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

Luca Pacioli - mathematician and geometrist

Friar who became known as ‘Father of Accounting’

Jacopo de' Barbari's portrait of Luca Pacioli with
an unknown geometry student attending

Luca Pacioli, the Franciscan friar and mathematician who would become known as the ‘Father of Accounting’, died on this day in 1517 in Sansepolcro, a town in eastern Tuscany in the province of Arezzo.

Taking advantage of the development of the printing press, Pacioli is thought to have published at least 10 mathematical textbooks, of which the best known is his Summa de arithmetica, geometria, Proportioni et proportionalita - usually known as simply Summa.

Published in Venice in 1494, it was a comprehensive treatise of every aspect of mathematical knowledge that had been explored to that time and the first book to include a description of the double-entry book-keeping system, widely used by Venetian merchants. The principals he outlined in Summa still influence business practices today.

Pacioli, who taught mathematics in several Italian cities and was appointed the first chair in mathematics at the University of Perugia, was a figure of influence in the arts world as well as commerce.

Having possibly been a student of Piero della Francesca, a pioneer of the use of geometry and perspective in painting and, like Pacioli, a native of Sansepolcro, he later became a close friend of Leonardo da Vinci.

Da Vinci’s drawings illustrated another of his notable works, Divina proportione, an exploration of mathematical and artistic proportion, focussing especially on the so-called golden ratio of proportionality and its application in architecture.

The title page of a 1523 edition of
Pacioli's Summa, his greatest work

Pacioli was around 70 years old when he died, having been born between 1446 and 1448. He received an education based around maths and commerce in Sansepolcro, before moving to Venice in around 1464, continuing his studies there and being appointed tutor to the three sons of a wealthy merchant, Antonio Rompiasi.

From Venice, he moved to Rome, where he became friends with the architect, artist and mathematician Leon Battista Alberti, before returning to Sansepolcro to enter the Franciscan Order in 1470. In the following years, he taught mathematics in Perugia, Florence, Venice, Milan, Pisa, Bologna and Rome. 

After the publication of Summa in 1494, he accepted an invitation from Duke Ludovico Sforza to work in Milan. There he met and taught Leonardo da Vinci, for a time living with the polymath as a house guest. Da Vinci acquired his knowledge of geometry and its applications in art and architecture from his association with Pacioli.

Pacioli might have remained in Milan longer had the city not been overrun by Louis XII of France at the start of the Second Italian War. Ludovico Sforza fled the city, as did Pacioli and da Vinci, first to Mantua, and then Venice.  

Although Pacioli left a significant intellectual legacy in the fields of accounting and mathematics, he was effectively accused of plagiarism by 16th-century artist and historian Giorgio Vasari.

Vasari was critical of the inclusion in Divina proportione - without credit - of the translated text of della Francesca’s book, originally written in Latin, De quinque corporibus regularibus, about the geometry of polyhedra - solid objects with polygonal faces, such as pyramids. Other scholars, though, argue that the edition of Divina proportione that Vasari read may have been appended to include della Francesca’s work after Pacioli’s death.

Pacioli’s final university teaching post is thought to have been in Rome during 1514 and 1515, before returning to Sansepolcro as his health began to decline.

Piero della Francesca's painting, The Resurrection,
which may have spared Sansepolcro a WW2 attack

Travel tip:

Sansepolcro, a town nestled in the Valtiberina valley at the foot of the Apennines, has a rich artistic and cultural heritage. As well as being the home town of Luca Pacioli,  it is known as the birthplace of Renaissance master Piero della Francesca, whose brilliant painting, The Resurrection, is housed in the Museo Civico di Sansepolcro. The presence of the painting probably saved the town from destruction in World War Two after Tony Clarke, an art-loving British Royal Horse Artillery officer who, halted a planned  Allied artillery attack. Another treasure, a 12th-century polychrome wooden crucifix known as the Volto Santo, can be seen in the town’s beautiful Romanesque duomo, the Cattedrale di San Giovanni Evangelista. Look out also for The Lamentation over the Dead Christ, by the Mannerist painter Rosso Fiorentino, in the church of San Lorenzo. Other museums include the Aboca Museum, dedicated to the history of medicinal herbs, featuring antique books, laboratory tools, and botanical collections, as well as the Bernardini-Fatti Museum of Antique Windows, the world’s first museum dedicated to stained glass windows. Sansepolcro’s medieval streets, fortified walls, and historic palazzos make it a delightful place to explore. 

One of Arezzo's notable sights is its sharply
sloping medieval main square, Piazza Grande

Travel tip:

Arezzo is one of the wealthiest cities in Tuscany. It is situated about 80km (50 miles) southeast of Florence, at the confluence of four valleys - Tiberina, Casentino, Valdarno and Valdichiana. Its medieval centre suffered massive damage during the Second World War yet the Basilica di San Francesco, with its beautiful frescoes by Piero della Francesca, the central Piazza Grande, with its sloping pavement in red brick, and the Medici Fortress, the duomo and a Roman amphitheatre survived, among other historic sights.  Arezzo’s original cathedral was built on the nearby Pionta Hill, over the burial place of Donatus of Arezzo, who was martyred in 363. In 1203 Pope Innocent III had the cathedral moved within the city's walls, to the current site in another elevated position a short walk from Piazza Grande.  The interior contains several notable artworks, including a relief by Donatello, entitled Baptism of Christ, and a cenotaph to Guido Tarlati, lord of Arezzo until 1327, said to be designed by Giotto, near to which is Piero della Francesca's Mary Magdalene.  The wooden choir of the Grand Chapel was designed by Giorgio Vasari, who was born in Arezzo. The city is home to an annual medieval festival called the Giostra del Saracino (Saracen Joust), in which "knights" on horseback representing different areas of the town charge at a wooden target attached to a carving of a Saracen king and score points according to accuracy. Arezzo had a starring role in Roberto Benigni's film Life Is Beautiful, which won three Academy Awards, as the place in which the main characters live before they are shipped off to a Nazi concentration camp.

Also on this day:

1918: The death in action of WW1 fighter pilot Francesco Baracca

1932: The birth of actress twin sisters Pier Angeli and Marisa Pavan

1951: The birth of Giro d’Italia-winning cyclist Francesco Moser

Home

Ulisse Dini – mathematician and politician

Patriotic professor was proud to serve the new Kingdom of Italy

Ulisse Dini went to Paris to further
his mathematical education

The mathematician Ulisse Dini, who wrote many books and papers based on his research and came up with original theories that advanced the knowledge in his field, died on this day in 1918 in Pisa.

Now regarded as one of the 19th century's most important contributors to the evolution of mathematics, Dini was also active as a politician and was elected to Pisa city council before becoming a member of the parliament of the new Kingdom of Italy. 

His political views were shaped by the changing landscape of Italy while he was growing up, as the country moved closer to unification, and he was always keen to help his local area and his country.

Originally intending to become a teacher, Dini, who was born in Pisa in 1845 when the city was part of the Grand Duchy of Tuscany, attended the Scuola Superiore in Pisa, a teachers’ college, where one of his teachers was the mathematician, Enrico Betti.

However, in 1865, Dini received a scholarship that enabled him to go to Paris to further his mathematical studies, where he was taught by the French mathematicians, Charles Hermite and Joseph Bertrand. He produced seven mathematical publications based on the research he was able to do while living in Paris.

The following year he was appointed by the University of Pisa to teach algebra and geodesy, the science of measuring and representing the geometry, gravity, and spatial orientation of the earth in temporally varying 3D. 

Dini succeeded Betti as professor for analysis and geometry at the university in 1871. He was rettore - rector - of Pisa University from 1888 until 1890, and of the Scuola Superiore in Pisa from 1908 until his death. One of his students at Pisa University was the Italian mathematician, Luigi Bianchi.

Enrico Betti was 
Dini's teacher

Professor Dini is particularly known for his contribution to the branch of mathematics known as real analysis, which studies the behaviours of real numbers, sequences and series of real numbers, and real functions. He collected his theories in his book, ‘Fondamenti per la teorica delle funzioni di variabili reali’, a collection of ideas that were entirely originated by himself. 

Despite his heavy academic workload, Dini had entered politics by the age of 25, when he was elected to the city council in Pisa.

When Dini was 13, the fight had begun to win back areas of the country from the Austrian occupying forces. Within a few years, forces representing the Kingdom of Sardinia had gained control of many areas in central Italy. Victor Emmanuel II of Sardinia later assumed the title of King of Italy, and Giuseppe Garibaldi and his 1000 volunteers set out to unify the country, starting by invading Sicily. With his forces, Garibaldi gradually moved northwards up the peninsula and this led to the official proclamation of the Kingdom of Italy in 1861.

Ulisse Dini is remembered by historians and writers as an upright, honest, and kind man, and for being devoted to the well-being of his city and country. He divided his time between teaching and research and public service, and in 1892 he became a senator in the Italian parliament. 

In the field of mathematical analysis, he is remembered for being the originator of Dini criterion and Implicit function theorem. He was considered one of the most important European mathematicians of the 19th century and he was elected as an honorary member of the London Mathematical Society.

After his death, Dini was buried in Pisa’s monumental cemetery, Campo Santo, on the northern edge of the Campo dei Miracoli. There is a statue commemorating his life in Via Ulisse Dini in the city’s historic centre. 

The 15th century Palazzo della Sapienza, built by
the Medici family, remains the heart of the university

Travel tip: 

The University of Pisa, founded in 1343, is one of the oldest in Italy and rivals Rome’s Sapienza University for the title of the country’s best. Various scholars place its origins in the 11th century, although those claims have never been verified. What is certain is that the papal seal “In Supremae dignitatis”, issued by Pope Clement VI on 3 September 1343, granted the Studium in Pisa the title of Studium Generale. At the outset in Pisa, lessons in Theology, Civil Law, Canon Law and Medicine were established. In its early years, the university struggled to survive at times, but investment from the Medici family in the 15th century saw the construction of the Palazzo della Sapienza, still the centre of the present-day university. Cosimo I de’ Medici instituted programmes to improve the quality of teaching and later Galileo Galilei, universally seen as the founder of modern science, was initially a student and then a teacher of Mathematics at the university. Today, Pisa has a student population of around 50,000, who give the city a vibrant cafe and bar scene.

The bronze statue of Ulisse 
Dini was finished in 1927

Travel tip: 

The bronze sculpture of Ulisse Dini in Via Ulisse Dini was created in 1927 by Leonardo Bistolfi, a sculptor from Casale Monferrato in Piedmont, whose work was praised for its likeness to the subject.  Via Ulisse Dini goes from Borgo Stretto to Piazza dei Cavalieri and Dini’s statue stands beside the Church of Santo Stefano dei Cavalieri. Once a stream flanked by wooden houses belonging to the city’s higher social classes, the street subsequently became a centre for forges and metalworkers’ workshops. Some of the stone arches lining the modern street date back to the 12th century.  Aside from the Campo dei Miracoli, the biggest attraction of which is the city’s world famous leaning bell tower, Pisa offers visitors a wealth of well-preserved Romanesque buildings, Gothic churches and Renaissance piazzas.

Also on this day:

312: The Battle of Ponte Milvio

1639: The death of composer Stefano Landi

1922: Mussolini’s Fascists march on Rome

1963: The birth of singer-songwriter Eros Ramazzotti

1973: The death of actor and illustrator Sergio Tòfano

Home