He studied these questions intensely as a young engineer at Cornell University in Ithaca, New York. But he failed to publish most of his ideas — and eventually drifted out of academia. By the late 1990s, he was working for a company that makes the machines that manufacture toilet paper. “In the end, if no one ever finds your work, then it was pointless,” he says. But then someone did find his work. In 2003, his old friend and collaborator from Cornell, engineer Andy Ruina, called him up. A scientist from the Netherlands, Arend Schwab, had come to his lab to resurrect the team's research on bicycle stability. “Jim, you need to be a part of this,” Ruina told him. Two wheels good Together, the researchers went on to crack a century-old debate about what allows a bicycle without a rider to balance itself, publishing in Proceedings of the Royal Society1 and Science2. They have sought to inject a new level of science into the US$50-billion global cycling industry, one that has relied more on intuition and experience than on hard mathematics. Their findings could spur some much needed innovation — perhaps helping designers to create a new generation of pedal and electric bikes that are more stable and safer to ride. Insights from bicycles also have the potential to transfer to other fields, such as prosthetics and robotics."/>

The bicycle problem that nearly broke mathematics

Jim Papadopoulos has spent a lifetime pondering the maths of bikes in motion. Now his work has found fresh momentum.  Seven bikes lean against the wall of Jim Papadopoulos's basement in Boston, Massachusetts. Their paint is scratched, their tyres flat. The handmade frame that he got as a wedding present is coated in fine dust. “I got rid of most of my research bikes when I moved,” he says. The bicycles that he kept are those that mean something to him. “These are the ones I rode.”Papadopoulos, who is 62, 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?  He studied these questions intensely as a young engineer at Cornell University in Ithaca, New York. But he failed to publish most of his ideas — and eventually drifted out of academia. By the late 1990s, he was working for a company that makes the machines that manufacture toilet paper. “In the end, if no one ever finds your work, then it was pointless,” he says.But then someone did find his work. In 2003, his old friend and collaborator from Cornell, engineer Andy Ruina, called him up. A scientist from the Netherlands, Arend Schwab, had come to his lab to resurrect the team's research on bicycle stability.“Jim, you need to be a part of this,” Ruina told him.

Two wheels good

Together, the researchers went on to crack a century-old debate about what allows a bicycle without a rider to balance itself, publishing in Proceedings of the Royal Society1 and Science2. They have sought to inject a new level of science into the US$50-billion global cycling industry, one that has relied more on intuition and experience than on hard mathematics. Their findings could spur some much needed innovation — perhaps helping designers to create a new generation of pedal and electric bikes that are more stable and safer to ride. Insights from bicycles also have the potential to transfer to other fields, such as prosthetics and robotics.