The bicycle problem that nearly broke mathematics

Scientific American:

Jim Papadopoulos has spent much of his life fascinated by bikes, often to the exclusion of everything else. He competed in amateur races while a teenager and at university, but his obsession ran deeper. He could never ride a bike without pondering the mathematical mysteries that it contained. Chief among them: What unseen forces allow a rider to balance while pedalling? Why must one initially steer right in order to lean and turn left? And how does a bike stabilize itself when propelled without a rider?

As kids, we “counterbalanced” by instinct. When I was learning to ride a motorcycle, the explanation of “steer right, go left” confused the living daylights out of me.