When homing insects go on a foraging journey, often helpfully pollinating our gardens as they go, they meander from flower to flower. Yet no matter how tortuous their journey, they know how to return home by the shortest route. But how do they do it? Turns out they’re doing vector mathematics! Unlike bees, fruit flies are not great navigators, but they still know how to get around, and their relatively simple brains have enabled researchers to see, neuron by neuron, how they perform this innate navigational mathematics. (Spoiler alert: they’re adding sine waves!) Research on bees and other insect navigators supports this finding, while migratory birds use even more sophisticated vector maths. You can find out about all this and more – including why human mathematicians struggled to create the abstract idea of vectors – in my new article here (if you have a subscription to Cosmos magazine).