Eamon de Valera might not have made it to the 1916 Rising had he got the job he wanted at UCC three years earlier, writes CORMAC SHERIDAN

THE COURSE of Irish history might have looked very different had a job fallen right for an aspiring young mathematician. Éamon de Valera very nearly won a post as professor of mathematics in 1913, something that would have diverted him from his eventual life in politics.

Dev got close to securing the professorship of mathematical physics at University College Cork three years before the Rising. Had he won the post, the course of Irish history would have changed dramatically, says researcher Cáit Ní Shúilleabháin of UCC.

“If he had gotten that job in 1913 he would definitely have continued at the maths,” she believes.

Ní Shúilleabháin has recently completed an intriguing PhD thesis on the mathematical life of de Valera. It shows he was accomplished in the field and had a particular fascination for quaternions, a mathematical discovery made by Irish mathematician William Rowan Hamilton.

De Valera’s interest in mathematics has largely been overlooked in conventional historical treatments, according to Des MacHale, of UCC’s school of mathematical sciences, who co-supervised Ní Shúilleabháin’s research along with UCC historian Gabriel Doherty. “It’s been neglected because people couldn’t cope with the technical details,” he says.

Éamon de Valera was often derided for his narrow views on the Ireland’s economic development. Yet he was intellectually better equipped than most of his political colleagues to recognise the value of today’s “smart economy”.

Quaternion mathematics is highly complicated – it being a system for representing complex numbers in four-dimensional space. Quaternions are now used in high-tech areas, such as computer graphics, robotics and signal processing, for handling spatial rotations. Yet Dev seemed more than able to engage with this difficult subject.

De Valera made no lasting contribution to the subject and did not publish any research papers. But Ní Shúilleabháin discovered that Arthur Conway, his former professor at UCD who was a leading authority on the subject, credited Dev as having “gone deeply into the subject of quaternions”.

Conway further stated that: “He is at present prosecuting an important research in them, which promises to be of considerable interest”.

The post in Cork was not to be and de Valera found other things to occupy his mind. Yet even as his political career began to take off, mathematics always remained close to his heart.

While awaiting his execution in Kilmainham gaol after the Easter Rising in 1916, he scratched into the wall of his cell the fundamental equation for quaternion multiplication, i2 = j2 = k2 =ijk = -1, a poignant echo of Hamilton’s famous flash of insight at Broome Bridge, on Dublin’s Royal Canal, in 1843.

While in Lewes Jail in East Sussex, after his death sentence was commuted, de Valera studied the problem of astronomical obliquity – or the tilt between Earth’s rotational axis and the plane of its orbit around the sun.

This in turn was prompted by the prison governor’s interest in the topic. The governor was interested in the now-discredited work of the British astronomer Alfred Drayson. In a mathematical critique of Drayson’s work, de Valera observed that it was difficult not to dismiss him as “a sore-head and a crank”.

Ní Shúilleabháin also proposes that de Valera found ways to apply mathematical concepts to his political thinking. She suggests, for example, that he drew on his knowledge of set theory – then a relatively new field – in sketching in diagram form his vision of “external association”, or Ireland’s relationship to the British Commonwealth.

The mathematics were not strictly correct however, reflecting, perhaps, a certain degree of political imprecision in his scheme.

“De Valera probably stretched the analogy to fit his purposes, using the Venn diagram to his advantage, knowing that certain ambiguities in his approach would go unnoticed by the average person,” Ní Shúilleabháin observes.

Even in old age, when almost completely blind, de Valera continued to work on mathematical problems for recreational purposes. But how good was he really? “He never got the opportunity to become a great mathematician,” says Ní Shúilleabháin.

MacHale believes Dev’s level of attainment was the equivalent of a Master’s graduate, although his early aptitude indicated that he could have gone further. “He retained a lifelong interest in maths but never realized his potential,” MacHale says.

De Valera’s most lasting contribution to science in Ireland was of course his establishment in 1940 of the Dublin Institute for Advanced Studies. However, MacHale is critical de Valera’s wider neglect of the subject. “He really didn’t encourage mathematics in secondary school, as far as I can see.”