Modern mathematics is used to solve question about medieval war

Battle of Clontarf

In the year 1014, the fate of Ireland would be decided at the Battle of Clontarf. The Irish King Brian Boru would defeat a Viking army, although at the cost of his own life. However, there is one historical debate about this conflict – was it really a war against the Vikings, or an internal civil war?

Battle of Clontarf
Battle of Clontarf, oil on canvas painting by Hugh Frazer, 1826

The mainstream view is that the Battle of Clontarf was the climax of a war between the Irish and Vikings. However, other historians have long challenged this view believing, instead, it was a conflict between opposing Irish sides with Munster and its allies victorious over Leinster and Dublin, and Viking warriors on each side. The debate about the conflict has lasted at least 250 years and medieval texts have been used by both sides to support their cases.


Modern mathematical techniques – similar to those used to analyse social-networking websites – are being used to answer this question, with researchers at Coventry, Oxford and Sheffield Universities focusing on a key medieval text – Cogadh Gaedhel re Gallaibh.

Their findings, now published in the journal Royal Society Open Science, support the long-standing popular view that the Battle of Clontarf was mainly between the Irish and Vikings.

To perform the study, the academics examined Cogadh Gaedhel re Gallaibh (“The War of the Irish with the Foreigners”), a chronicle from the early twelfth-century that reported on events in Ireland between 967 and 1014. They wanted to know how all the Irish and Viking characters in the text fit together in a network, monitoring whether the interactions between them were benign or hostile. They developed a mathematical measure to quantify whether hostility in the network mainly connected Irish to Irish or Irish to Vikings.


They then calculated the difference between the measure of hostilities between each type of character (Irish and Viking) and what would have been hostile interactions in the network, indiscriminate of whether characters were Irish or Viking.

A positive value of the resulting measure would signal Irish civil war and a negative number would reflect an Irish versus Viking conflict. The results gave an overall negative value suggesting that the text mainly describes an Irish against Viking conflict.

However, because the negative value was moderate (-0.32 on a scale from -088 to 1) they suggest the text does not describe a fully “clear-cut” Irish versus Viking conflict. Instead, the network portrays a complex picture of relationships and social networks of the time.


“Every school child in Ireland is taught about the battle of Clontarf; it’s an iconic event in our country’s history,” explains lead author Ralph Kenna, a theoretical physicist at Coventry University. “We’ve used network science to give a greater understanding of medieval accounts and to give new insight into the relationships and hostilities from this period, a topic that has been argued about for hundreds of years.

“The medieval composer of the text certainly did not think in terms of social networks but, in recording a cast of hundreds with well over a thousand connections between them, he imprinted them into the narrative. This is why the networks approach delivers unique new insights; it extracts an unintended message. The paper goes beyond previous works in that it generates a new quantitative element to the complexity and conflicts of a long-standing debate about the Viking age in Ireland.”

PhD student Joseph Yose, who analysed the data, added “There are no detailed independent historical records of the time and the data come from a skilfully written medieval text replete with bias, exaggerating virtues and vices of many of its characters.


“Our statistical analysis delivers aggregate characteristics, largely insensitive to such individual and rhetorical elements. While it cannot decisively resolve the debate, we hope it delivers useful statistical information on the Viking Age in Ireland.”

The article “Network Analysis of the Viking Age in Ireland as portrayed in Cogadh Gaedhel re Gallaibh,” is now published in the journal Royal Society Open Science. Click here to read it.

This type of mathematical research has been used with other medieval texts as well.

To learn more, see Can Statistics show if the Icelandic Sagas were true?

Learn more about the Vikings in this issue of Medieval Warfare


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