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The story of a brilliant mathematician who wanted to become a nun

What we owe to Maria Gaetana

 Cosa dobbiamo a Maria Gaetana  DCM-006
01 June 2024

As often happens to those who possess exceptional talents, Maria Gaetana Agnesi had two lives within a single lifetime. She was one of the most brilliant mathematicians of all time, and then, radically changing her existence in the middle of her journey, she became a generous benefactor for the poor and the marginalized.

There is a portrait of her, an engraving by Maria Longhi, where Agnesi is depicted as a young Milanese woman dressed in the aristocratic manner of 18th-century Europe, with a severe and penetrating gaze and wearing fine earrings. In reality, she harbored a profound indifference towards wealth and high society. The life of the Milanese salons, which her father Pietro Agnesi aspired to frequent, did not interest her, nor did she enjoy evenings at the theater, balls, or the idle pastimes of the upper class. Idleness at the time was expected of women of her rank, who were destined to grow up with little education to one day become mothers. Maria Gaetana Agnesi, born in Milan in 1718, would have followed this preordained path had her father not leveraged her extraordinary intelligence. To do so, Pietro had to go against not only the social norms of the time but also the will of his daughter, Maria Gaetana.

The eldest of 21 children, though some sources suggest there were likely 22 or 23, she astonished her family as a child by demonstrating an exceptional talent for learning foreign languages, including Latin. At a very young age, she learned Hebrew, English, French, Spanish, and German. At nine years old, her tutor helped her write an oration in favor of women’s education, which she recited in front of her emotional father.

Pietro Agnesi was not an aristocrat; having become wealthy through the silk industry, he aspired to become a prominent figure in Milanese intellectual circles. His wife, Anna Fortunata Brivio, was a noblewoman who died after giving birth to eight children, many of whom were talented and brilliant, such as their second daughter Teresa Agnesi, who was a superb musician. However, none in the lineage equals Maria Gaetana, who represented their passport to high society. Dozens of intellectuals from across Italy and Europe entered the Agnesi salon to meet this young prodigy who, at nineteen, had mastered philosophy, physics, ethics, metaphysics, biology, to the extent of writing an entire treatise – Propositiones Philosophicae – which she effortlessly elucidates to her audience, debating and disputing in Latin while her sister Teresa played the harpsichord. Her fame even reached Frenchman Charles Brosses, a friend of Enlightenment encyclopedists, who, after meeting her, admitted to never having encountered someone as excellent in “latineggiare”. Yet Maria Gaetana Agnesi, though flattered by sincere compliments, harbored a radical desire, opposed to everything she had experienced up to this point: to become a nun and distance herself from the world that worshipped her.

She implored her father to exempt her from married life and allow her to live in a convent. Pietro Agnesi viewed his daughter’s choice as a waste and an insult, so he did not grant consent. As an enlightened pater familias, he was one of the few to have encouraged his female daughters to cultivate the gifts of intellect and art; Maria Gaetana’s intelligence once again played against her desire, so intensely and disruptively that Agnesi decided to immerse herself both soul and body in the study of mathematics, the subject that perhaps more than any other brought her closer to God. After a short while, she became an exceptional mathematician, and unraveled the disputes over Newton and Leibniz’s infinitesimal calculus, being translated in France and England, her light shining wherever her name was mentioned. At Cambridge (UK), which was already one of the most important centers of wisdom in the world at that time, mathematicians of the caliber of John Colson read with amazement Maria Gaetana Agnesi’s volume, Instituzioni Analitiche ad uso della gioventù italiana [Analytical Institutions for the Use of the Italian Youth]. This was the first systematic manual ever published on algebra, geometry, and integral and differential calculus, which she translated from Italian to Latin for greater dissemination and had printed in her father’s salon, convincing the printers to carry out the work according to her dictates.

The work became obligatory for anyone wishing to delve into the systems of Newton and Leibniz, and receive universal acclaim. The Accademia della Crusca, the institution overseeing the Italian language, used the mathematical terms employed by Agnesi in its first Dictionary. The young Milanese mathematician decided to dedicate the two volumes of her prodigious work to Maria Teresa D’Austria, her Empress, to whom she wrote of feeling somewhat akin, as both are women, and thus accustomed to fighting more for the consideration of others. Despite being one of the most powerful sovereigns of the time, Maria Teresa appreciated those words written by a brilliant woman, and sent Maria Gaetana Agnesi a bag of diamonds as a token of gratitude. Pope Boniface XIV is even more concrete and offered her the chair of the University of Bologna, which made Agnesi the first female mathematics professor at the university since its founding year. At that time, the Fields Medal, awarded to the world’s best mathematicians starting from 1936, had not yet been established, yet the esteem and honors bestowed upon Maria Gaetana Agnesi when she was only thirty years old equaled those of today’s Nobel Prizes. Letters from scholars arrived at the Milanese palace of Pietro Agnesi, requesting the woman’s commentary on their geometry and algebra queries; the Royal Academy of France included her work among the most advanced texts of human knowledge. Agnesi also ventured into geometry, and gave a name to a type of curve still referred to today as the Agnesi curve, which in Anglo-Saxon countries, due to a translation error, is called the “witch’s curve”. This happens to be a paradox considering the extraordinary transformation that Maria Gaetana was about to imprint on her own existence, to follow that charity of the heart that until then she had never had the chance to put into practice. Her father, the only one capable of imposing his vision on his daughter, died suddenly during a dispute. If paternal authority had granted her the freedom to become an extraordinary woman of science, Agnesi now found the courage to give form to her authentic vocation and in 1750 she abandoned mathematics, refused the chair at the Alma Mater of Bologna, and devoted herself completely to a project that bewildered the entire family. In a short time, the Agnesi palace became a place where women would study to become nurses, and Maria Gaetana herself dedicated herself to the care of the poor and the sick, finding time to teach anyone seeking an education, including the palace servants. When she realized that her pious work ws incompatible with family life, she sold Empress Maria Teresa’ diamonds and opened a hospital where she secured a small room all for herself, to share the suffering with the sick. In Milan, Agnesi’s name was then associated with philanthropy, to the extent that in 1771 she was invited to preside over the Pio Albergo Trivulzio as Priora, a place that welcomed the neediest patients and where the woman continued to receive scientists and members of the most prestigious academies in Europe, eager to submit new algebraic calculations and mathematical theories to her attention. Only she, they were convinced, could offer an authoritative opinion on the studies they were conducting. All, without exception, were asked to give up their quest. Only the Holy Scriptures and the lives of the saints filled the long evening hours of the now destitute woman. Maria Gaetana, who could have lived in comfort, did not even possess the money to buy new clothes and shoes, and for this reason her brother Giuseppe offered her hospitality in his Milanese appartments, from which Agnesi could continue her now saintly commitment by tending to her health and enjoying proper meals. However, the woman, now sixty years old, refused even this gesture of generosity and continued to spend her days at the bedside of the sick. She never wrote about herself, her spirit, or her exceptional life. She did not want to leave comments on her past life; to attract attention was the least of her interests. However, she did exploit her celebrity to occasionally gain access to Milanese gatherings in order to make the plight of the city’s poor known and to solicit funds to alleviate poverty. If she was welcomed and sought after as a scientist, now her insistence to obtain money for the unfortunate led her to become an unwelcome visitor. One after another, the doormen of the wealthy received orders not to admit Maria Gaetana Agnesi anymore. Expelled and marginalized, she tirelessly worked at the Pio Trivulzio for twenty-three years until she fell ill with pneumonia. She left behind a single letter, requesting that she be buried in a common grave, anonymously alongside the forgotten.

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