*This is part 3 of a three-part series of mathematical speculations about bees. Part 1 looked at honeycomb geometry, and part 2 looked at how bees estimate nest volumes.*

The sight of bumblebees roaming around British gardens, foraging for nectar, is common and comforting. The movement of these fuzzy bees between flowers and plants can often seem deliberate yet erratic. Charles Darwin was intrigued by “humble-bee” routines ((Bumblebees were generally known as “humble-bees” until the modern term really caught on in the 1890s.)), and observed them with the assistance of his six children, but always regretted not attaching strands of cotton wool to the bees so he could follow them more easily ((Freeman, *Charles Darwin on the Routes of Male Humblebees*)).

Within the last decade there has been renewed interest from a number of collaborating researchers into studying bumblebees’ movement between flowers and their foraging techniques. The prevailing journalistic spin on this research seems to be ‘Bees solve the Travelling Salesman Problem – a problem that mathematicians and computers cannot solve’. This is unfortunate, not least because it is gleefully misleading, confusing various meanings of ‘solve’, but also it obscures a lot of the fascinating underlying scientific investigations.