Identifying and creating a strategy for breakthrough innovation happens by building a team, not by hiring and relying on one key individual. A strong team can look at the way things have been done and identify a new way to approach a problem by working together to make connections.

While in graduate school in mathematics at the University of Wisconsin-Madison, I took a logic course from David Griffeath. The class was fun. Griffeath brought a playfulness and openness to problems. Much to my delight, about a decade later, I ran into him at a conference on traffic models. During a presentation on computational models of traffic jams, his hand went up. I wondered what Griffeath – a mathematical logician – would have to say about traffic jams. He did not disappoint. Without even a hint of excitement in his voice, he said: ‘If you are modelling a traffic jam, you should just keep track of the non-cars.’

The collective response followed the familiar pattern when someone drops an unexpected, but once stated, obvious idea: a puzzled silence, giving way to a roomful of nodding heads and smiles. Nothing else needed to be said.

Griffeath had made a brilliant observation. During a traffic jam, most of the spaces on the road are filled with cars. Modelling each car takes up an enormous amount of memory. Keeping track of the empty spaces instead would use less memory – in fact almost none. Furthermore, the dynamics of the non-cars might be more amenable to analysis.

Versions of this story occur routinely at academic conferences, in research laboratories or policy meetings, within design groups, and in strategic brainstorming sessions. They share three characteristics. First, the problems are complex: they concern high-dimensional contexts that are difficult to explain, engineer, evolve or predict. Second, the breakthrough ideas do not arise by magic, nor are they constructed anew from whole cloth. They take an existing idea, insight, trick or rule, and apply it in a novel way, or they combine ideas – like Apple’s breakthrough repurposing of the touchscreen technology. In Griffeath’s case, he applied a concept from information theory: minimum description length. Fewer words are required to say ‘No-L’ than to list ‘ABCDEFGHIJKMNOPQRSTUVWXYZ’. I should add that these new ideas typically produce modest gains. But, collectively, they can have large effects. Progress occurs as much through sequences of small steps as through giant leaps.

Third, these ideas are birthed in group settings. One person presents her perspective on a problem, describes an approach to finding a solution or identifies a sticking point, and a second person makes a suggestion or knows a workaround. The late computer scientist John Holland commonly asked: ‘Have you thought about this as a Markov process, with a set of states and transition between those states?’ That query would force the presenter to define states. That simple act would often lead to an insight.

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