Maria Gaetana Agnesi

Maria Gaetana Agnesi (Milan, 1718 – Milan, 1799) was an Italian mathematician, philosopher, theologian and philanthropist, born into a wealthy and enlightened family in Milan, then part of the Habsburg Monarchy. She matters because she wrote one of the first complete textbooks on calculus at a time when mathematics was almost entirely a male preserve, and because she was the first woman appointed to a mathematics chair at a university, although she never actually took up the post.

Her childhood unfolded in a household where her father, Pietro Agnesi, a silk merchant who hoped to enter the Milanese nobility, hosted gatherings of intellectuals to discuss questions of natural philosophy, close to what we now call physics. Maria Gaetana, who was shy and solitary, disliked these evenings, yet her skill in Latin and other languages made her something of a local marvel. Many of the stories about her precocity, such as the essay on women's education supposedly written at nine or the command of seven languages before thirteen, were likely embellished by witnesses and by the family's taste for display. What seems reliable is that she received a broad education in which religion and science went hand in hand, in the spirit of what some historians call the Catholic Enlightenment.

Deeply devout, she wished to enter a convent, but her mother's death after the birth of her eighth child led to an arrangement with her father: she would stay at home, look after him and her many siblings, and live a simple, withdrawn life in exchange for avoiding society. Around 1738 her father published the Propositiones Philosophicae, a summary of 190 philosophical theses discussed at those gatherings. From about the age of twenty she withdrew almost entirely from social life and devoted herself to mathematics, guided by former teachers such as Ramiro Rampinelli and by the Riccati family.

The fruit of this work was the Instituzioni analitiche ad uso della gioventù italiana, published in Milan in 1748. Divided into a volume on finite quantities and a second on infinitesimal analysis, it offered a clear and orderly account of calculus, bringing together results that had been scattered among many mathematicians. It treated differential and integral calculus together, presenting them as inverse problems, and was admired for its clarity and its well-chosen examples. It had gaps, however, such as its limited treatment of trigonometric functions and its omission of power series. The work was translated into French in 1775 and into English in 1801, two years after her death.

After her father died in 1752, she gave the next forty-seven years to theology, especially the Church Fathers, and to caring for the poor and the sick in Milan. She died in the hospice she had directed. Today she is probably best known for the curve called the "Witch of Agnesi", a name that came from a mistranslation of the Italian word, but her lasting influence lies in her way of presenting calculus as an ordered whole.