Clelia Grillo Borromeo Arese – mathematician and natural philosopher

Noble woman made an important geometrical discovery

Clelia Borromeo Arese was from an aristocratic
family but was also an eminent scientist

An aristocratic woman who was recognised as a brilliant mathematician and scientist of her time, Clelia Grillo Borromeo Arese, died on this day in 1777 in Milan.

Borromeo Arese had become known for her outstanding ability to solve difficult mathematical problems and she was also considered to be a natural philosopher, having made a study of how the world worked.

She was born in Genoa in 1684, the daughter of Duke Marcantonio Mondragone and his wife, Antonia. 

As young Clelia grew up she received a good education, at first from her mother, Antonia, and then at a convent that she attended. She became proficient in eight languages and was interested in geometry and how things worked.

In 1707 she married Count Giovanni Benedetto Borromeo Arese and they had eight children together. Her husband was the son of Carlo Borromeo Arese, one of the most wealthy and powerful men in Italy at the time.

Borromeo Arese often invited scientists to her home in Milan, both from Italy and abroad. A frequent visitor there was Antonio Vallisneri, who was  a physician, naturalist and a professor of Medicine at the University of Padua. 

His host was an avid reader of books and journals and visitors to her house were often struck by the breadth and depth of her extensive library.

She started her own academy at her home in 1717, which was called the Academia Vigilantium Cleli and she became famous for being able to solve any mathematical problem that she was given. Her academy also played a major role in the ongoing scientific debates of the time.

Among the Academy’s members were the mathematicians Giovanni Saccheri and Tomasso Ceva, and physicists such as Giovanni Crivelli and Alessandro Volta. The Academy played a prominent role in the dissemination of the physics of Newton and the philosophy of Leibnitz.

Scientist Alessandro Volta was a member
of Borromeo Arese's academy

In 1726, Borromeo Arese made an important discovery of her own in geometry. She identified a special kind of curve, on the surface of a sphere, which became known as the Clelia curve.

As an example, a path marked on the surface of a planet to correspond with an orbiting satellite's trajectory would follow a Clelia curve.

An independent woman, Borromeo Arese formed her own opinions and she chose to support Spain against Austria during the war in 1746, As a result, she had to leave Milan for a while, but when she was allowed to return home she was welcomed back as a heroine by the Milanese people.

Genoa, the city where she was born, honoured her contribution to geometry by awarding her a medal, which was inscribed with the words ‘Genuensium Gloria’, which means ‘The Honour of Genoa’.

After her death in 1777, Clelia Grillo Borromeo Arese was buried in the Church of Santa Maria Podone, a Greek Orthodox church in the centre of Milan.

The Italian monk and mathematician, Luigi Guido Grandi, who had also been a member of Borromeo Arese’s Academy, wrote about the Clelia curve in a book that he dedicated to her. He wrote that ‘Clelia curves are curves on the earth’s sphere for whose points there is a linear relationship between longitude and colatitude’. 

A colatitude is the complement of a given latitude. It is found by subtracting the latitude angle from 90 degrees. Instead of measuring distance up or down from the equator, it measures the angle down from the North Pole.

The striking black-and-white
facade of San Lorenzo Cathedral

Travel tip:

The port city of Genoa, where Clelia Grillo Borromeo Arese was born, is capital of the Liguria region. It has a rich history as a trading centre with wealth built on its shipyards and steelworks. It also has fine buildings, many of which have been restored to their original splendour. The Palazzo Ducale - the Doge's Palace - the 16th century Palazzo Reale, a lavish royal residence with frescoes, tapestries and a rooftop garden, and the Romanesque-Renaissance style San Lorenzo Cathedral, with its striking black-and-white façade, are three examples worth visiting.  At the heart of the city centre is the Piazza De Ferrari, which features a monumental bronze fountain and is flanked by the Palazzo Ducale, the Palazzo della Borsa and the Teatro Carlo Felice.  The area around the restored harbour area has some fascinating alleyways and squares to explore and it has been enhanced in recent years by the Genoa architect Renzo Piano. 

Stay in Genoa with Expedia

Palazzo Borromeo is one of the finest 
examples of a Milanese patrician palace

Travel tip:

The Borromeo family of Milan, into which Clelia Grillo Borromeo Arese married, were rich nobles, who started out as merchants and then became bankers. They played important roles in politics, and as cardinals during the Counter-Reformation movement in Italy. Federico Borromeo, who was Archbishop of Milan, founded the Bibliotheca Ambrosiana in Milan, one of Europe’s first, free public libraries. The ancestral home of the Borromeo family in Milan is Palazzo Borromeo, a late 14th century palace in Piazza Borromeo, about 10 minutes’ walk from the Duomo. It was originally built as both the home and business headquarters of the family. They had moved to Milan after fleeing from San Miniato, outside Florence, when the head of the family, Filippo, was executed.  It contains an important fresco cycle from the 1440s and is one of the finest examples of a Milanese patrician palace from the early Renaissance. Parts of the building were badly damaged during Allied bombings in World War II but were reconstructed and restored to their original appearance. 

Search Hotels.com for accommodation in Milan

More reading:

Federico Borromeo, the Archbishop of Milan who founded the Biblioteca Ambrosiana

Saint Charles Borromeo and the movement to combat the spread of Protestantism

Luigi Guido Grandi – monk, philosopher and mathematician

Also on this day:

1923: The murder by Fascist thugs of Catholic priest Don Giovanni Minzoni

1943: The birth of bass player and composer Pino Presti 

1945: The birth of teenage singing star Rita Pavone

1974: The death of psychiatrist Roberto Assagioli 

Home

Maria Gaetana Agnesi – mathematician

Brilliant scholar gave her time and money to the poor

Maria Gaetana Agnesi learned
seven languages by the age of 11

Maria Gaetana Agnesi, the first woman to write a mathematics handbook, was born on this day in 1718 in Milan.

Maria became a mathematician, philosopher, theologian and humanitarian and was also the first woman to be appointed as a mathematics professor at a university.

She was one of at least 21 children born to Pietro Agnesi, a wealthy man whose family had made their money from silk production. Her mother was his first wife, Anna Fortunato Brivio, who was from a noble Milanese family.

Maria was soon recognised as a child prodigy, who could speak Italian and French by the time she was five and had learnt Greek, Hebrew, Spanish, German and Latin by the time she was 11.

When she became ill at the age of 12, it was thought to have been because of excessive studying and reading, but after she was prescribed vigorous dancing and horse riding to improve her health, she suffered convulsions and was then advised to moderate her activities.

By the time Maria was 14 she was studying ballistics and geometry. Her father regularly invited learned men to his house to listen to her read and to discuss philosophical questions with her.

The cover page of Agnesi's Instituzioni
 analitiche ad uso della gioventu italiana

After Maria’s mother died, her father remarried twice and Maria was given the task of teaching all her siblings and half-siblings.

This stopped her from fulfilling her wish to enter a convent.  Instead, her father agreed to let her live away from society and devote herself to the study of mathematics.

In 1740 she began studying differential and integral calculus with esteemed Italian mathematician Ramiro Rampinelli.

By 1748 Maria had published her Instituzioni analitiche ad uso della gioventù italiana. She said this was to give a systematic illustration of the different results and theorems of infinitesimal calculus. The work was translated into French and English and Maria received letters and gifts from the Habsburg Empress Maria Theresa and Pope Benedict XIV.

In the book, Maria discusses a curve that had been studied earlier by the mathematician Luigi Guido Grandi. He had called the curve ‘versoria,’ the Latin word for a rope that turns a sail, because that is what it reminded him of.  This was mistranslated as the word ‘witch’ in the English version and so the curve became known as ‘The Witch of Agnesi’.

The bust of  Agnesi at the
Palazzo di Brera in Milan

In 1750 Pope Benedict XIV appointed Maria to the chair of mathematics and natural philosophy and physics at Bologna University, although she never actually taught there. She was the second woman in the world to be granted a professorship at a university, Laura Bassi, an Italian physicist being the first.

After the death of her father in 1752, Maria finally had the chance to study theology. She then worked with the poor, sick and homeless, founding a home for the elderly in Milan, where she went to live.

In January 1799, Maria Gaetana Agnesi died at the age of 80. She was buried in a mass grave for the poor along with 15 other bodies.

An asteroid, 16765 Agnesi, a crater on Venus and a brandy are all named after her, as well as the mathematical curve, the Witch of Agnesi.

The Villa Agnesi Albertoni at Montevecchia in the province
of Lecco, where Maria and her family spent the summer

Travel tip:

You can visit the Villa Agnesi Albertoni, where Maria and her family spent time during the summer, which is in Largo Maria Gaetana Agnesi at Montevecchia in the province of Lecco, about 30 kilometres (19 miles) northeast of Milan. The villa has been preserved in the rococo style in which it was built during the 17th century. Visitors can still see the ‘salotto’, where eminent visitors would discuss philosophy with Maria Gaetana Agnesi and hear one of her sisters, Maria Teresa Agnesi play her own compositions on the harpsichord.

The famous Archiginnasio, the
university's anatomical theatre

Travel tip:

Bologna University, where Maria Gaetana Agnesi was the first woman to be appointed as a mathematics professor, was founded in 1088, making it the oldest university in the world. It attracted popes and kings as well as students of the calibre of Dante, Copernicus and Boccaccio. You can still visit one of the original university buildings in the centre of Bologna, the former anatomy theatre, the Archiginnasio, in Piazza Galvani. It is open Monday to Saturday from 9 am to 1 pm, admission free.

Also on this day:

1915: The birth of film director Mario Monicelli

1945: The birth of business tycoon Massimo Moratti

1974: The birth of singer-songwriter Laura Pausini


Home

Luigi Guido Grandi – monk, philosopher and mathematician

Man of religion who advanced mathematical knowledge

Luigi Guido Grande was an
acclaimed mathematician

Luigi Guido Grandi, who published mathematical studies on the cone and the curve, died on this day in 1742 in Pisa.

He had been court mathematician to the Grand Duke of Tuscany, Cosimo III de’ Medici, and because he was also an engineer, he was appointed superintendent of water for the Duchy.

Grandi was born in 1671 in Cremona and was educated at the Jesuit College in the city.

He joined the Camaldolese monks at Ferrara when he was 16 and a few years later he was sent to the monastery of St Gregory the Great in Rome to complete his studies in philosophy and theology in preparation for taking holy orders.

Having become a professor in both subjects at a monastery in Florence, he became interested in mathematics, which he studied privately.

Grandi soon developed such a reputation in the field of mathematics that he was appointed court mathematician by Cosimo III.

Grandi was involved with the drainage of the
Chiana Valley, south of Arezzo

While also serving as Superintendent of Water at the Medici court, he was involved in the drainage of the Chiana valley, which runs north to south between Arezzo and Orvieto.

In 1709 Grandi visited England, where he was elected a Fellow of the Royal Society, and in 1714 he was named Professor of Mathematics by the University of Pisa.

He published studies on the conical loxodrome and on the curve, which he named versiera from the Latin verb, to turn. The curve was later studied by the female scientist Maria Gaetana Agnesi. Through a mistranslation into English, the curve became known in England as Agnesi’s witch, because the translator mistook the word for curve, for the word for witch.

Grandi was perhaps best known for his work on the rose curve, which he named rhodonea. The mathematician died in Pisa on 4 July 1742.

The Sperlari shop in Cremona specialises in torrone (nougat)

Travel tip:

Cremona, where Grandi was born, is famous for having the tallest bell tower in Italy, il Torrazzo, which measures more than 112 metres in height. As well as being well known for making violins, Cremona also produces confectionery. Negozio Sperlari in Via Solferino specialises in the city’s famous torrone (nougat). This concoction of almonds, honey and egg whites was created in the city to mark the marriage of Bianca Maria Visconti to Francesco Sforza in 1441, when Cremona was given to the bride as part of her dowry.

The Bapistery in Pisa's Campo dei Miracoli

Travel tip:

Pisa, where Grandi was a professor at the university until he died, is famous for its Leaning Tower. The tower is one of the four buildings that make up the cathedral complex in the Field of Miracles (Campo dei Miracoli). The Duomo was the first to be constructed and then the Baptistery was added. While work on the tower was being carried out, a cemetery (Campo Santo) was added. During the summer, the Leaning Tower is open to visitors from 08.30 to 22.00. Tickets to climb the tower are limited and booking in advance is recommended if you want to avoid queuing. For more details, visit www.towerofpisa.org/tickets.

More reading:

Why Einstein nodded his respect to this mathematician from Padua

Scientist who emerged from Galileo's shadow

When Italy needed the world's help to save the Leaning Tower

Also on this day:

1914: The birth of the car designer Giuseppe Bertone

1927: The birth of the actress Gina Lollobrigida

Home