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Back To The Future For Irish Maths Discovery

A mathematical discovery made 150 years ago - but thought to be of little significance at the time - is now widely used in computer games, revealed the University of Ulster’s Dr Mark McCartney.

The Mathematics lecturer, who is based at the Jordanstown campus, has co-authored an article in the prestigious Nature journal featuring seven little known examples of mathematical discoveries that found their purpose many years later.

Dr McCartney’s example, which was written alongside Tony Mann from the University of Greenwich in London, was entitled From Quaternions to Lara Croft.

“Famously, the idea of quaternions came to the Irish mathematician William Rowan Hamilton on 16 October 1843 as he was walking over the Brougham Bridge in Dublin,” said Dr McCartney.

“Hamilton had been seeking a way to extend the complex-number system into three dimensions: his insight on the bridge was that it was necessary instead to move to four dimensions to obtain a consistent number system.

“He spent the rest of his life promoting the use of quaternions, as mathematics both elegant in its own right and useful for solving problems in geometry, mechanics and optics.

“Hamilton was a brilliant and precocious scholar and was famously appointed to the Chair of Astronomy at Trinity College Dublin while still an undergraduate.

“Quaternions were considered to be a very clever piece of mathematics, but were also considered to be of limited practical use, and by the end of the 19th century they were dropping rapidly into obscurity. When I was an undergraduate they didn’t get a mention.

“So it was a surprise when my co-author, Tony Mann was approached by one of his colleagues, who teaches computer games development and asked which mathematics module students should take to learn about quaternions. It turns out that they are particularly valuable for calculations involving three-dimensional rotations, where they have various advantages over matrix methods. This makes them useful in robotics and computer vision and in ever-faster graphics programming.”

The article, which has proved a big hit with bloggers on the Nature website, demonstrates that mathematical breakthroughs which can initially seem ‘useless’ in real world scientific or engineering applications, can end up being very useful indeed, explained Dr McCartney.

“Therefore looking for short-term impact or relevance of mathematics can be a big mistake.”

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