant this wish, he agreed to let her live from that time on in an almost conventual semi-retirement, avoiding all interactions with society and devoting herself entirely to the study of mathematics.[9] After having read in 1739 the Traité analytique des sections coniques of the Marquis Guillaume de l'Hôpital, she was fully introduced into the field in 1740 by Ramiro Rampinelli, an Olivetan monk who was one of the most notable Italian mathematicians of that time.[11] During that time, Maria studied with him both differential and integral calculus. Her family was recognized as one of the wealthiest in Milan.

Contributions to mathematics

Instituzioni analitiche

Il frontispizio delle Instituzioni analitiche dell' Agnesi
First page of Instituzioni analitiche (1748)

According to Britannica, she is "considered to be the first woman in the Western world to have achieved a reputation in mathematics". The most valuable result of her labours was the Instituzioni analitiche ad uso della gioventù italiana, (Analytical Institutions for the Use of Italian Youth) which was published in Milan in 1748 and "was regarded as the best introduction extant to the works of Euler".[4] The goal of this work was, according to Agnesi herself, to give a systematic illustration of the different results and theorems of infinitesimal calculus.[11] The model for her treatise was Le calcul différentiel et intégral dans l’Analyse by Charles René Reyneau.[11] In this treatise, she worked on integrating mathematical analysis with algebra.[9] The first volume treats of the analysis of finite quantities and the second of the analysis of infinitesimals.

A French translation of the second volume by P. T. d'Antelmy, with additions by Charles Bossut (1730–1814), was published in Paris in 1775; and Analytical Institutions, an English translation of the whole work by John Colson (1680–1760), the Lucasian Professor of Mathematics at Cambridge, "inspected" by John Hellins, was published in 1801 at the expense of Baron Maseres.[12] The work was dedicated to Empress Maria Theresa, who thanked Agnesi with the gift of a diamond ring, a personal letter, and a diamond and crystal case. Many others praised her work, including Pope Benedict XIV, who wrote her a complimentary letter and sent her a gold wreath and a gold medal.[9]

In writing this work, Agnesi was advised and helped by two distinguished mathematicians: her former teacher Ramiro Rampinelli and Jacopo Riccati.[11]

Witch of Agnesi

The Instituzioni analitiche..., among other things, discussed a curve earlier studied and constructed by Pierre de Fermat and Guido Grandi. Grandi called the curve versoria in Latin and suggested the term versiera for Italian,[13] possibly as a pun:[14] 'versoria' is a nautical term, "sheet", while versiera/aversiera is "she-devil", "witch", from Latin Adversarius, an alias for "devil" (Adversary of God). For whatever reasons, after translations and publications of the Instituzioni analitiche... the curve has become known as the "Witch of Agnesi".[15]


5407 - Palazzo di Brera, Milano - Busto a Gaetana Agnesi - Foto Giovanni Dall'Orto, 1-Oct-2011
Bust of Maria Gaetana Agnesi in Milan

Agnesi also wrote a commentary on the Traité analytique des sections coniques du marquis de l'Hôpital which, though highly praised by those who saw it in manuscript, was never published.[16]

Later life

In 1750, on the illness of her father, she was appointed by Pope Benedict XIV[15] to the chair of mathematics and natural philosophy and physics at Bologna, though she never served.[9] She was the second woman ever to be granted professorship at a university, Laura Bassi being the first.[17] In 1751, she became ill again and was told not to study by her doctors. After the death of her father in 1752 she carried out a long-cherished purpose by giving herself to the study of theology, and especially of the Fathers and devoted herself to the poor, homeless, and sick, giving away the gifts she had received and begging for money to continue her work with the poor. In 1783, she founded and became the director of the Opera Pia Trivulzio, a home for Milan's elderly, where she lived as the nuns of the institution did.[9] On 9 January 1799, Maria Agnesi died poor and was buried in a mass grave for the poor with fifteen other bodies.[18]

In popular culture

In 1996, an asteroid, 16765 Agnesi, was named after Agnesi. There is a crater on Venus named after her, too.[19] There is also a mathematical curve named the Witch of Agnesi.

In 2017, the Family Coppola released a brandy named after Agnesi.[20]

See also


  1. ^ Canepari, L. (1999, 2009) Dizionario di pronuncia italiana Archived 15 May 2013 at the Wayback Machine. Bologna, Zanichelli.
  2. ^ WOMEN'S HISTORY CATEGORIES (archived from the original), About Education
  3. ^ Mazzotti, Massimo. "Maria Gaetana Agnesi: Mathematics and the Making of the Catholic Enlightenment." Isis, Vol. 92, No. 4 (Dec. 2001), 657-683).
  4. ^ a b A'Becket 1913.
  5. ^ "Maria Gaetana Agnesi". Retrieved 16 May 2014.
  6. ^ Maor, Eli (2013). "Maria Agnesi and Her "Witch"". Trigonometric Delights. Princeton University Press. pp. 108–111. ISBN 9780691158204.
  7. ^ Findlen, Paula, Calculations of faith: mathematics, philosophy, and sanctity in 18th-century Italy (new work on Maria Gaetana Agnesi) Historia Mathematica 38 (2011), 248-291. doi:10.1016/
  8. ^ Spradley, Joseph (2016). Salem Press Biographical Encyclopedia,. Salem Press – via Ebsco.
  9. ^ a b c d e f g h Ogilvie, Marilyn Bailey (1986). Women in science: antiquity through the nineteenth century : a biographical dictionary with annotated bibliography (3rd print ed.). Cambridge, Mass.: MIT Press. p. 27. ISBN 0-262-15031-X.
  10. ^ Swaby, Rachel (2015). Headstrong 52 Women Who Changed Science-and the World. New York: Broadway Books. p. 179.
  11. ^ a b c d Gliozzi, Mario. "Agnesi, Maria Gaetana". Dizionario Biografico degli Italiani (in Italian). Enciclopedia Italiana. Retrieved 17 September 2015.
  12. ^ Analytical institutions... (four volumes), London, 1801 vol. 1, p. PR3, at Google Books
  13. ^ C. Truesdell, "Correction and Additions for 'Maria Gaetana Agnesi'", Archive for History of Exact Science 43 (1991), 385–386. doi:10.1007/BF00374764
    • Per Grandi: "...nata da' seni versi, che da me suole chiamarsi la Versiera in latino pero Versoria..."
  14. ^ S.M.Stigler, "Cauchy and the witch of Agnesi: An historical note on the Cauchy distribution", Biometrika, 1974, vol. 61, no.2 p. 375–380
  15. ^ a b Chisholm 1911.
  16. ^ Encyclopædia Britannica, 1911, p. 378
  17. ^ Pickover, Clifford. The Math Book. Sterling Publishing, 2009, p. 180.
  18. ^ "Agnesi". Retrieved 18 September 2017.
  19. ^ Atlas of Venus, by Peter John Cattermole, Patrick Moore, 1997, ISBN 0-521-49652-7, p. 112
  20. ^ Stierch, Sarah (27 September 2017). "Coppola Family Launches Spirits Line Named After Historic Women". Sonoma Magazine. Retrieved 27 September 2017.

Further reading

External links

16765 Agnesi

16765 Agnesi, provisional designation 1996 UA, is a stony Eunomia asteroid from the middle region of the asteroid belt, approximately 4 kilometers in diameter. It was discovered on 16 October 1996, by Italian-American amateur astronomer Paul Comba at his private Prescott Observatory in Arizona, United States. The asteroid was named after Italian mathematician Maria Gaetana Agnesi.

1718 in literature

This article presents lists of the literary events and publications in 1718.

1718 in science

The year 1718 in science and technology involved some significant events.

1748 in science

The year 1748 in science and technology involved some significant events.


Agnesi is an Italian surname. Notable people with the surname include:

Alberto Agnesi (born 1980), Mexican telenovela actor

Luigi Agnesi (1833–1875), Belgian operatic bass-baritone, conductor and composer

Maria Gaetana Agnesi (1718–1799), Italian linguist, mathematician and philosopher; sister of Maria Teresa

Maria Teresa Agnesi Pinottini (1720–1795), Italian composer; sister of Maria Gaetana

Nicolas Agnesi (born 1988), French rugby player

Troilo Agnesi, 15th-century Roman Catholic prelate

Agnesi (crater)

Agnesi is a crater on the planet Venus. It was named after Maria Gaetana Agnesi, an Italian mathematician; Venusian craters are named after notable women. The crater was named by the International Astronomical Union's Working Group on Planetary System Nomenclature in 1991. It is located at 39.4 degrees south and 37.7 degrees east. The crater is 42.4 kilometers in diameter.


Bovisio-Masciago (Brianzöö: Bovis-Masciagh [buˈʋiːs maˈʃɑːk]), is a comune (municipality) in the Province of Monza and Brianza in the Italian region Lombardy, located about 15 kilometres (9 mi) north of Milan.


Calculus (from Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus) is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.

It has two major branches, differential calculus (concerning instantaneous rates of change and slopes of curves), and integral calculus (concerning accumulation of quantities and the areas under and between curves). These two branches are related to each other by the fundamental theorem of calculus. Both branches make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit.

Modern calculus was developed independently in the late 17th century by Isaac Newton and Gottfried Wilhelm Leibniz. Today, calculus has widespread uses in science, engineering, and economics.Calculus is a part of modern mathematics education. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. Calculus has historically been called "the calculus of infinitesimals", or "infinitesimal calculus". The term calculus (plural calculi) is also used for naming specific methods of calculation or notation as well as some theories, such as propositional calculus, Ricci calculus, calculus of variations, lambda calculus, and process calculus.

Ciro in Armenia

Ciro in Armenia is a dramma per musica or opera in three acts by composer Maria Teresa Agnesi Pinottini. The work premiered in Milan on 26 December 1753 at the Teatro Regio Ducal. The work uses an Italian language libretto by the composer which is based on a work by Umberto Manferrari and G. Manfredi.

Ernesta Legnani Bisi

Ernesta Legnani Bisi (June 18, 1788 – November 13, 1859) was an Italian painter and engraver.

Born in Milan, she became a student of the Brera Academy, where she studied under the direction of Giuseppe Longhi. She was recognized as a brilliant student, and won the prize in 1810 for the design of the Academy. In 1811 she married Giuseppe Bisi from Genoa, a painter and professor of the Academy, by whom she had five children. She was a strong supporter of Italian independence, and a friend of many women of the Carbonari (the so-called charcoal burners), such as the painter Bianca Milesi. In his poem "Dodes sonitt all'abaa Giovan", Carlo Porta remembered her: "È in tra i donn la Milesi, la Legnana" ("Among the women, Milesi, Legnana").

In her artistic activity Bisi devoted herself mainly to portraits. In the field of engraving on copper she reproduced five works of France, Marco d'Oggiono, Giacomo Cavedone, Palma il Giovane and Paris Bordone for the Art Gallery of the Palazzo Reale in Milan, and the portraits of Maria Gaetana Agnesi, Vittoria Colonna and Giovanni Battista Monteggia for the Lives and portraits of illustrious Italians. She also produced portraits in watercolor. Two of her daughters went on to become painters as well: Antoinette (1813–1866) and Fulvia (1818–1911).

Giuseppina Masotti Biggiogero

Giuseppina Masotti Biggiogero (8 August 1894 – 24 October 1977) was an Italian mathematician and historian. Known for her work in algebraic geometry, she also wrote noted histories of mathematicians, like Maria Gaetana Agnesi and Luca Pacioli. She was a member of the Lombard Institute Academy of Science and Letters and won both the Bordoni Prize and Torelli Prize for her work.

History of calculus

Calculus, known in its early history as infinitesimal calculus, is a mathematical discipline focused on limits, functions, derivatives, integrals, and infinite series. Isaac Newton and Gottfried Wilhelm Leibniz independently discovered calculus in the mid-17th century. However, both inventors claimed that the other had stolen his work, and the Leibniz-Newton calculus controversy continued until the end of their lives.

Jacopo Riccati

Jacopo Francesco Riccati (28 May 1676 – 15 April 1754) was a Venetian mathematician and jurist from Venice. He is best known for having studied the equation which bears his name.

John Hellins

This subject should not be confused with his grandson John Hellins, 1829–87, clergyman and entomologist.John Hellins FRS (c. 1749 – 5 April 1827) was an autodidact, schoolteacher, mathematician, astronomer and country parson.

Liceo M.G.A.

Liceo M.G.A. (which stands for "Maria Gaetana Agnesi") is a nationwide group of Italian high schools. The Liceos offer some of the most challenging courses in Europe, including Latin, Math, Italian, German, French, Technology, Architecture, and the History of Italian Arts. They usually require at least 5 hours of study a day, and the students attend school from 8.05 am to 1.05 pm with only a 15-minute break.

List of Italian philosophers

This list of Italian philosophers contains a collection of philosophers who hail from Italy specifically or, more broadly, from the Italian peninsula.

Maria Agnesi

Maria Agnesi may refer to:

Maria Gaetana Agnesi (1718–1799), Italian mathematician, philosopher, theologian and humanitarian

Maria Teresa Agnesi (1720–1795), Italian composer

Ramiro Rampinelli

Ramiro Rampinelli, born Lodovico Rampinelli (1697 – 1759), was an Italian mathematician and physicist. He was a monk in the Olivetan Order. He had a decisive influence on the spread of mathematical analysis, algebra and mathematical physics in the best universities of Italy. He is one of the best known Italian scholars in the field of infinitesimal mathematics of the first half of the 18th century.

Witch of Agnesi

In mathematics, the witch of Agnesi (Italian pronunciation: [a.ˈɲe.zi]) is a cubic plane curve defined from two diametrically opposite points of a circle.

It gets its name from Italian mathematician Maria Gaetana Agnesi, and from a mistranslation of an Italian word for a sailing sheet. Before Agnesi, the same curve was studied by Fermat, Grandi, and Newton.

The graph of the derivative of the arctangent function forms an example of the witch of Agnesi.

As the probability density function of the Cauchy distribution, the witch of Agnesi has applications in probability theory. It also gives rise to Runge's phenomenon,

has been used to approximate the energy distribution of spectral lines, and models the shape of hills.

The witch is tangent to its defining circle at one of the two defining points, and asymptotic to the tangent line to the circle at the other point. It has a unique vertex (a point of extreme curvature) at the point of tangency with its defining circle, which is also its osculating circle at that point. It also has two finite inflection points and one infinite inflection point. The area between the witch and its asymptotic line is four times the area of the defining circle, and the volume of revolution of the curve around its defining line is twice the volume of the torus of revolution of its defining circle.

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