April 10, 2021

Maria Agnesi, the great math of the Enlightenment | Science

Maria Agnesi, the great math of the Enlightenment | Science


In the Europe of the Enlightenment (eighteenth century – early nineteenth century) the gatherings among prominent personalities of science and culture were articulators of the social life of the nobility and the bourgeoisie. There, intellectuals of the time, both men and women, exchanged knowledge and opinions on various topics, from philosophical and literary to scientists or politicians. In the house of Pietro Agnesi and his family, in Milan, these appointments were frequent. The man, a silk merchant, according to some; A university professor, according to others, he married three times and he had twenty-one children, all well trained and assiduous participants of such meetings. Your oldest daughter, Maria Agnesi (Milan, Italy, 1718-1799), could speak, from a very early age, about philosophy, theology, languages, sciences and, specifically, mathematics, discipline to which he would end up dedicating himself.

Agnesi, born on May 16, 1718, was a child prodigy. When she was nine years old, she spoke in Latin about the right of women to study science, and at 17 she wrote a criticism, not published, about the Traité analytique des sections coniques (treatise on the conics) of the French mathematician Guillaume François de L'Hôpital. At 21, after his father refused to be ordained as a nun and wasted, according to him, his talent, he decided to dedicate himself completely to mathematics. His father provided him with the best possible mentors. Among them was the monk Ramiro Rampinelli, university professor and key in the development of the analysis, algebra and physics of the time, who put her in contact with the family of mathematicians Riccati (Jacopo, father of Vincenzo and Giordano, is known by the differential equation of Riccati), among others.

Due to the success of its publication, Pope Benedict XIV granted him in 1750 a Chair of Mathematics, Natural Philosophy and Physics at the University of Bologna

Agnesi studied the work of important mathematicians such as Pierre de Fermat, Isaac Newton, Leonhard Euler or Gottfried Leibniz, and with thirty years published his famous book Instituzioni analitiche ad uso della gioventú Italian (1748), with whom, initially, he wanted to teach mathematics to his younger brothers. That text, with clear and attractive descriptions, and numerous examples, became the first manual on differential and integral calculus and was used for more than fifty years in schools in several European countries. The main attraction of the work lay in its ability to analyze and relate the different investigations in calculus that had been studied to date, especially those of Newton and Leibniz, thus providing a unique teaching material so far.

In this text appeared the differential curve known for years as "witch Agnesi" (and not "Agnesi curve"), Due to an error in the translation from Italian to English. Although it had already been studied by other mathematicians such as Guido Grandi (who gave it its original name, versiera), Fermat, Leibniz and Newton, the translator attributed it to Agnesi.

Agnesi curve. Source: GeoGebra
Agnesi curve. Source: GeoGebra

This curve fulfills certain curious properties: the area between the witch and her asymptote (given by the line y = 0) is four times the area of ​​the given fixed circle, and the volume of revolution of the witch, if her asymptote is taken as axis , is three times the volume of the sphere obtained by rotating the given circumference on the same axis. Beyond this, at present this curve is used in statistics to study atmospheric phenomena and topographic reliefs and also to provide counterexamples in probability theory, since it is directly associated with the Cauchy distribution. It is also used to study the generation of ocean waves or those created in the atmosphere. It also appears in the study of periods of drought. In physics it helps to describe the resonance of bodies.

Thanks to the work of Agnesi, these results were known throughout the European continent. This work made her the first woman with a reputation in the world of mathematics. Also due to the success of its publication, Pope Benedict XIV granted him in 1750 a Chair of Mathematics, Natural Philosophy and Physics at the University of Bologna. However, it is considered an honorary title; Agnesi did not get to take possession of the position because after the death of his father, and with only 34 years, decided to devote his life to the catholic religion and to perform works of charity. Despite this, she is considered the first professor of mathematics in Europe. He died on January 9, 1799 in Milan.

Laura Moreno Iraola He is a member of the ICMAT Communication and Dissemination Unit.

Coffee and Theorems is a section dedicated to mathematics and the environment in which they are created, coordinated by the Institute of Mathematical Sciences (ICMAT), in which researchers and members of the center describe the latest advances in this discipline, share points of contact between the mathematics and other social and cultural expressions and remind those who marked their development and knew how to transform coffee into theorems. The name evokes the definition of the Hungarian mathematician Alfred Rényi: "A mathematician is a machine that transforms coffee into theorems".

Editing and coordination:Agate Rudder (ICMAT).

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