Maria Gaetana Agnesi: A Brief Discussion of Her Contribution to the Study of Mathematics

In the Middle Ages, higher education for women was frowned upon by many European countries and women were basically deprived of even the basic fundamentals Ð'- reading, and writing Ð'- arithmetic was out of the question. The only acceptable forum for educating women was nunneries, or convents. However, in Italy, where the Renaissance originated, women of knowledge were admired by men and were encouraged to expand their minds. This unusual attitude enabled Italian women to participate in the expansion and exploration of the arts, sciences, medicine, literature and mathematics (Unlu, 1995). One such lucky girl child was Maria Gaetana Agnesi, born of educated, wealthy parents in what is now modern day Milan, on May 16, 1718. The following will provide a basic biography of Maria Gaetana Agnesi and her contribution to the world in mathematics which included authoring several books; she wrote the first mathematics book by a woman that still survives today and she was the first woman appointed as a mathematics professor at any university (Women's History, no date). The importance of her contributions to mathematics will be briefly discussed in the conclusion.

Maria Gaetana Agnesi was born to Pietro Agnesi and his first wife. She was the eldest of 21 children born to Pietro and his three wives. Her father was a wealthy silk trader and a professor of mathematics at the University of Bologna. Unlike most female children that were educated in convents, Maria was recognized by her father to be brilliant; thus, he did not send her away but instead provided very high quality tutors that nurtured her remarkable talents in language and mathematics. At the age of 9, Maria published a Latin discourse applauding higher education for women (O'Connor and Robertson, no date). She was recognized as a prodigy by the age of five - she spoke fluent French; by the age of nine she had mastered Latin, Greek, Hebrew, German and Spanish (O'Connor and Robertson). In her teen years, Maria had "mastered" mathematics (Unlu, 1995).

Maria's father's home was the gathering place of many of the most distinguished intellectuals of the day and Pietro insisted that Maria participate in most of the Ð''seminars'. She engaged the intellectuals in philosophical and mathematical discussions. Shy in nature, she preferred to absent these meetings however, to please her father she continued to participate until the death of her mother. With the death of her mother, Maria retired from public life and took over the management of her father's house. She was 20 years old (About Women's History, 2003). Maria never married Ð'- probably a result of the heavy toll excised on her from managing 20 children, the house, and her father! However, her retirement from public speaking and performances did not keep her from her continued study of mathematics.

In fact, in the year her mother died, 1738, she published "Propositiones Philosophicae", which were complex essays on natural science and philosophy; these were based on the wonderful discussions with the intellectuals that had gathered in her father's home during the previous years (Unlu). It should be noted that the topics in this publication "went beyond the philosophy as [as it is thought of] today, and included scientific topics like celestial mechanics, Isaac Newton's gravitation theory and elasticity (About Women's History)." It was also during this year that she began her work on what is considered to be her most important contribution to the study of mathematics.

"Analytical Institutions", begun in 1738 and published in 1748 and 1749, using her father's money (O'Connor and Robertson), was a clear, comprehensive textbook written specifically for her brothers to educate them about differential and integral calculus. The first volume covered arithmetic, algebra, trigonometry, analytic geometry, and calculus (About Women's History); the second volume, which provided complete works on finite and infinitesimal analysis, rocked the academic world as it was one of the first of its kind (Unlu). This body of work brought the contributions of various mathematicians together to provide a systematic approach to her own mathematical interpretations (Unlu).

It is in "Analytical Institutions" that Maria illustrates the equation of the cubic curve called the "Witch of Agnesi"; that equation provides: y=a*sqrt(a*x-x*x)/x where she considered the x-axis to be the vertical axis and the y-axis to the horizontal axis. Because today Cartesian methods