The Ham Sandwich Theorem has been a treat and a spur to mathematicians for more than half a century. There was a bit of a kerfuffle about who invented it, but that question did get settled.

The Ham Sandwich Theorem cropped up in a branch of mathematics called algebraic topology.

The theorem describes a particular truth about certain shapes. Most published papers on the topic make a hash of explaining it to anyone who is not an algebraic topologist. But the authors of a 2001 paper called Leftovers from the Ham Sandwich Theorem wrapped up an important little leftover – they put the idea into clear language.

The Ham Sandwich Theorem, they wrote, “rescues the careless sandwich maker by guaranteeing that it is always possible to slice the sandwich with one cut so that the ham and both slices of bread are each divided into equal halves, no matter how haphazardly the ingredients are arranged”….

*So begins this week’s Improbable Research column in The Guardian.*