Diary – 26 January 2008

It’s said that vampires suffer from a syndrome called arithmomania or an obsessive love of counting, so much so that to escape a vampire you just need to throw loads of cloves of garlic on the floor and the vampire can’t resist counting them, allowing you to make a hasty exit. It was this obsession with counting that inspired my favourite Muppet character, the vampire Count von Count. But I’m actually not in Transylvania to track down vampires but another local inhabitant who was obsessed with mathematics: János Bolyai. At the age of 21 this brilliant mathematician discovered that Euclid’s geometry was not the only possible geometry. He constructed a totally consistent universe where triangles have angles that add to less than 180 degrees and parallel lines do strange things that Euclid never thought possible. Writing to his father in 1823 from the army base where he was stationed at the time, he described the amazing experience of ‘creating out of nothing a totally new world’. It was the beginning of what we now call non-Euclidean geometry, a geometry that seems to fit the shape of space far better than Euclid’s. I’ve spent the day in Bolyai’s hometown of Tirgu Mures filming a sequence for a new series I’m making for the BBC on the history of mathematics. Our ten-month journey round the world in 80 theorems will attempt to condense 7,000 years of mathematics into four one-hour programmes that will be shown this autumn.

I think I actually saw a vampire today. Just next to where we were filming, this woman leant down next to a car and bore her teeth in the car’s wing mirror. Fangs! Huge fangs! Her canines were enormous and definitely very pointy. However, she almost lost all her teeth when the car suddenly reversed, the wing mirror knocking her to the ground.