Maria Gaetana Agnesi – 18th century mathematician

“How long will I have to do this?” must have been the thought that frequently ran through the mind of Maria Agnesi as she stood in her parlor on Friday nights.  Maria Gaetana Agnesi was the oldest of 21 children born into the family of Pietro Angesi.  The Agnesi family was a well to do family in Milan, Italy in the 18^th century.  Pietro came from a merchant class family who had made their money in cloth goods.  The family owned many properties and had furnished them exquisitely.

Pietro’s grandfather, father, and uncle had built the business into a sort of empire.  For some unknown reason, Pietro was never trusted with the business.  Even when his father died, provision was made in his will that prevented him from making any decisions concerning the business without the approval of his uncle.  However, when his uncle died childless, the responsibility for the business fell entirely onto Pietro’s shoulders.

Pietro was a very ambitious man.  He had almost everything that he could want, materially.  The one thing he didn’t have was a position in the aristocracy.  He tried many things to be recognized as a member of this class which eventually ran up a huge debt.  One of these things was hosting “conversazione” on Friday nights.  There were many such events held around the city for the wealthy to indulge themselves.  Some were for music and dancing, some for gambling, but at the Agnesi household discussions of philosophy were held.  These events served their purpose and attracted many distinguished persons to the Agnesi home such as Monsieur Charles Brosses, president of the parliament of Burgundy and Frederick Christian, heir to the throne of Poland.

One thing Pietro never scrimped on, even when he was accumulating debt, was his children’s education.  He hired the best tutors from around Europe for both the boys and the girls.  This was during a time when women across Europe were rarely educated.  Genius was, however, recognized and Maria Gaetana was that – a child prodigy.  By the age of 11, she could speak, read, and write Italian, French, German, Spanish, Latin, Greek, and Hebrew.  At the age of 9, she translated a treatise written in Italian into Latin, memorized it, and delivered the oration at one of her father’s “conversations”.  The treatise was on the education of women, arguing that they should be allowed access to “the fine arts and sublime sciences”.

She and her sister were regularly put on display in the salon of their family home.  Here her father entertained many wealthy and noble men.  Maria Gaetana was asked questions by the participants and she would expound on the subject.  She was adept at discussing philosophy as well as the sciences and mathematics.  She was brilliant, and the men who attended were amazed that she could discuss the philosophy of Descartes as easily as celestial mechanics or the theory of gravitation.  Her sister, Maria Teresa, was a composer.  She would play the harpsichord and sing, sometimes accompanied by Maria Gaetana on the viola.

Maria Gaetana (1718 – 1799) was basically shy and reserved person.  She didn’t enjoy being put on display, but was obedient to her father’s wishes.  A devout Catholic, at one point during her teens, she approached him to ask if she could be excused from further events.  She wanted to enter the cloister.  Her father refused to allow this and she continued participating.  Maria Gaetana never married and most of her time was spent teaching the younger children and after her mother (Anna Brivio) died in 1732, managing the household.  What time she could spare, she gave in helping ill and homeless people, primarily women.

As she got older, one of Maria Gaetana’s responsibilities was to tutor her younger brothers in mathematics.  She had a passion for scholarship including mathematics and had absorbed works by Newton, Fermat, and Descartes among others.  She found all of the texts available to be inadequate for the task of teaching her younger siblings.  For this reason she decided to write her own.  Originally, it was intended to be used only for their lessons but 10 years after she began it, Analytical Institutions was published to wide acclaim.  It was a comprehensive look at mathematical analysis at the time, from algebra through differential and integral calculus, infinite series, and differential equations.  She managed to synthesize work from many of the masters including Newton and Leibnitz to write a text that made these topics accessible to the lay person.

Maria had previously published Propositiones Philosophicae a volume of about 200 essays on various topics presented at her father’s conversations.  But she is primarily known for Analytical Institutions.  It is the earliest surviving math text written by a woman and was translated into English and French for use as a textbook.  She was honored by such people as Pope Benedict XIV with a gold medal and Empress Maria Theresa with jewels.  She was also elected to the Bologna Academy of Sciences.  This position included a faculty post.  There is some disagreement as to whether or not she ever taught there.

Whether or not Maria Gaetana taught outside the home, this would have ended when her father died in 1752.  He had left the family in tremendous debt and most of their possessions had to be sold to cover it.  This changed Maria’s lifestyle and set her free to pursue her passion.  Until her death in 1799, Maria Gaetana gave selflessly to others.  She worked with the ill and homeless people of Milan with both her time and what resources she had left.

Maria Gaetana Agnesi is most well known for a curve that she worked with called the “Witch of Agnesi.”  Known for, that is, outside of Italy.  In Italy she is known as a great humanitarian and woman of God.  She was buried in a common grave with 15 other women and her childhood home was destroyed during WWII.  But the city of Milan is proud of their daughter and there are monuments that have been erected to celebrate her life.

References
The World of Maria Gaetana Agnesi, Mathematician of God
by Massimo Mazzotti
Women in Mathematics by Lynn Osen

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