Maria Gaetana Agnesi was an Italian mathematician, philosopher, theologian and humanitarian. She is credited with writing the first book discussing both differential and integral calculus and was an honorary member of the faculty at the University of Bologna. She was the first woman in the Western world who can accurately be called a mathematician.
Background
Maria Gaetana Agnesi was born in Milan, Italy, on the 16th of May, 1718. Her father Pietro Agnesi was a professor of mathematics in the university of Bologna. He married Anna Fortunato Brivio of the Brivius de Brokles family in 1717. Her family was a very wealthy one and like all wealthy families of that time they were literate. Maria was the eldest of 21 children. Agnesi invited both local celebrities and foreign noblemen to his soirées. During the intermissions between Maria Gaetana’s defenses, her sister, Maria Teresa, a composer and noted harpsichordist, entertained the guests by playing her own compositions.
Education
Maria's father encouraged his daughter’s interest in scientific matters by securing a series of distinguished professors as her tutors and by establishing in his home a cultural salon where she could present theses on a variety of subjects and then defend them in academic disputations with leading scholars.
In all her discourses at these gatherings, Maria Gaetana demonstrated her genius as a linguist. At age five she spoke French fluently. At age nine, she translated into Latin, recited from memory, and released for publication a lengthy speech advocating higher education for women. By age eleven, she was thoroughly familiar with Greek, German, Spanish, and Hebrew. The disputations were conducted in Latin, but during the subsequent discussions a foreigner would usually address Maria in his native tongue and would be answered in that language. The topics on which she presented covered a wide range—logic, ontology, mechanics, hydromechanics, elasticity, celestial mechanics and universal gravitation, chemistry, botany, zoology, and mineralogy, among others.
Some 190 of the theses she defended appear in the Propositiones philosophicae (1738), her second published work.
Although the 1738 compilation does not contain any of Agnesi’s purely mathematical ideas, various other documents indicate her early interest in mathematics and her original approach to that subject. At fourteen she was solving difficult problems in analytic geometry and ballistics. Her correspondence with some of her former tutors indicates that, as early as age seventeen, she was beginning to shape her critical commentary on the Traité analytique des sections coniques of Guillaume de L’Hospital, a leading mathematician of the Newtonian era. The manuscript material that she prepared, although judged excellent by all the professors who examined it, was never published.
Career
In 1738, after the publication of the Propositiones philosophicae, Agnesi indicated that the constant public display of her talents at her father’s gatherings was becoming distasteful to her, and she expressed a strong desire to enter a convent. Persuaded by her father not to take that step, she nevertheless withdrew from all social life and devoted herself completely to the study of mathematics. In the advanced phases of the subject she was guided by Father Ramiro Rampinelli, a member of the Olivetan order of the Benedictines, who later became professor of mathematics at the University of Pavia.
A decade of concentrated thought bore fruit in 1748 with the publication of her Jstituzioni analitiche ad uso della gioventu italiana, which she dedicated to Empress Maria Theresa of Austria. This book won immediate acclaim in academic circles all over Europe and brought recognition as a mathematician to Agnesi. The Jstituzioni analitiche consisted of two huge quarto volumes containing more than a thousand pages. Its author’s objective was to give a complete, integrated, comprehensible treatment of algebra and analysis, with emphasis on concepts that were new (or relatively so) in the mid-eighteenth century. In this connection one must realize that Newton was still alive when Agnesi was born, so that the development of the differential and integral calculus was in progress during her lifetime. With the gioventu (youth) in mind, she wrote in Italian rather than in Latin and covered the range from elementary algebra to the classical theory of equations, to coordinate geometry, and then on to differential calculus, integral calculus, infinite series (to the extent that these were known in her day), and finally to the solution of elementary differential equations. She treated finite processes in the first volume and infinitesimal analysis in the second.
In the introduction to the Jstituzioni analitiche, Agnesi—modest as she was, with too great a tendency to give credit to others—had to admit that some of the methods, material, and generalizations were entirely original with her. Since there were many genuinely new things in her masterpiece, it is strange that her name is most frequently associated with one small discovery which she shared with others: the formulation of the versiera, the cubic curve whose equation is x2y = a2 (a—y) and which, by a process of literal translation from colloquial Italian, has come to be known as the “witch of Agnesi.” She was apparently unaware (and so were historians until recently) that Fermat had given the equation of the curve in 1665 and that Guido Grandi had used the name versiera for it in 1703.
Agnesi’s definition of the curve may be stated as follows: If C is a circle of diameter a with center at ('0, 1/2 a), and if the variable line О A through the origin О intersects the line у = a at points and the circle at point B, then the versiera is the locus of point P, which is the intersection of lines through A and В parallel to the Y axis and X axis, respectively. The curve, generated as the line О A turns (Latin vertere, hence the name versiera), is bell-shaped with the X axis as asymptote. There are interesting special properties and some applications in modem physics, but these do not completely explain why mathematicians are so intrigued by the curve. They have formulated a pseudo-versiera by means of a change in the scale of ordinates (a similarity transformation). Even Giuseppe Peano, one of the most formidable figures in modern axiomatics and mathematical logic, could not resist the temptation to create the “visiera of Agnesi,” as he called it, a curve generated in a fashion resembling that for the versiera.
The tributes to the excellence of Agnesi’s treatise were so numerous that it is impossible to list them all, but those related to translations of the work will be noted. The French translation (of the second volume only) was authorized by the French Academy of Sciences.
An English translation of the Jstituzioni analitiche was made by John Colson, Lucasian professor of mathematics at Cambridge, and was published in 1801 at the expense of the baron de Maseres. In introducing the translation, John Hellins, its editor, wrote: “He [Colson] found her [Agnesi’s] work to be so excellent that he was at the pains of learning the Italian language at an advanced age for the sole purpose of translating her book into English, that the British Youth might have the benefit of it as well as the Youth of Italy.”
The recognition of greatest significance to Agnesi was provided in two letters front Pope Benedict XIV. The first, dated June 1749, a congratulatory note on the occasion of the publication of her book, was accompanied by a gold medal and a gold wreath adorned with precious stones. In his second letter, dated September 1750, the pope appointed her to the chair of mathematics and natural philosophy at Bologna.
But Agnesi, always retiring, never actually taught at the University of Bologna. She accepted her position as an honorary one from 1750 to 1752, when her father was ill. After his death in 1752 she gradually withdrew from all scientific activity. By 1762 she was so far removed from the world of mathematics that she declined a request of the University of Turin to act as referee for the young Lagrange’s papers on the calculus of variations.
The years after 1752 were devoted to religious studies and social work. In 1771 Agnesi became directress of the Pio Albergo Trivulzio, a Milanese home for the aged ill and indigent, a position she held until her death.
Maria Agnesi died on 9 January 1799, and was buried in a mass grave for the poor with fifteen other bodies. This was not uncommon at that time. The cemetery is on the outside of the Roman gate in the city walls of Milan. No monument was added at this tomb.
Religion
She was a devout Catholic and wrote extensively on the marriage between intellectual pursuit and mystical contemplation, most notably in her essay Il cielo mistico (The Mystic Heaven).
She saw the rational contemplation of God as a complement to prayer and contemplation of the life, death and resurrection of Jesus Christ.
Personality
The nature of Maria`s personality was rather modest, so she had never wanted a fabulous lifestyle. At the end of her life she even asked to be buried with no elaborate monument over her grave. Whatever she did, she did with all her heart and tried her hardest.
Agnesi was also very kind and received great respect for her charity work and love to mankind, making great material sacrifices to help the poor of her parish. She had always mothered her numerous younger brothers (there were twenty-one children from Pietro Agnesi’s three marriages), and after her father’s death she took his place in directing their education.
Physical Characteristics:
Agnesi suffered a mysterious illness at the age of twelve that was attributed to her excessive studying and was prescribed vigorous dancing and horseback riding. This treatment did not work; she began to experience extreme convulsions.
Quotes from others about the person
In 1749 a French Academy of Sciences` committee recorded its opinion about Agnesi’s treatise: “This work is characterized by its careful organization, its clarity, and its precision. There is no other book, in any language, which would enable a reader to penetrate as deeply, or as rapidly, into the fundamental concepts of analysis. We consider this treatise the most complete and best written work of its kind.”