A group of academic scholars at Rydal Penrhos tested their problem solving skills during a special seminar.
In the final session of the year, which took place on Thursday, June 29, pupils were guided through a journey of mathematical curiosity, designed to instill systematic, rather than random, working, and to promote the use of conjectures over simple pattern spotting under the guidance of Head of Mathematics Pete Richmond.
After beginning with a mathematical 'trick' involving dice, pupils were presented with the problem '1089 and all that' (taken from the book of the same name, by David Acheson) before moving on to the task of finding, without the use of a calculator, the sum of the first 100 natural numbers, something that notorious mathematician Carl Friedrich Gauss, at the age of only 10 in 1787, was allegedly able to solve in a matter of seconds.
The latter half of the session led pupils on a whistle-stop tour, from a geometrical problem involving regions in a circle through a popular theoretical river crossing involving a wolf, a sheep and some cabbages, before moving on to one of the most famous mathematical curiosities of all time; Fermat's Last Theorem.
Pupils were given a brief introduction to this age-old problem, which baffled even the greatest mathematicians for centuries, from its inception in 1637 through to the final 129-page proof, provided by Andrew Wiles, some 357 years later in 1994, something that he had spent around eight years of his life completely dedicated to.
Rounding off the session, the academic scholars were invited to consider one of the oldest and best-known unsolved problems in number theory and all of mathematics, the Goldbach Conjecture, and to spend some of their summer holiday working on one or more of the Millennium Prize Problems.
These are a set of six problems in mathematics, at least one of which has remained unsolved since 1859.
A correct solution to any of the problems results in a US $1 million prize being awarded by the Clay Mathematics Institute to the discoverer(s).
Mr Richmond, said: “Throughout, pupils were encouraged to consider explanations and proofs to back up their statements, and to think about 'What if...?'
“All it takes is perhaps one person's mathematical curiosity to take them that necessary step further.”