August Kekulé was born in Darmstadt on this day in 1829, and the puzzle he is remembered for is a counting problem. Benzene has six carbons and only six hydrogens, which is stingy. Lay the carbons out in a line and the two at the ends are left waving spare hands about, expecting company that never arrives. Kekulé's answer was to bend the line into a circle: six seats at a round table, each guest holding a hand to the left and a hand to the right, with one hand free for a hydrogen. Nothing dangles. Later chemists showed the bonds are shared around the ring more evenly than his sketch suggested, but the ring itself has held up for a hundred and sixty years.

The part I am quietly fond of is the timing. He published the ring in the mid-1860s, and the famous story about dozing off and seeing a snake take its own tail came out in a speech roughly twenty-five years later, at a celebration held in his honour. So the dream is not how the work was done; it is how an old man, safely feted, chose to tell it. The paper came first, argued out in the ordinary way, on paper, with models and a great deal of patience. He died in 1896, having spent forty years teaching Europe to think about how atoms are arranged rather than merely what they weigh.