Maria Gaetana Agnesi

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Maria Agnesi redirects here. This article is about the mathematician. For her sister the composer see Maria Teresa Agnesi

Maria Gaetana Agnesi (May 16, 1718 – January 9, 1799) was an Italian linguist, mathematician, and philosopher. Agnesi is credited with writing the first book discussing both differential and integral calculus. She was an honorary member of the faculty at the University of Bologna. Her father, Pietro, was a wealthy man of business who desired to elevate his family into the Milanese nobility. (Some historians have incorrectly identified him as a mathematics professor.) According to Struik, Agnesi is 'the first important woman mathematician since Hypatia (fifth century A.D.)'.

Maria was recognized as a child prodigy very early; she could speak both French and Italian at five years of age. By her thirteenth birthday she had acquired Greek, Hebrew, Spanish, German, Latin, and probably a few more languages, as she was referred to as the "Walking Polyglot". She even educated her younger brothers. When she was 9 years old, she composed and delivered an hour-long speech in Latin to an academic gathering. The subject was women's right to be educated. 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 de Brosses' Lettres sur l'Italie and in the Propositiones Philosophicae, which her father had published in 1738. These displays, being probably not altogether congenial to Maria (who was of a retiring disposition) ceased by her twentieth year because she strongly desired to enter a convent at that time. 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.

The most valuable result of her labours was the Instituzioni analitiche ad uso della gioventu italiana, a work of great merit, which was published at Milan in 1748 and "was regarded as the best introduction extant to the works of Euler." [1] 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), appeared at Paris in 1775; and an English translation of the whole work by John Colson (1680-1760), the Lucasian professor of mathematics at Cambridge, was published in 1801 at the expense of Baron Maseres. Madame Agnesi also wrote a commentary on the Traite analytique des sections coniques of the marquis de l'Hôpital, which, though highly praised by those who saw it in manuscript, was never published. She discussed the curve known as the "witch of Agnesi" or "versiera" as she named it in 1748. (Italian for the rope that turns a sail, taken from the Latin "versoria" which was the term used by Luigi Grandi before her. Colson, who translated Agnesi's text to English, perhaps confused "la versiera" with "l'avversiera", and so mistranslated it as "she-devil" or "the witch", with the result that English-speakers and, for some reason, Spanish speakers from Mexico, Cuba, and Spain, know the curve as the "Witch of Agnesi"(La bruja de Agnesi).). Struik mentions that

The word [versiera] is derived from Latin vertere, to turn, but is also an abbreviation of Italian avversiera, female devil. Some wit in England once translated it 'witch', and the silly pun is still lovingly preserved in most of our textbooks in English language. ... The curve had already appeared in the writings of Fermat (Oeuvres, I, 279-280; III, 233-234) and of others; the name versiera is from Guido Grandi (Quadratura circuli et hyperbolae, Pisa, 1703). The curve is type 63 in Newton's classification. ... The first to use the term 'witch' in this sense may have been B. Williamson, Integral calculus, 7 (1875), 173; see Oxford English Dictionary.

Examples of the curve are those given by the equations

where a is any non-zero constant. The equation

is the simplest among these.

In 1750, on the illness of her father, she was appointed by Pope Benedict XIV to the chair of mathematics and natural philosophy at Bologna. She was the second woman to be appointed professor at a university. 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. After holding for some years the office of directress of the Hospice Trivulzio for Blue Nuns at Milan, she herself joined the sisterhood, and in this austere order ended her days.

[edit] References

• This article incorporates text from the Encyclopædia Britannica Eleventh Edition, a publication now in the public domain.
• Larson, Ron; Hostetler, Robert P.; and Edwards, Bruce H. (2003). Calculus of a Single Variable: Early Transcendental Functions (3rd edition). Houghton Mifflin Company. ISBN 0-618-22307-X.
• Mathematics History archive entry for Maria Gaetana Agnesi at the University of Andrews, Scotland

• D. J. Struik, editor, A source book in mathematics, 1200-1800 (Princeton University Press, Princeton, New Jersey, 1986), pp. 178-180. ISBN 0-691-08404-1, ISBN 0-691-02397-2 (pbk).

[edit] Further reading

• Kramer, Edna E.. (1970). "Agnesi, Maria Gaetana". Dictionary of Scientific Biography 1: 75-77. New York: Charles Scribner's Sons.
• Mazzotti, Massimo. (2001). "Maria Gaetana Agnesi: Mathematics and the making of the Catholic Enlightenment." Isis. v. 92, n. 4: p. 657-683.