While other kids dressed up as ghosts or zombies on Hallowe'en, I always chose to don false fangs and my grandfather's tails. Recently I discovered that my desire may have been an early sign of my obsession for all things mathematical, as vampires are said to suffer from a condition called arithmomania: a compulsive desire to count things.

Although less well-known than garlic or crosses, one way to ward off the Prince of Darkness is to scatter poppy seeds around his coffin. Theoretically, before Dracula finishes trying to count how many are scattered around his resting place, the sun will have driven him back to his resting place.

Arithmomania is a serious medical condition. The inventor Nikola Tesla, whose studies into electricity gave us the AC current, was obsessed by numbers divisible by three: he insisted on 18 clean towels a day and counted his steps to make sure they were divisible by three. Perhaps the most famous fictional depiction of arithmomania is the Muppets' Count von Count, a vampire who has helped generations of viewers in their first steps along the mathematical path.

Vampires are said to have their own numbers: these are defined as a number that can be written as the product of two smaller numbers of half the length which contain all the digits of the larger number. For example 1395=15x93. The two smaller numbers are called the vampire number's fangs. Although this is little more than a numerical curiosity, mathematicians have proved that there are an infinite number of vampire numbers.

However, research into the science of Hallowe'en has also proved that vampires cannot exist. Vampires need to feed on the blood of a human being at least once a month to survive. The trouble is that once you have feasted on the human, the victim too becomes a vampire. So next month there are twice as many vampires in the search for human blood to feast on.

The world's population is estimated to be 6.7 billion. Each month the population of vampires doubles. Such is the devastating affect of doubling that within 33 months a single vampire would end up transforming the world's population into vampires. Even if one factors in the effect of the birthrate, humans can't reproduce quickly enough to counter the mathematical effect of doubling.

So forget the garlic and the mirrors, it's mathematics that is your best protection against the Prince of Darkness.

Marcus du Sautoy will be the new Simonyi Professor for the Public Understanding of Science at Oxford University, succeeding the evolutionist Richard Dawkins.

Explore Tech & Web

• Personal Tech

• The Web

• Gadgets & Gaming