Maria Gaetana Agnesi

The life of Maria Gaetana Agnesi

Timeline 1718Born in Milan on 16 May, the first of the 21 children of Pietro Agnesi, a wealthy silk merchant. 1727At nine, recites in Latin a speech defending women’s education. 1738Publishes the Propositiones philosophicae, 191 theses on philosophy and natural science that she defended at the gatherings in her father’s house. 1739Asks her father to let her enter a convent; he refuses. 1748Publishes the first volume of the Instituzioni analitiche, dedicated to Empress Maria Theresa. The second comes out in 1749. 1750Pope Benedict XIV appoints her to the chair of mathematics at the University of Bologna. She never goes to Bologna. 1752Her father dies. Agnesi leaves mathematics and begins caring for poor and sick women. 1771The Pio Albergo Trivulzio, a hospice for the elderly poor, is founded in Milan. Agnesi is asked to direct the women’s wing. 1799Dies on 9 January, at the hospice, and is buried in a common grave. The girl of the salons Maria Gaetana Agnesi was born in Milan on 16 May 1718. The city was then the capital of a duchy ruled by the Habsburgs of Vienna. Her father, Pietro Agnesi, had grown rich in the silk trade and wanted the family to rise in Milanese society. He married three times and had 21 children. Maria Gaetana was the eldest.

October 28, 2026 Read

The curve of Agnesi

Agnesi did not discover the curve that bears her name. But it was through her book that the curve became known, because she used it as an example of how to pass from a geometric construction to an equation, which was exactly what Descartes’s new method promised. The construction Start with a circle of diameter $OM = a$, with $O$ at the bottom and $M$ at the top, and draw the line tangent to the circle at $M$. Now:

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The Instituzioni analitiche

In the middle of the eighteenth century, anyone who wanted to learn calculus had a problem. Newton and Leibniz’s invention was only seventy years old, and its results were scattered across papers in scientific journals, letters and books written in Latin, French and English, in different notations. The only famous textbook, the Marquis de L’Hôpital’s Analysis of the Infinitely Small, of 1696, dealt only with differential calculus. There was no book that led the student, step by step, from algebra to differential equations.

October 28, 2026 Read

Maxima, minima and points of inflection

The second book of the Instituzioni analitiche is devoted to differential calculus, and one of its main applications is the one every student learns: finding maxima and minima. Agnesi teaches the method with dozens of examples, of curves and of geometric problems, always in the same sequence: write the quantity, differentiate, set the differential equal to zero and check. The highest point At a maximum or a minimum, the curve is momentarily horizontal: the tangent line has slope zero. Since the slope of the tangent is the derivative, the candidates for maximum and minimum are the points where $y' = 0$.

October 29, 2026 Read

The area under the curve and the number π

The third book of the Instituzioni deals with integral calculus: areas under curves, volumes, lengths. The versiera gives a surprising example. The curve never touches the $x$-axis; it stretches out without end on both sides. Even so, the region between the curve and the axis has a finite area. A well-known antiderivative With $a = 1$, the curve is $y = \frac{1}{1 + x^2}$. We need a function whose derivative is $\frac{1}{1 + x^2}$. It exists and is an old acquaintance: the arctangent. If $u = \arctan x$, then $x = \tan u$ and

October 29, 2026 Read

The inverse method of tangents

Differential calculus answers a question: given a curve, what is its tangent at each point? The mathematicians of the seventeenth century soon realized that the inverse question was harder and more useful: given a property the tangents must have, what is the curve? This problem was called the inverse method of tangents, and it is the subject of the fourth and last book of the Instituzioni analitiche. Today we call it solving a differential equation.

October 29, 2026 Read

The witch in statistics: the Cauchy distribution

Agnesi died in 1799 without imagining that her curve would have a second life, far from geometry. In the nineteenth century it reappeared in probability theory, as one of the most treacherous examples in statistics. A probability density We saw in The area under the curve that the total area under $y = \frac{1}{1 + x^2}$ is $\pi$. Dividing by $\pi$, the area becomes 1, and the curve becomes a probability density:

October 29, 2026 Read

A woman at the university: the speech of 1727 and the chair at Bologna

Oratio qua ostenditur artium liberalium studia a femineo sexu neutiquam abhorrere. — Title of Agnesi's speech, 1727 The Latin sentence means: “A speech in which it is shown that the study of the liberal arts is by no means unsuited to the female sex”. Agnesi was nine when she recited it before her father’s guests, in 1727. The text had been written in Italian by one of her teachers; she translated it into Latin and learned it by heart.

October 29, 2026 Read

The legacy of Maria Gaetana Agnesi

For a long time Agnesi was remembered in two ways that had little to do with what she did. For English-speaking mathematicians, she was the name of a curve with a witch’s nickname. For the Milanese, she was a saint of charity who, as a young woman, had written a difficult book. Both images hid the author of one of the most influential mathematics books of the eighteenth century. The book For decades the Instituzioni analitiche were the most complete calculus course available in Europe. In Italy they were used by generations of students. The French translation of the second volume, of 1775, and John Colson’s English translation, of 1801, carried the book to other readers. The order Agnesi chose, from algebra to curves, from derivatives to integrals and differential equations, is essentially that of calculus courses to this day.

October 29, 2026 Read

Image credits

Historical images and photographs All come from Wikimedia Commons. We use the thumbnails provided by Commons, reduced to 800 pixels wide, with no other editing. Portrait of Maria Gaetana Agnesi, line engraving by Ernesta Legnani Bisi after a drawing by Maria Longhi (1812): source page · public domain. Agnesi at her study table, drawing by Jean François Bozio, Metropolitan Museum of Art: source page · CC0. Title page of the first volume of the Instituzioni analitiche (Milan, 1748): source page · public domain. Plate with the construction of the versiera, from the first volume of the Instituzioni analitiche (1748): source page · public domain. Diploma of appointment to the University of Bologna (1750): source page · public domain. Portrait in Antonio Francesco Frisi’s Historical Eulogy (1799): source page · public domain. The Pio Albergo Trivulzio, Milan, photo by Joaquin008: source page · CC BY-SA 4.0. Bust of Agnesi at the Palazzo di Brera, Milan, photo by Giovanni Dall’Orto: source page · free use with attribution. Plaques at the place where Agnesi died, Milan, photo by Bramfab: source page · CC BY-SA 4.0. Figures made for the blog The cover and the four interactive figures (the construction of the versiera, the tangent line and the points of inflection, the area under the curve, and the averages of Cauchy draws) are original illustrations, with text in each of the site’s languages.

October 29, 2026 Read