The Mathematician Maria Gaetana Agnesi

Maria Gaetana Agnesi  (died 9 January 1799)

Born in Milan in 1718, Maria Gaetana Agnesi was recognized as a prodigy when she was still quite young. In writing about the young Agnesi, Lynn Olsen notes that, by the age of five, she had already learned French; by the time she was nine, she had expanded her knowledge of modern languages and "mastered" Greek, Latin, and Hebrew before turning her attention to mathematics.

An eighteenth-century engraving
of Maria Gaetana Agnesi

With her father's encouragement--or, perhaps, at his insistence--she attended his ongoing series of intellectual gatherings, where she was urged to participate in the philosophical and mathematical discussions. 

She contributed to these "seminars" by publishing the Propositiones philosophicae (Propositions of Philosophy), a collection of essays on natural science and philosophy.  The essays were based on the discussions in which she had taken part, including her defense of liberal studies for women, "Oratio qua ostenditur artium liberalium studia femineo sexu neutiquam abhorrere" ("Oration in which it is shown that the study of the liberal arts by the feminine sex is in no way to be despised").

For her part, however, Agnesi Gaetana's preference was for a religious life, a vocation her father opposed, although he eventually allowed her to withdraw from the formal intellectual discussions he promoted and devote herself instead to the study of mathematics and to the education of her siblings. (Married three times, Agnesi's father eventually had twenty-some children, so there were plenty of children for the young woman to instruct.)

Her most significant work, her Instituzioni analitiche ad uso della gioventù italiana (Analytical Institutions for the Use of Italian Youth), published in 1748, seems to have grown out of this experience, but, as Olsen argues, while the work may have been begun as an instructional aid "for her younger brothers," it eventually grew "into a more serious effort," becoming a detailed mathematical study, "the first comprehensive textbook" on the differential and integral calculus. 

Title Page of the first volume of Agnesi's
Analytical Institutions

In 1750, Agnesi was elected to the Bologna Academy of Sciences, was awarded a diploma by the University of Bologna, and was appointed to the mathematics faculty by Pope Benedict XIV, though she did not travel to Bologna and take on teaching responsibilities there. (There is a lovely account of the pope's correspondence with Agnesi in John Augustine Zahm's 1913 Woman in Science, available at Google Books).

In any case, after her father's death in 1752, Agnesi ended her mathematical work. She devoted the rest of her life to caring for the old and infirm at the Pio Albergo Trulzio in Milan, eventually becoming its director. She died in 1799 at the age of eighty, having dedicated the majority of her life not to the study of mathematics but to her faith and to the service of the poor and the sick.

An asteroid identified by Paul G. Comba in 1996 was named in her honor, 16765 Agnesi.

A Google Doodle from 16 May 2014, celebrating Agnesi's 296th birthday, plays with the mathematical curve she discussed in the Analytical Institutions that later came to be called the "witch of Agnesi":

There is a full-length biography of Agnesi by Massimo Mazzotti, The World of Maria Gaetana Agnesi: Mathematiciam of God, but I also like the excellent--and very accessible--account of Agnesi in Lynn Olsen's 1974 Women in Mathematics, which I have quoted here.