Students show no fear of great unsolved problems

PURE MATHEMATICS:COMPLEX ISN'T a big enough word when it comes to some of the maths projects on display at the BT Young Scientist and Technology Exhibition. Frightening is more like it for the rest of us who struggle with percentages and can't balance the cheque book.

Andrei Triffo from Synge Street CBS in Dublin has just such a project with the obscure title, “Infinite Sums of Zeta Functions and other Dirichlet Series”.

It goes without saying it is not the type of maths you might encounter at the supermarket or visiting your local. It is pure maths at its most complex, but the 17-year-old fifth-year student had no difficulty with it.

Andrei, whose family came to Ireland some years ago from Romania, was interested in infinite series, mathematical functions that can run to infinity. In particular he wanted to study Zeta functions, which are an infinite series of powers, from the second power to the third power, fourth and on to infinity, functions which can also be written as something called a Dirichlet Series.

The idea came from earlier work done by his brother, Stefan, who was a three-year veteran of the young scientist exhibition. It is all about infinite sums which contain within them other infinite sums.

Lost yet? Andrei wasn’t as he described one of his key questions, the connection between infinite sums of Zeta functions and infinite products, what you might get if you multiplied something. He tracked effortlessly through his research and the logical steps that drove them along.

“You wouldn’t come into contact with this sort of thing in school,” Andrei admitted, in gross understatement and without irony.

It brought him into contact with work done by others, but he also seems to have arrived at something unique, functions that Andrei could not find referenced in any book or on the internet. It will be for the judges to determine whether he has uncovered something new.

Also on the hunt for something new were Gary Carr, Darragh Moriarty and Graham McGrath, all 14 and third years also at Synge Street. Their similarly difficult maths research project focused on the Riemann Hypothesis, one of the great unsolved problems in mathematics and one of seven millennium problems put as a challenge before the world’s mathematicians.

Berhard Riemann also worked with Zeta functions and he proposed a function that has yet to be proven. While the three didn’t come up with a way to prove the hypothesis, they believe they have discovered a way towards a proof for any mathematician willing to take it on. “If we could help solve the Riemann Hypothesis it would be great,” Darragh suggested. Gary said that part of the reason they pursued such a difficult project was its very complexity. “The mystery of it was attractive,” he said.

Gregory McElhinney and Lee Welsh were also in challenging mathematical territory with their project, “Application of the Kolmogorov-Smirnov Test for Normality to Continuous and Discontinuous Variation”.

The fourth years from Oakgrove Integrated College in Derry city collected a range of continuous data (such as height, hand span and foot length) and also discontinuous data (hair and eye colour, gender and whether a student could curl their tongue) from 150 students in their school.

They conducted a statistical analysis on their own data to confirm that in a typical group continuous data will always be normally distributed, the kind of distribution that gives a nice bell curve. They also showed non continuous data will never be normally distributed.