We all know the euphoria of intellectual epiphany--the thrill of sudden understanding. But coupled with that excitement is a sense of loss: a moment of epiphany can never be repeated. In Geometry of Grief, mathematician Michael Frame draws on a career's worth of insight--including his work with a pioneer of fractal geometry Benoit Mandelbrot--and a gift for rendering the complex accessible as he delves into this twinning of understanding and loss. Grief, Frame reveals, can be a moment of possibility.

Frame investigates grief as a response to an irrevocable change in circumstance. This reframing allows us to see parallels between the loss of a loved one or a career and the loss of the elation of first understanding a tricky concept. From this foundation, Frame builds a geometric model of mental states. An object that is fractal, for example, has symmetry of magnification: magnify a picture of a mountain or a fern leaf--both fractal--and we see echoes of the original shape. Similarly, nested inside great loss are smaller losses. By manipulating this geometry, Frame shows us, we may be able to redirect our thinking in ways that help reduce our pain. Small‐scale losses, in essence, provide laboratories to learn how to meet large-scale losses.

Interweaving original illustrations, clear introductions to advanced topics in geometry, and wisdom gleaned from his own experience with illness and others' remarkable responses to devastating loss, Frame's poetic book is a journey through the beautiful complexities of mathematics and life. With both human sympathy and geometrical elegance, it helps us to see how a geometry of grief can open a pathway for bold action.