If you can solve a previously unsolved mathematical problem you have done something remarkable. David Michael O'Doherty (17) of Gonzaga College, Dublin, has done something remarkable.
David decided to have a look at the Encyclopaedia Britannica's list of unsolved mathematical problems when seeking a project topic for the Esat Young Scientist and Technology Exhibition 2002. He found one in the numerical distribution of the prime numbers sprinkled among large numbers as they stretch into infinity.
Prime numbers are a select band of digits that have the distinction of being divisible only by themselves and by one. In the lower reaches of the numerical world they include 1, 3, 5, 7 and 11, but their count never ends, there are always new ones further along the way.
Their uniqueness and the chaotic nature of their appearance make prime numbers a choice target for mathematicians looking for a challenge, hence David's interest.
"There are thousands of unsolved problems in number theory," he said, and after looking through the Britannica list he chose one related to the number of prime numbers and whether there was an order to their appearance.
"I understood it and thought it was reasonably true," David said. He felt it was a worthwhile problem that if solved would give some value, but one that wouldn't take two or three years of hard labour to achieve, at least if he hoped to have its solution ready for this year's Young Scientist.
Sure enough, he solved the unsolved problem, which will make it necessary for the Britannica to change its unsolved list in the next publication. He also identified and proved two related corollaries.
In the process he helped to prove again the second law of thermodynamics, that the chaos in a physical or numerical system must remain the same or increase over time, but never decrease.
This "chaos" is known as entropy, and David's solutions showed there is a predictable order of primes amid the chaos as numbers retreat to infinity. Equally, the entropy increases but never reaches a conclusion given there is an infinite number of numbers and so an infinite number of primes.
Needless to say, David, in fifth year, is quite handy with maths. "I finished the Leaving Cert course a year and a half ago," he admits. To keep things interesting he plans to tackle 11 subjects when he does the Leaving next year.
His goal is to become a theoretical physicist, something that demands significant number-crunching ability.
The main category winners will be announced tomorrow afternoon and will also be available on the Irish Times website ireland.com
