Sevenoaks Maths Society: Alan Turing Year 2012

Next year, 2012, marks the hundredth anniversary of the birth of Alan Turing, the most influential Mathematician of the 20th century and the founding father of Computer Science. To mark this jubilee the Maths Society has a whole range of events to commemorate Turing’s life and work, including his role in the invention of the computer, his philosophical insights into Artificial Intelligence and the pivotal role he played in breaking the German Enigma Code during the Second World War.

However the first talk in our programme looked at perhaps the least well known aspect of Turing’s work: his investigation into the mysteries of developmental biology. Dr Jonathan Swinton, formerly a Mathematics lecturer at Turing’s own College of King’s, Cambridge and more recently Head of Computational Biology at AstraZeneca, gave a fascinating talk to members of the Sixth Form about how Turing sought to explain the emergence of Fibonacci Numbers in nature.

Most school children are taught about the famous Fibonacci Sequence which starts 1,1,2,3,5,8,13,21,34,55... But what few people may have spotted is that from pineapples to pine cones to cauliflowers, countless plants exhibit spiral patterns, and that almost invariably if you count the spirals you will obtain a Fibonacci Number. This result was first noticed by the great Romantic Poets, including Goethe, and was seen as a proof of the order and symmetry of the world. However, despite numerous efforts no satisfactory Mathematical explanation had been found.

Dr Swinton explained how this problem had fascinated Turing from an early age, including a delightful picture drawn by his mother showing the young Turing counting the petals on a daisy. After the end of the war an exhausted Turing threw himself into Mathematical Biology and he managed to develop the Reaction-Diffusion theory which explained why certain common patterns, including spots, stripes and dappling, occur in many animals. Dr Swinton gave a great insight into the imaginative mind of a Mathematical Genius, explaining how Turing visualised different types of protein as Missionaries and Cannibals.

Turing’s obsession about Mathematical Biology was fuelled by a desire to understand how it is possible for something as complicated as a brain to develop from a simple egg, and soon Turing became side-tracked by questions of whether the newly invented computer could think in the same way as a brain. However, he returned to the question of Fibonacci Phyllotaxis later in life after he lost his position at the National Computer Laboratory due to his homosexuality. His posthumously published papers show that he came tantalisingly close to a full solution shortly before his tragic suicide. In the subsequent 55 years various Mathematicians have tried and failed to finish the proof. A full explanation remains one of the great unsolved problems in Mathematics.

Dr Swinton spoke movingly about Turing’s life and how it inspired his own research, and despite touching on some advanced Mathematics it was accessible throughout. It was a truly fascinating talk unifying the wonders of nature with the beauty of Mathematics. Hopefully it will have whetted the appetite for some of the future guest speakers and trips.