Showing posts with label Mathematics. Show all posts
Showing posts with label Mathematics. Show all posts

24 September 2021

Girolamo Cardano - doctor and mathematician

Polymath was also a gambler and womaniser

Girolamo Cardano was the leading mathematician of Renaissance Italy
Girolamo Cardano was the leading
mathematician of Renaissance Italy
The Renaissance polymath Girolamo Cardano, whose range of talents included mathematics and medicine but who also invented a number of mechanical devices still in use today, was born on this day in 1501 in Pavia, then part of the Duchy of Milan.

Cardano, also known as Gerolamo, Hieronymus Cardanus in Latin and Jerome Cardan in English, is notable for writing Ars Magna which was the first Latin treatise devoted solely to algebra.

Far from being a stuffy academic, however, Cardano led a controversial life, practising as a physician without a licence and becoming proficient at gambling to keep himself solvent, while as a university professor being regularly accused of sexual impropriety with students.

In his wide range of interests, he seemed to be inspired by Leonardo da Vinci, who was a close friend of his father. Like Da Vinci, he wanted to put his mathematical and scientific skills to practical use and is credited with inventing among other things the first combination locks, the gimbal that allows a supported compass or gyroscope to rotate freely, and a universal joint that allows the transmission of rotation between the components of a drive train even when out of alignment.

A version of the joint in use today to connect the gearbox of a rear-wheel drive car with the rear axle is called a Cardan Shaft.

Girolamo Cardano was the illegitimate child of Fazio Cardano, a Milanese lawyer and university professor, and Chiara Micheria, a widow 20 years Fazio’s junior. Despite his mother’s attempts to abort the pregnancy, Girolamo was born at the home of some wealthy friends of his father in Pavia, where his mother was sent to escape an outbreak of plague in Milan that claimed the lives of her three other children.

The cover page of Ars Magna, seen as Cardano's magnum opus
The cover page of Ars Magna, seen
as Cardano's magnum opus
Girolamo survived a sickly childhood and, fascinated with philosophy and science, enrolled to read medicine at the University of Pavia, against the wishes of his father, who wanted him to study law.  The Italian War of 1521-26 forced the University of Pavia to close but he was able to resume his studies at the University of Padua.

There, however, he gained a reputation for being awkward and confrontational and while he obtained a doctorate he was denied admission to the College of Physicians in Milan, partly because he was not well liked and partly because of his illegitimacy.  

Unable to practise medicine legally in Milan, he moved to Saccolongo, a village outside Padua where he set up a practice despite his lack of a licence. He married Lucia, the daughter of a local militia captain, with whom he had three children.  His practice was not particularly successful, however, and he increasingly turned to gambling to make money, a habit he had developed while studying, but slipped further into debt.

Desperate for a change of fortune, he moved the family back to Milan. They had so little money they were forced to live in a poorhouse but Girolamo eventually elicited help from contacts of his father in the Milanese nobility, who arranged for him to be given his father’s former post of lecturer in mathematics at the Piatti Foundation in Milan.

For all that he was a difficult character, his brilliant mind was never in doubt and when the College of Physicians changed their attitude to illegitimacy he was granted his licence.  His success in treating his patients, some of whom had wide influence in Milan society, soon made him the most sought-after doctor in the city.

Cardano's universal joint is still used in the drive shafts of motor vehicles today
Cardano's universal joint is still used in the
drive shafts of motor vehicles today 
The next few years were his most productive. In 1537, he published the first of some 130 printed works, the most famous of which was Ars Magna, published in 1545. It included the first comprehensive solution for finding roots of cubic equations, which at the time was a subject that was the focus of much attention. Even that was the subject of controversy as Nicolo Tartaglia, another mathematician of note, accused Cardano of publishing results shared with him in confidence. 

He also wrote Liber de ludo aleae - Book on Games of Chance - which contains the first systematic treatment of probability, the basic concepts of which he had learned through his gambling. He also shared some of his secrets on how to cheat successfully.

Cardano did much of his inventing during this period, and enhanced his reputation as one of the world’s finest physicians, becoming rector of the College of Physicians that for so long rejected him. 

He turned down most invitations to work outside Italy but made an exception when asked to travel to Scoland, where John Hamilton, Archbishop of St Andrews, was suffering increasingly severe asthma attacks that the physicians of both the French king and German emperor had been unable to keep in check.

Cardano was also known for his chaotic and controversial personal life
Cardano was also known for his chaotic
and controversial personal life
Cardano was welcomed as a celebrity when he landed in Scotland, where he was promised a substantial payment if he could treat the Archbishop successfully. In the event, he quickly established that feather pillows were the cause of the Archbishop’s malady and the patient made a full recovery.

For all that he was ultimately hailed as a genius, Cardano's personal life was filled with tragedy.

Lucia died in 1546, his eldest son was executed for poisoning his wife and his daughter died of syphilis. He disowned his second son, who stole money from him to fund his own gambling addiction.

Cardano was appointed a professor of medicine at the University of Bologna but as the father of a convicted murderer he was shunned by many colleagues, while his arrogant manner made him many enemies.  A shameless womaniser, he was frequently accused of using his power to coerce female students into inappropriate relationships.

In 1570 he spent a short time in jail, having been accused of heresy after publishing a horoscope of Jesus Christ.  It cost him his position at the University of Bologna.

Nonetheless, on moving to Rome he received a lifetime annuity from Pope Gregory XIII and was accepted in the Royal College of Physicians. He continued to practise medicine and expanded his philosophical studies. 

He died in Rome in 1576 at the age of 74. 

The covered bridge linking Pavia with the area known as Borgo Ticino
The covered bridge linking Pavia with the
area known as Borgo Ticino
Travel tip:

Pavia is a city in Lombardy, about 46km (30 miles) south of Milan. Its university was founded in 1361 and was the sole university in the Duchy of Milan until the 19th century. As well as Girolamo Cardano, its alumni include explorer Christopher Columbus, physicist Alessandro Volta and the poet and revolutionary Ugo Foscolo. Pavia is also famous for its Certosa, a magnificent Renaissance monastery complex north of the city that dates back to 1396 and includes a number of important sculptures and frescoes. A pretty covered bridge over the River Ticino leads to Borgo Ticino, where the inhabitants claim to be the true people of Pavia.

Giotto's frescoes cover the inner walls of the Scrovegni Chapel
Giotto's frescoes cover the inner
walls of the Scrovegni Chapel
Travel tip:

Padua in the Veneto is one of the most important centres for art in Italy and home to the country’s second oldest university. Padua has become acknowledged as the birthplace of modern art because of the Scrovegni Chapel, the inside of which is covered with frescoes by Giotto, an artistic genius who was the first to paint people with realistic facial expressions showing emotion. His scenes depicting the lives of Mary and Joseph, painted between 1303 and 1305, are considered his greatest achievement and one of the world’s most important works of art. At Palazzo Bo, where Padua’s university was founded in 1222, you can still see the original lectern used by Galileo and the world’s first anatomy theatre, where dissections were secretly carried out from 1594.

Also on this day:

1934: The birth of exiled Princess Maria Pia of Bourbon-Parma

1954: The birth of footballer Marco Tardelli

1955: The birth of businessman Riccardo Illy


16 May 2020

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 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
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 Maria Gaetana Agnesi at the Palazzo di Brera in Milan
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
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
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


20 January 2019

Rafael Bombelli – mathematician

First person to explain algebra in simple language

The front cover of the 1579 edition of Bombelli's text, published in Bologna
The front cover of the 1579 edition of
Bombelli's text, published in Bologna
Rafael Bombelli, the mathematician regarded as the inventor of complex numbers, was baptised and was also probably born on this day in 1526 near Bologna.

He wrote a book about algebra in simple language that could be understood by everyone, giving a comprehensive account of what was known about the subject at the time. The first three volumes, published in 1572, were the first European texts to explain how to perform computations with negative numbers.

Rafael Bombelli was the eldest son of Antonio Mazzoli, a wool merchant, who had changed his name to Bombelli to disassociate himself from the reputation of his family. His grandfather had taken part in a failed attempt to seize Bologna on behalf of the Bentivoglio family but had been caught and executed. Antonio Mazzoli was able to return to Bologna only after changing his name to Bombelli.

It is thought that Rafael Bombelli did not attend university but was taught by an engineer-architect named Pier Francesco Clementi.

He followed Clementi into the profession and acquired a patron, Alessandro Rufini. His patron was given the right to reclaim marsh land in the Val di Chiana by the Pope and Bombelli worked on this project until 1555 when there was an interruption to the reclamation work.

Bombelli wrote his algebra book while staying in his patron's villa in Frascati, outside Rome
Bombelli wrote his algebra book while staying in
his patron's villa in Frascati, outside Rome
While he was waiting for the project to start again he decided to write an algebra book, while living in the comfortable surroundings of his patron’s villa just outside Rome in Frascati.

He felt that the reason for arguments between mathematicians was the lack of a careful exposition of the subject. The only books about algebra were not accessible to people without a thorough grasp of mathematics and he deliberately used simple language to make the book available to people who had not received higher education.

He died in Rome in 1572, soon after the first three volumes of the book were published. The unfinished manuscript of the other two volumes was discovered in a library in Bologna in 1923 and published in 1929.

Despite the delay in publication, Bombelli’s Algebra was a very influential work and was praised by later mathematicians because his analysis of the subject showed him to be far ahead of his time.

A crater on the moon has been named the Bombelli crater in honour of him.

The church of Santa Maria Assunta in Borgo Panigale
Travel tip:

Bombelli’s family lived in Borgo Panigale, a small town to the north of Bologna, which was annexed to the city by the Fascist government in 1937. It is now home to Bologna’s Guglielmo Marconi airport and the motorbike manufacturer Ducati. The Bologna artist Elisabetta Sirani painted an altarpiece for the parish church of Borgo Panigale. It is thought the name stems in part from the land around the site of the town, which was formerly used for the cultivation of the foxtail millet cereal called panìco in Italian.

The facade of the Villa Falconieri in Frascati, where Bombelli stayed
The facade of the Villa Falconieri in
Frascati, where Bombelli stayed
Travel tip:

The Villa Falconieri in Frascati, to the south of Rome, was originally called Villa Rufina, having been built for Alessandro Rufini in 1546. It was while staying in this villa that Bombelli wrote his famous work on Algebra, which he dedicated to his patron, Rufini. The villa, which was renovated by the leading Roman Baroque architect Francesco Borromini after it was sold in 1628, houses many beautiful frescoes and is surrounded by splendid Italian gardens with a small lake bordered by cypresses. Now the headquarters of the Vivarium Novum Latin and Humanities Academy, it is open to the public from 10am to 1pm each Sunday.

More reading:

The mathematician who turned down Peter the Great of Russia

The maths professor who won the equivalent of a Nobel Prize at just 34

The mathematician and scientist who discovered the secret of embalming

Also on this day:

1920: The birth of filmmaker Federico Fellini

1950: The birth of former Vogue editor Franca Sozzani

1987: The birth of motorcycle racer Marco Simoncelli


26 November 2018

Enrico Bombieri – Mathematician

Brilliant professor who won top award in his field at just 34

Enrico Bombieri is one of the world's leading mathematicians
Enrico Bombieri is one of the
world's leading mathematicians
The mathematician Enrico Bombieri, one of the world’s leading authorities on number theory and analysis, which has practical application in the world of encryption and data transmission, was born on this day in 1940 in Milan.

Bombieri, who is also an accomplished painter, won the Fields Medal, an international award for outstanding discoveries in mathematics regarded in the field of mathematical sciences as equivalent to a Nobel Prize, when he was a 34-year-old professor at the University of Pisa in 1974.

As well as analytic number theory, he has become renowned for his expertise in other areas of highly advanced mathematics including algebraic geometry, univalent functions, theory of several complex variables, partial differential equations of minimal surfaces, and the theory of finite groups.

Mathematics textbooks now refer to several discoveries named after him in his own right or with fellow researchers, including the Bombieri-Lang conjecture, the Bombieri norm and the Bombieri–Vinogradov theorem.

Enrico Bombieri read his first book of algebra when he was eight and wrote his first scholarly article when he was 17
Enrico Bombieri read his first book of algebra when he was
eight and wrote his first scholarly article when he was 17
He has been described as a "problem-oriented" scholar - one who tries to solve deep problems rather than to build theories.

According to colleagues, his analytical ability, combined with great powers of innovation, enable him to recognize elements of a solution that may already be present and to apply techniques and results from other fields to reach a final conclusion.

The fourth child and only son of a banker in Milan, Bombieri is said to have read his first algebra book at the age of eight.

He became more seriously interested in maths began at high school when, as a 15-year-old student, he picked up a book on number theory that introduced him to the great 19th century German mathematician Bernhard Riemann. He developed a fascination with numbers that never left him.

He published his first scholarly article in 1957, while still only 16 years old. In 1963, aged 22, he graduated in mathematics at the University of Milan and then studied at Trinity College, Cambridge.

Enrico Bombieri emigrated to the United States in 1977
Enrico Bombieri emigrated to the
United States in 1977
Between 1963 and 1966, Bombieri was an assistant professor and then a full professor at the University of Cagliari, holding the same position at the University of Pisa until 1974 and then at the Scuola Normale Superiore in Pisa from 1974 to 1977.

From Pisa he emigrated in 1977 to the United States, where he became a professor at the School of Mathematics at the Institute for Advanced Study in Princeton, New Jersey. In 2011 he became professor emeritus.

Bombieri has always been keen to disprove the notion that mathematicians are by nature single-focused nerds with no interests beyond their own field.

As a young man, he was a student of Alpine botany, in particular wild orchids, and has become an accomplished painter.

He experimented with pencil drawings and water colours at a young age and throughout his academic life has always carried paints and brushes with him on his travels.

He began to take his art more seriously after moving to the United States, enrolling to study study painting and printmaking at Mercer County Community College at West Windsor, New Jersey.

Bombieri paints people, animals and landscapes. His paintings are described as often surreal or intentionally ambiguous, although he also accepts commissions for portraits.

One work he is said to have been particularly proud of depicts a giant chessboard by a lake, with pieces placed to represent a critical point in the historic match between world champion Garry Kasparov and the chess-playing computer, Deep Blue.

Bombieri himself was a member of the Cambridge University chess team during his time at Trinity College.

The cloister at the main building of the University of Milan, founded in 1924 after the merger of other institutions
The cloister at the main building of the University of Milan,
founded in 1924 after the merger of other institutions 
Travel tip:

The University of Milan was founded in 1924 from the merger of the Accademia Scientifico-Letteraria (Scientific-Literary Academy)and the Istituti Clinici di Perfezionamento (Clinical Specialisation Institutes), established in 1906. By 1928, the University already had the fourth-highest number of enrolled students in Italy, after Naples, Rome and Padua. Its premises are located primarily in Città Studi, the university district which was developed from 1915 onwards to the northeast of the city centre, although there are other buildings around the city that are now part of the University.  The streets of the Città Studi area are notable for bars, pizza restaurants and ice cream shops.

There is much more to historic Pisa than the Campo dei Miracoli and the Leaning Tower
There is much more to historic Pisa than the
Campo dei Miracoli and the Leaning Tower
Travel tip:

Many visitors to Pisa confine themselves to the Campo dei Miracoli, where the attractions are the famous Leaning Tower, the handsome Romanesque cathedral and its impressive baptistry. But there is much more to Pisa. The University of Pisa, founded in 1343, now has elite status, rivalling Rome’s Sapienza University as the best in Italy, and a student population of around 50,000 makes for a vibrant cafe and bar scene. There is also much to see in the way of Romanesque buildings, Gothic churches and Renaissance piazzas.

More reading:

Einstein's favourite mathematician

Salvador Luria - Nobel Prize-winning microbiologist

Grazia Deledda - the first Italian woman to win a Nobel Prize

Also on this day:

1908: The birth of businessman and hotelier Charles Forte

1949: The birth of politician and businesswoman Letizia Moratti

1963: The death of opera singer Amelita Galli-Curci


4 July 2018

Luigi Guido Grandi – monk, philosopher and mathematician

Man of religion who advanced mathematical knowledge

Luigi Guido Grande was an acclaimed mathematician
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)
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
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

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


15 April 2018

Jacopo Riccati – mathematician

Venetian nobleman who was fascinated by Maths

Jacopo Francesco Riccati turned down several important posts to remain with his family
Jacopo Francesco Riccati turned down several
important posts to remain with his family

Respected mathematician, Jacopo Francesco Riccati, who had an equation named after him, died on this day in 1754 in Treviso.

He had devoted his life to the study of mathematical analysis, turning down many prestigious academic posts offered to him. He is chiefly remembered for the Riccati differential equation, which he spent many years studying.

Riccati was born in 1676 in Venice. His father, Conte Montino Riccati, was from a noble family of land owners and his mother was from the powerful Colonna family. His father died when Riccati was only ten years old, leaving him a large estate at Castelfranco Veneto.

Riccati was educated first at the Jesuit school for the nobility in Brescia and in 1693 went to the University of Padua to study law.

After receiving a doctorate in law in 1696 be began to study mathematical analysis.

He was invited to Russia by Peter the Great to be president of the St Petersburg Academy of Sciences, also to Vienna to be an imperial councillor, and he was offered a professorship at the University of Padua, but he declined them all, preferring to remain on his estate with his family studying on his own.

Riccati's works were published in four volumes
Riccati's works were published in four volumes
Mathematician Maria Gaetani Agnesi included some of his work on multinomials in the book on integral calculus within her work, Analytical Institutions.

Riccati married Elisabetta dei Conti d’Onigo and they had 18 children. Nine died during infancy, but nine survived. The two most famous were Vincenzo Riccati, who made important contributions to mathematical physics and Giordano Riccati, who carried out scientific experiments.

After his wife died in 1749, Riccati moved to live at his house in Treviso. He died there in 1754 and was buried in Treviso’s Duomo, where the Riccati family had their own chapel.

Riccati’s Opere - Works - were published in four volumes in 1765, edited by his son, Giordano.

The impressive walls of Castelfranco Veneto
The impressive walls of Castelfranco Veneto
Travel tip:

Castelfranco Veneto, where Riccati had his estate, is an ancient walled town in the Veneto region of Italy. It is also famous for being the birthplace of the Renaissance artist, Giorgione. The Duomo, which is inside the walls, contains one of his finest works, Madonna with St Francis and Liberalis, which was painted in 1504.

Treviso is famed for its picturesque canals
Treviso is famed for its picturesque canals
Travel tip:

Treviso, where Riccati lived towards the end of his life, is an historic, walled city in the Veneto region, with picturesque canals and water wheels. It is the headquarters of the clothing firm, Benetton, and is famous for producing Prosecco wine and the vegetable, radicchio.

More reading:

Tullio Levi-Civita, the mathematician who influenced Einstein

How Vincenzo Viviani was a friend of Galileo and studied the surface of the moon

Francesca Porcellato - inspiring paralympian from Castelfranco Veneto

Also on this day:

1446: The death of architect Filippo Brunelleschi

1452: The birth of the great painter and inventor Leonardo da Vinci


1 January 2018

Guglielmo Libri – book thief

Nobleman stole more than 30,000 books and documents

Guglielmo Libri is thought to have stolen more than 30,000 books, manuscripts and letters
Guglielmo Libri is thought to have stolen more
than 30,000 books, manuscripts and letters
The notorious 19th century thief Guglielmo Libri, who stole tens of thousands of historic books, manuscripts and letters, many of which have never been found, was born on this day in 1803 in Florence.

A distinguished and decorated academic, Libri was an avid collector of historic documents whose passion for adding to his collections ultimately became an addiction he could not satisfy by legal means alone.

He stole on a large scale from the historic Laurentian Library in Florence but it was after he was appointed Chief Inspector of French Libraries in 1841 – he had been a French citizen since 1833 – that his nefarious activities reached their peak.

As the man responsible for cataloguing valuable books and precious manuscripts across the whole of France, Libri had privileged access to the official archives of many cities and was able to spend many hours in dusty vaults completely unhindered and unsupervised.

He was in a position to “borrow” such items as he required in the interests of research with no pressure to return them. Where the removal of a book or document was forbidden, he would smuggle them out under the huge cape that he insisted on wearing – on the grounds of supposedly poor health – even in the height of summer.

Although he began to arouse suspicion, it was not until 1848 that a warrant was issued in France for his arrest.  Tipped off, Libri had already fled to London, taking with him about 18 trunks containing more than 30,000 documents.

Some 72 letters written by Descartes were thought to have been stolen by Libri
Some 72 letters written by Descartes were
thought to have been stolen by Libri
These included 72 letters written by the great French philosopher and mathematician René Descartes, as well as the Tours Pentateuch, a late sixth or early seventh-century illuminated Latin manuscript of the first five books of the Old Testament, which he stole from the Library of Tours.

With no extradition agreement existing between France and Britain at that time, Libri was thus able to evade justice, even though he was tried in absentia in 1850 and sentenced to 10 years’ jail.

Indeed, he lived a good life in London, mainly by selling books, often to members of the English nobility, or else at auction.

The Tours Pentateuch later became known as the Ashburnham Pentateuch after it was sold to the 4th Earl of Ashburnham by Libri in 1847.  Two auction sales in 1861 are said to have netted him more than one million francs.

Born Count Guglielmo Libri Carucci dalla Sommaja, he was a precocious academic who began studying law at the University of Pisa at the age of 16 before switching to mathematics and being appointed professor of mathematical physics at the age of just 20.

He made many friends in Paris during a sabbatical visit in 1824 and when his involvement back in Italy with the secret revolutionary plotters known as the Carbonari led to the threat of arrest, it was to Paris that he escaped.

Libri's History of Mathematical Sciences drew on stolen documents
Libri's History of Mathematical Sciences
drew on stolen documents
He became a French citizen in 1833 and his academic stock continued to rise. He obtained a professorship at the Collège de France and in 1834 he was elected as assistant professor in the calculus of probabilities at the Sorbonne and elevated to the French Academy of Sciences.

Between 1838 and 1841, Libri wrote a four-volume tome entitled History of the Mathematical Sciences in Italy from the Renaissance of literature to the 17th Century, drawing from 1800 manuscripts and books by Galileo, Descartes, Leibniz and others which he claimed were in his personal collection. It was discovered later that many had been stolen from the Laurentian Library.

He cultivated contacts in high places to protect his reputation. His appointment as Chief Inspector of French Libraries, for example, came about through his friendship with the influential French Chief of Police, François Guizot.

Libri remained in England until 1868, when his declining health persuaded him to return to Italy.  He died the following year in Fiesole, just outside Florence, at the age of 66.

Although many of the huge number of items Libri stole have never been returned, having been forgotten about or left to gather dust in private libraries and storerooms, one of the missing Descartes letters, written in 1641 to Father Marin Marsenne, the priest and polymath who oversaw the publication of his Meditations on First Philosophy, turned up at Haverford College in Pennsylvania in 2010.

The Laurentian Library - the long building in the middle of this picture - was fitted out to a design by Michelangelo
The Laurentian Library - the long building in the middle of
this picture - was fitted out to a design by Michelangelo
Travel tip:

The Laurentian Library – the Biblioteca Medicea Laurenziana – dates back to 1523, when the Medici pope Clement VII commissioned it to be built in a cloister of the Basilica of San Lorenzo in Florence, which is situated between the Duomo and Santa Maria Novella railway station. Home to some 11,000 manuscripts and 4,500 historic books, it was built to designs by Michelangelo in Mannerist style and is considered one of his greatest achievements, not only for elegance of its architectural features but for the innovative use for space to maximise the library’s capacity without detracting from its aesthetic beauty.

The remains of the Roman amphitheatre at Fiesole
The remains of the Roman amphitheatre at Fiesole 
Travel tip:

Fiesole, a town of around 14,000 inhabitants, is situated about 8km (5 miles) northeast of Florence on a hill offering panoramic views. It was built on the site of an Etruscan city probably founded in the eighth or ninth century BC. In the middle ages it grew to be as powerful as Florence until it was conquered by the latter in 1125 after a series of wars. Among several notable sights is its 11th century Romanesque Cathedral of St Romulus and many Roman remains, including those of an amphitheatre still used for open-air concerts during the summer.  Historically popular with wealthy Florentines as a place to build their villas, it still has the reputation of an upmarket residential area.

28 January 2017

Paolo Gorini – scientist

Teacher invented technique for preserving corpses

The statue of Paolo Gorini in  Piazza Ospedale in Lodi
The statue of Paolo Gorini in
Piazza Ospedale in Lodi
Mathematician and scientist Paolo Giuseppe Antonio Enrico Gorini, who made important discoveries about organic substances, was born on this day in 1813 in Pavia.

He is chiefly remembered for preserving corpses and anatomical parts according to a secret process he invented himself. His technique was first used on the body of Giuseppe Mazzini, the politician and activist famous for his work towards the unification of Italy.

Gorini was orphaned at the age of 12, but thanks to financial help from former colleagues of his father, who had been a university maths professor, he was able to continue with his studies and he obtained a mathematics degree from the University of Pavia.

He paid tribute in his autobiography to his private teacher, Alessandro Scannini, who he said first inspired his interest in geology and volcanology.

Gorini went to live in Lodi, just south of Milan, in 1834, where he became a physics lecturer at the local Lyceum.

As well as teaching, he dedicated his time to geology experiments, actually creating artificial volcanoes to illustrate their eruptive dynamics. He also made his first attempts at the preservation of animal substances.

Gorini took an interest in politics at a time when Italy was moving towards unification and was in touch with some of the famous names of the time, such as Mazzini and Giuseppe Garibaldi. He even came up with an innovative plan of attack against the Austrians during a secret meeting of revolutionaries in Lodi in 1848.

The Mazzini Mausoleum in Genoa, where the body of Giuseppe Mazzini, preserved by Gorini, was laid to rest
The Mazzini Mausoleum in Genoa, where the body of
Giuseppe Mazzini, preserved by Gorini, was laid to rest
He retired from teaching at the age of 43 to spend more time on his experiments. He was commissioned by the Government to write a report on the characteristics and dangers of the volcanoes in Italy and in 1871 he published Sull’origine dei vulcani - On the Origins of Volcanoes.

He was asked to preserve the remains of Mazzini after the latter's death in Pisa in 1872, ahead of a funeral in Genoa that drew a crowd of some 100,000 people.

Mazzini’s body now lies in the cemetery of Stigliano near Genoa and the last examination of the corpse in 1946 acknowledged its substantial preservation.

Gorini had arrived in Pisa two days after the death of Mazzini when the body’s condition was already compromised.

Gorini embalmed the body of the novelist Giuseppe Rovani
Gorini embalmed the body of
the novelist Giuseppe Rovani
But although the process of mineralisation of the tissues did not produce excellent results because of the delay, the Gorinian technique was praised and brought the scientist international fame.

After successfully preserving the body of the novelist Giuseppe Rovani, who died in Milan in 1874, Gorini began to focus his energies on cremation. He planned the first crematorium in Italy, which was built in the cemetery of Riolo near Lodi in 1877.

In 1878 he was commissioned by the Cremation Society of Great Britain to construct the cremator at Woking Crematorium.

Gorini died in 1881 at the age of 67 in Lodi. There is now a statue of him and a museum dedicated to his work in Lodi.

The beautiful Piazza della Vittoria in Lodi is famous  for the porticoes that line all four sides
The beautiful Piazza della Vittoria in Lodi is famous
 for the porticoes that line all four sides
Travel tip:

Lodi, where Gorini taught and carried out his experiments, is a city in Lombardy, south of Milan and on the right bank of the River Adda. The main square, Piazza della Vittoria, has been listed by the Touring Club of Italy as among the most beautiful squares in Italy and it has porticoes on all four sides. Nearby Piazza Broletto has a 14th century marble baptismal font from Verona.

Travel tip:

A museum in Lodi houses the Collezione Anatomica Paolo Gorini, where you can see some of the animal and human anatomical preparations created by the scientist as he focused his efforts on preserving dead bodies. The collection is on display inside the Ospedale Vecchio of Lodi in the beautiful 15th century Chiostro della Farmacia. It is open on Wednesday from 10.00 to 12.00, on Saturday from 9.30 to 12.30 and on Sunday from 14.30 to 16.30. Entry is free of charge.

More reading:

Giuseppe Mazzini, the revolutionary who became the hero of Italian unification

Why the discoveries of 18th century anatomist Antonio Maria Valsava still help astronauts today

How physicist Luigi Galvani's name entered scientific terminology

Also on this day:

1968: The birth of Italy and Juventus goalkeeper Gianluigi Buffon


29 December 2016

Tullio Levi-Civita – mathematician

Professor from Padua who was admired by Einstein

Tullio Levi-Civita
Tullio Levi-Civita
Tullio Levi-Civita, the mathematician renowned for his work in differential calculus and relativity theory, died on this day in 1941 in Rome.

With the collaboration of Gregorio Ricci-Curbastro, his professor at the University of Padua, Levi-Civita wrote a pioneering work on the calculus of tensors. Albert Einstein is said to have used this work as a resource in the development of the theory of general relativity.

Levi-Civita corresponded with Einstein about his theory of relativity between 1915 and 1917 and the letters he received from Einstein, carefully kept by Levi-Civita, show how much the two men respected each other.

Years later, when asked what he liked best about Italy, Einstein is reputed to have said ‘spaghetti and Levi-Civita.’

The mathematician, who was born into an Italian Jewish family in Padua in 1873, became an instructor at the University of Padua in 1898 after completing his own studies.

He became a professor of rational mechanics there in 1902 and married one of his own students, Libera Trevisani, in 1914.

Albert Einstein: the German physicist held Levi-Civita in high regard
Albert Einstein: the German physicist
held Levi-Civita in high regard
In 1917, having been inspired by Einstein’s theory of general relativity, Levi-Civita made his most important contribution to this branch of mathematics, the introduction of the concept of parallel displacement in general curved spaces.

This concept immediately found many applications and in relativity is the basis of the unified representation of electromagnetic and gravitational fields. In pure mathematics his concept was instrumental in the development of modern differential geometry.

Levi-Civita also worked in the fields of hydrodynamics and engineering. He made great advances in the study of collisions in the three-body problem, which involves the motion of three bodies as they revolve around each other.

His books on these subjects became standard works for mathematicians and his collected works were published in four volumes in 1954.

Levi-Civita was invited by Einstein to visit him in Princeton in America and he lived there for a while in 1936, returning to Italy with war looming.

He was removed from his post at the University of Rome in 1938 by the Fascist regime because of his Jewish origins, having taught there since 1918.

Deprived of his professorship and his membership of all academic societies by the Fascists, Levi-Civita became isolated from the scientific world and in 1941 he died at his apartment in Rome, aged 68.

Travel tip:

The University of Padua, where Levi-Civita studied and later taught, was established in 1222 and is one of the oldest in the world, second in Italy only to the University of Bologna. The main university building, Palazzo del Bò in Via VIII Febbraio in the centre of Padua, used to house the medical faculty. You can take a guided tour to see the pulpit used by Galileo when he taught at the university between 1592 and 1610.

The Caffè  Pedrocchi is an historic meeting place for students and intellectuals in Padua
The Caffè  Pedrocchi is an historic meeting place
for students and intellectuals in Padua
Travel tip:

Right in the centre of Padua, the Caffè Pedrocchi has been a meeting place for business people, students, intellectuals and writers for nearly 200 years. Founded by coffee maker Antonio Pedrocchi in 1831, the caffè was designed in neoclassical style and each side is edged with Corinthian columns. It quickly became a centre for the Risorgimento movement and was popular with students and artists because of its location close to Palazzo del Bò, the main university building. It became known as the caffè without doors, as it was open day and night for people to read, play cards and debate. Caffè Pedrocchi is now a Padua institution and a must-see sight for visitors, who can enjoy coffee, drinks and snacks all day in the elegant surroundings.

More reading:

Also on this day

1966: The birth of footballer Stefano Eranio


5 April 2016

Vincenzo Viviani – mathematician and scientist

Galileo follower's name lives on as moon crater

This portrait of Viviani is owned by Nice Art Gallery
Vincenzo Viviani
Forward-thinking scientist Vincenzo Viviani was born on this day in 1622 in Florence.

Viviani worked as an assistant to Galileo Galilei and after his mentor's death continued his experimental work in the field of mathematics and physics. This work was considered so important that Viviani has had a small crater on the moon named after him.

While at school in Florence, Viviani was given a scholarship to buy mathematical books by the Grand Duke Ferdinando II de' Medici. He later became a pupil of Evangelista Torricelli and worked with him on physics and geometry.

By the time he was 17 he was working as an assistant to Galileo Galilei. After Galileo’s death in 1642, Viviani edited the first edition of his teacher’s collected works.

Viviani was appointed to fill Torricelli’s position at the Accademia dell’Arte del Disegno in Florence after his death in 1647.

In 1660 Viviani conducted an experiment with another scientist, Giovanni Borelli, to determine the speed of sound by timing the difference between seeing the flash and hearing the noise of a cannon being fired from a distance.

As his reputation as a mathematician grew, Viviani started to receive job offers from abroad. As a result the Grand Duke offered him a post as court mathematician in order to keep him in Italy.

Viviani had published a book on engineering and had almost completed a major work on the resistance of solids when he died in Florence in 1703 at the age of 81.

Viviani decorated his home with an elaborate facade paying tribute to Galileo
The extraordinary façade of Vincenzo Viviani's former home
in Florence, with a bust of Galileo over the entrance
(Photo: Jebulon CC0 1.0)
Travel tip:

Palazzo dei Cartelloni, formerly known as Palazzo Viviani, in Via Sant’Antonino in Florence, has prominent inscriptions on the façade in Latin celebrating and glorifying the life and discoveries of Galileo Galilei. Viviani had these applied to the front of his home as a tribute to his mentor and there is also a bust of Galileo over the entrance. Today the building is owned by an American art institution.

Travel tip:

Galileo’s tomb in the Basilica of Santa Croce in Florence was not erected until 1737 when his remains were finally allowed a Christian burial. With the help of money left by Viviani in his will for a tomb for himself and Galileo, the scientist was reburied below a bust of himself by Giovanni Battista Foggini. Viviani’s own remains were transferred to the grave at the same time, according to his wishes.

Read more: