A TRALEE-BASED mathematician is believed to have helped solve an 80-year-old mathematical conundrum, widely recognised as notoriously difficult, and has been invited to address leading international mathematics and physics institutions.
Since posting their solution to a seemingly unsolvable geometry problem on a respected maths site on the internet, Institute of Technology Tralee lecturer Dr Brendan Guilfoyle and his collaborator Dr Wilhelm Klingenberg of Durham University have received invitations to address their peers.
These invites include Oxford and Cambridge, the Humboldt University, the Albert Einstein Institute and Tokyo University.
Dr Guilfoyle (42) has spent nine years working on a problem in Euclidean geometry on spheres.
Known as the Carathéodory conjecture, it claims any closed convex body in 3D space such as a rugby ball has at least two umbilic points. This means it curves equally in all directions at those points. However, until now, no one has been able to prove how and why this is the case.
The new techniques used by Dr Guilfoyle in solving the problem will have applications in 3D computer graphics industry and in the medical field of bio-imaging. It is already exciting a number of research institutes.
Speaking at the IT Tralee where he lectures in the department of mathematics and computing, Dr Guilfoyle said a lot of seemingly intractable problems can be solved in centres away from the well-known institutions.
“Many mathematicians wouldn’t take this on. It would be considered too much work,” he said. He and his collaborator took the decision to publish their work in stages on the internet to protect it, but also to get feedback: “No one had ever come close to our approach.”
Essentially, the research would translate 3D into 4D, he said. Ireland is isolated in the maths world and America is widely recognised as the hub, while Germany and France would be the leading maths countries in Europe, he believes.
Dr Guilfoyle said the social acceptance in Ireland of being bad at maths needed to be tackled: “People feel it is okay to admit to being bad at maths, in a way they would never accept being bad at reading.”
A Trinity graduate, with a PhD from the University of Texas, Dr Guilfoyle has won awards and honours and secured research fellowships.
He has published papers on gravitational theory and other geometrical problems. Last year, he published research demonstrating how it has become easier to achieve higher grades in second- and third-level Irish education.