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Shipman was a researcher at the University of Rochester in New York State, and she studied ‘manifolds’, that is, exotic, theoretical shapes described by complex mathematics. Bizarrely, manifolds can be shown to exist in many more dimensions than the three that we are able to perceive. Specifically, Shipman had been working with a six-dimensional shape known as a ‘flag manifold’. How does a three-dimensional human attempt to comprehend a theoretical, six-dimensional shape? Well, she doesn’t. What you need to do is find a way to visualise the shape in a form that the human mind can actually grasp, and this is generally achieved by the detailed study of shadows cast onto a flat surface such as a wall (to the delight of Plato fans everywhere, Sophie had said). Just as a three-dimensional cube might cast a shadow that appears as a two-dimensional square, so a flag manifold can be made to cast its own complex two-dimensional shadow that the human brain is able to comprehend and work with. I imagine that a fair number of mathematicians have calculated and projected the shadow of a flag manifold, but when Barbara Shipman did so, her life as a mathematician collided unexpectedly with another part of who she was – it collided with her life as the daughter of a beekeeper, of all things. Because of this collision, Barbara Shipman saw something in the shadow of the flag manifold that no one else had ever seen before.