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Watching this soap film stretch, rupture and reform in slow motion is mesmerising – but mathematicians see more than a trippy image. The point where the bubble breaks explosively is a mathematical singularity – a violent moment when the surface changes.

Singularities also occur in solar flares and turbulent fluids, and predicting where they will happen within these bodies is a big challenge.

of the University of Cambridge and his team used observations like this one – and wilder soap surfaces including Klein bottles and Mobius strips – to determine a new way to predict where the singularity will occur for any shape.

Journal reference: PNAS DOI: