Physicists use quantum field theory to predict what happens when subatomic particles collide. In practice, these predictions require summing vast numbers of terms, one for each possible sequence of events a collision could follow. A longstanding puzzle is that these enormous calculations often collapse to remarkably simple answers, suggesting that the complexity is obscuring some deeper simplicity. Carolina Figueiredo discovered that three apparently unrelated theories – two governing nuclear particles called gluons and pions, and the third describing particles in a “toy model” that does not describe the existing world – all forbid exactly the same set of particle collisions. This was a big surprise, as the three theories are quite different, with no reason to think they are connected. But Figueiredo’s discovery revealed that the common behavior reflects a single underlying geometric structure: curves drawn on surfaces, within a framework now known as surfaceology. Intriguingly, this structure makes no reference to particles moving through space and time; yet it reproduces the predictions of conventional physics far more efficiently than the traditional approach, which tracks each particle’s movement through these dimensions. Figueiredo’s work thus advances – and perhaps brings closer to the real world – a broader program to reformulate the foundations of particle physics in purely geometric terms, with spacetime as an emergent phenomenon arising from a new set of principles.