Monday 9 May 2011
There are few things which capture the imagination more than Fermat’s Last Theorem, and despite the rather mundane sounding title ‘Rational Solutions of Equations’ the talk given by Professor Kevin Buzzard of Imperial College was packed to the rafters with captivated Sixth Formers and staff members, including many from other departments.
The reason for the enthusiasm was probably the speaker’s connection with the most famous Mathematical result of all time. Professor Buzzard is the academic grandson of Andrew Wiles (his PhD supervisor Richard Taylor was a student of Wiles) and he has worked closely with some of the other famous names in the field, including Barry Mazur and Ken Ribet, both of whom feature on the iconic Horizon documentary.
Many, myself included, were drawn by the opportunity to meet someone who fully understands the notoriously complicated proof, and one of the rare people who can answer such questions as what is a Modular Form? Or how exactly did Wiles prove the Taniyama-Shimura conjecture? While these questions were beyond the scope of a school level talk, Professor Buzzard gave a flavour of some of the ideas involved, especially the interplay between Number Theory and Geometry.
The talk opened with the question of which fractional points lie on the unit circle, which soon reduced to the search for Pythagorean Triples like 3, 4 and 5. He presented three solutions to this ancient problem, one was to find a general formula (helpfully provided to him by Catherine Xu), one was simply to spot the pattern which emerges, but the most fruitful was to show how simple geometric facts (a line meets a circle at two points) can be applied to generate new solutions from old ones. This method was extended to deal with more complicated curves- and the mathematical highlight of the talk was a discussion of the fractional solutions to the cubic equation x3 + y3 = 9, an example of a Mathematical object known as an Elliptic Curve, which was to feature heavily in Wiles’ proof.
Professor Buzzard’s enthusiasm and passion for Maths was infectious, and he happily continued the discussion over lunch. After lunch he spoke to the top set of Year 9, and answered such questions as: How do you come up with new Mathematics? What is your favourite mathematical trick? And what is your favourite number? Professor Buzzard is one of those great communicators who have the knack of making deep Mathematical results look obvious, and who can reveal the links between the seemingly simple and the profound. It was a pleasure to welcome him to Sevenoaks School.
For information his favourite number is 65537.
David Vaccaro