[5] 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.

[12] Agnesi suffered a mysterious illness at the age of twelve that was attributed to her excessive studying and reading, so she was prescribed vigorous dancing and horseback riding.

[12] 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.

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.

[12] After having read in 1739 the Traité analytique des sections coniques[14] 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.

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".

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

[15] In Instituzioni analitiche, Agnesi discussed a curve earlier studied and constructed by Pierre de Fermat and Guido Grandi.

[19] 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.

[20] In 1750, on the illness of her father, she was appointed by Pope Benedict XIV[19] to the chair of mathematics and natural philosophy and physics at Bologna, though she never served.