Ancient manuscripts show that Ireland was a major centre for the study of mathematics centuries ago.
We had some of the foremost practitioners of the fine art of Computus, the difficult business of calculating the date of Easter far into the future.
But
the manuscripts, along with later archaeological discoveries, also show
the Irish in the eighth century AD were adept engineers, making
improvements in technologies used for metal-working and agriculture, and
we even had a reputation as boat-builders.
Somehow
along the way to modern times, however, we released our grip on this
expertise, allowing others to make the breakthroughs and take the lead
on the advance of mathematics, science and engineering.
But the manuscripts remain, and they bear
witness to our past, something that has been brought back to life in a
book launched earlier this week by the Royal Society of Antiquaries of
Ireland.
Music and the Stars: Mathematics in Medieval Ireland
reveals this past and shows how we were an important contributor to
knowledge during the eighth century.
The book includes contributions by
12 authors, specialists in the various manuscripts and their meanings,
says Mary Kelly, who edited the book with Charles Doherty.
“If
you look at the medieval period, we are never mentioned in science. We
don’t appear. The work [by the Irish] is appearing in learned journals
but is not being incorporated into wider courses at third level,” says
Kelly.
Certainly Irish texts on Computus were
lodged in Irish monasteries abroad and in the libraries of Germany,
France and other countries. But our success in the field, which involved
complex mathematics, is not recognised today.
Glendalough manuscript
Kelly became interested when examining a single manuscript page on display at the visitors’ centre at Glendalough, Co Wicklow, where she works. It dates from the early 12th century, probably 1106, and is a maths text, and is thought to be a fragment on the use of the abacus, De Abaco, by Gerbert of Aurillac.
Intriguingly,
the page of Latin text includes a handwritten note in Irish. The note
was in a style called Irish minuscule, saying that it was Pentecost, and
mentioning that “Tuathal ua Cathal was ill”. The note then reveals that
he had died overnight.
This mix of Latin text and Irish made Kelly curious, so she translated the Latin.
“I
started to do research into this. I wanted to know what were the sums
and were they right, and what was the standard of education at
Glendalough,” she says. “I discovered it was extremely high. The book is
advanced maths, mathematical philosophy – much more than one and one is
two.”
She broadened her research, looking to assess how much material was available here.
“That
is when I discovered there is an enormous history of scientific and
mathematical work written in medieval Ireland,” she said. “It came as an
enormous shock there was this knowledge and it was not known in the
literature.”
The book explains how the monks here
were well connected to earlier thinkers, for example the sixth-century
philosopher Anicius Manlius Severinus Boëthius and his pivotal work De Institutione Arithmetica – De Institutione Musica. “There is a very lively engagement with mathematics between Ireland and Britain; it is high- level mathematics.”
One
key area where the Irish came to excel was in Computus, and the Irish
monk Cummian, thought to have been based in Munster, was a leading
researcher on the subject. “By the early seventh century there are three
ways to calculate when Easter occurs. It is the Irish who develop this
into an entire new genre of literature on Computus,” Kelly says.
Cummian’s expertise was shown in letters dating from
633 between him and the abbot of Iona, Ségéne. Cummian had changed his
method for calculating the fall of Easter, breaking away from the method
adopted by monasteries founded by Colm Cille and adopting the one used in Rome. This caused Ségéne to accuse Cummian of heresy.
“Cummian
knows of 10 methods and [in the letter] he goes through all the details
and compares them, and he finds that the system used in Rome was the
most reliable. He replies to Iona, saying this is the right method,”
says Kelly.
As Gaeilge
The manuscripts described in the book are mostly Latin but some of them revert to Irish.
The Einsiedeln monastery in the Swiss Alps holds a
manuscript on Computus that dates to the ninth century, but is taken to
be a copy of an older, seventh- century Irish manuscript, Kelly says.
“The manuscript is written in Latin but in
complicated parts it has embedded Irish where there is a need for
detailed explantation. The author of the text has intentionally included
Irish, incontrovertible truth it is of Irish origin. We have these
beautiful numbers from the Swiss Alps. It is really magic to see these.”
Music and the Stars: Mathematics in Medieval Ireland is in book shops or available from fourcourtspress.ie