Maria Gaetana Agnesi
By:Sydney Munro


Unlike other mathematicians, Maria Agnesi did not spend her whole life working onmariaagnesi.jpg mathematics, as she gave it up very early in life, yet her contributions have made such an impact on the world of mathematics. She wanted to help the less fortunate and was willing to give more than take, and she still made incredible accomplishments in mathematics. In a world around her where women were shunned upon and unable to get educated, she had the tools and the resources to succeed. She truly sent a message to us all.

Maria Gaetana Agnesi was born May 16th, 1718 in Milan, Italy to a wealthy and literate family. She was the eldest of twenty- one children, as after the death of her mother, her father married again two more times. Her parents (Dom Pietro Agnesi Miriami, a math professor, and her mother, Anna Brivia) planned her educated very carefully so she would get the most pristine schooling. She had already bared the label of a child prodigy early in life, as by the age of five she could speak French, and by nine she had mastered Latin, Greek, and Hebrew. On top of these languages, Maria also learned many more modern languages. Learning was a game for Maria, as she had an amazing memory.

The Agnesi home was a center for some of the post pristine intellects of the time to meet and have discussions, so Maria’s father had her “show-off” her talents to the groups that met frequently, and she was heavily involved in these discussions. She even wrote about two hundred speeches for her father to present at these assemblies. Maria did not like these meetings because of her shy nature, and around the age of twenty, she decided to ask her father if she could be removed from the weekly events. Her father declined her request.

Maria’s teenage years were full of intellectual activities and mathematics. She spent much of her time tutoring her brothers and doing other house duties since her mother passed away. Also during this stage in her life, Maria mastered mathematics developed by people such as Newton, Fermat, Euler, and the Bernoulli Brothers. She also published a “collection of complex essays on natural science and philosophy called the Propositiones Philosophicae.[Maria Gaetana Agnesi, Elif Unlu (Agnes Scott College)] in 1738. This piece of work was created from some of the discussions she had with the intellectuals who met at her home. She also expressed her feelings about how she thought women should be allowed to have an education.


Mathematical Accomplishments
Although she gave up mathematics early, Maria Agnesi’s contributions to the math world were extremely important and still are useful today. One of her most accomplished contributions was the text book she had originally started writing for her little brothers to aid in her tutoring, but then it evolved into a larger and more serious project. She started working on this two volume, 1070 handmade pages masterpiece when she was twenty, and it took ten years to complete. The book, Analytical Institutions, published in 1748, brought the works of many mathematicians together and made it simpler and clearer, and also giving her own interpretations. In the first section, she covered the analysis of finite quantities and elementary problems of maxima, minima, tangents, and inflection points. The second section contained the analysis of infinitely small quantities; the third section of her text book covers the inverse method of tangents and differential equations.

Maria received many gifts and recognitions for her text book. Acclaim came to her from around the world because of the success of her text book, including one of the most prestigious math associations in the world, The French Academy of Sciences. Maria’s book was also dedicated to Empress Maria Theresa of Austria, and the Empress even sent her a diamond ring and a jewel-embedded crystal box to commemorate her accomplishments. Also, the Bologna Academy of Sciences admitted her into their society. Agnesi’s favorite gifts though, were the letters sent by Pope Benedict XIV. In addition to the letters, her also sent her many gifts, and recommended that she be listed as an honorary lecturer at the University of Bologna.

Within this book contained her most well-known and brilliant work: The “Witch” of Agnesi. The term ‘witch’ was actually mistranslated by someone who was translating her Italian work to English. “It was called a versiera, a word derived from the verteere, meaning ‘to turn’, but it was also an abbreviation for the Italian word avversiera, meaning ‘the wife of the devil.’”(Olsen,45) John Colsen, the translator, confused the two meanings and interpreted it as a “witch” The name caught on despite its confusing meaning, and her curve was named the witch of Agnesi. The ‘witch’ of Agnesi is a curve in the shape of a bmaria_curve.jpgell, and Fermat originally studied it. Her reasoning behind it is that the “plane curve has the Cartesian equation xy2=a2(a-x). Agnesi begins with the geometrical principle that if the abscissa of the corresponding points on a curve is equal to that of a given semicircle, then the square of the abscissa is to the square of the radius of the semicircle in the same ratio as that in which the abscissa would divide the diameter of the semicircle." (Olsen 44) To draw the curve “start with a circle of diameter a, centered at the point (0,a/2) on the y-axis. Choose a point A on the line y = a and connect it to the origin with a line segment. Call the point where the segment crosses the circle B. Let P be the point where the vertical line through A crosses the horizontal line through B. The witch is the curve traced by P as A moves along the line y = a. This construction of the witch is a reflection of the one mentioned in the biography across the line y = x.” (Unlu, www.agnesscott.edu) living.witch

(Interesting Fact) Maria, while she was still in her mathematical years, would frequently walk and work in her sleep, as one time she was up late working on a math problem, but got frustrated with it and went to bed. When she woke up the next morning, she saw that the problem was solved, in her own handwriting! She could not figure out what had happened, as she clearly remembered going to bed because she could not solve it. Maria finally concluded that she must have been working in her sleep, and she continued to do it for times to come. She even became well known around her region for this strange yet fascinating feature she possessed. This characteristic really stood out to me because I could see how dedicated she was to her studies and how she was so determined to find the solution.


Life After Mathematics
After Maria’s father died in 1752, she gave up mathematics after only twenty years of work. Some say that Maria only did math to please her father, who wanted his little prodigy to be dealing with mathematics. Despite whether that theory is true or false, Maria, being the religious and caring person she was, spent the rest of her years aiding the poor and doing charity work, as this pleased her because she had always wanted to live a simple and quiet life. She donated her property, spent all her time helping the needy, and even sold her jewels and gave all the proceeds to the poor. At one point, she even gave up her own room to house homeless women! As it showed, Maria seemed to enjoy helping others and caring for the less fortunate more than she wanted to pursue her career in mathematics as her father and many others had predicted and wanted.
Maria Agnesi died at the age of 81 on January 9th, 1799. She had never wanted a fabulous lifestyle, and had even asked to be buried with no elaborate monument over her grave. Just as she had requested, Maria was buried in a grave outside the Roman gates of the city walls, with no monument over her grave. On the 100th anniversary of her death, many streets in Milan were named in her honor. Also, Maria Agnesi scholarships have been given to needy girls in the city who need an education. Maria led a fascinating life full of academics, successes, and generosity, and she still has made an impact on today’s world. She taught to be generous and follow what you really want to pursue in life, and gave up a life of luxury to become a “humble servant to the poor” (Wilbert,61). Whatever she did, she did with all her heart and tried her hardest, which is one of the most valuable virtues you can poses. She accomplished much in her life, and even made an impact on life today.