Stone Balls

I suppose you wouldn't expect perhaps to find a mathematician in a museum of historical objects, but actually, the objects that I've been drawn to in this museum have quite a lot of mathematical significance. These Neolithic stones, discovered in Scotland, dating back 5,000 years, are probably the first examples of humans exploring the concept of symmetry. And that's what I do as a practicing mathematician. I spend my life trying to understand what symmetries are possible, in nature and in mathematics and abstractly. And here I've got a connection, going back 5,000 years, to people who are already trying to understand how can I arrange patches on the side of these stone balls in a symmetrical manner? One of the intriguing things about these stones is that we don't actually know what they're for. They might have been for divination trying to predict the future. They might have been part of a game. They look very much like dice, but we don't really think there is any game associated with them. Maybe they were just for chucking around, they're very nice in the hand when you hold them. Or maybe they were symbols of power in the clan. I suppose that's why I like them because we don't really know what they are. If I had a theory about why they were doing this it would be that actually, they were starting to be mathematicians, and that here we see the first example of abstract thought at work. That these weren't for a purpose. Mathematics is a great subject, created a lot of the technology around us, but mathematicians we create our mathematical objects for the joy and the beauty, so it will be lovely to think that these didn't actually have a use, that they were just really a celebration of what's possible.