Geometry of Grief: Reflections on Mathematics, Loss, and Life (Paperback)
In this profound and hopeful book, a mathematician and celebrated teacher shows how mathematics may help all of us—even the math-averse—to understand and cope with grief.
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.
About the Author
Michael Frame retired in 2016 as adjunct professor of mathematics at Yale University. He is coauthor of Fractal Worlds: Grown, Built, and Imagined and coeditor of Benoit Mandelbrot: A Life in Many Dimensions.
"How the fractal nature of grief is both the key to understanding it and the doorway to moving through it is what mathematician Frame explores in his unusual book Geometry of Grief: Reflections on Mathematics, Loss, and Life. After twenty years of working with the visionary father of fractals and another twenty years of teaching fractal geometry at Yale, Frame draws on a lifetime of loss and a lifetime of delicate attention to the details of aliveness we call beauty to interleave memoir and mathematics in an uncommon tapestry of thought, twining Borges and quantum mechanics, evolutionary biology and Islamic art, music and multiverse theory. . . . Attentiveness to beauty is the instrument of transcendence—that essential facet of Frame’s geometry of grief and readjustment."
— Maria Popova
"Frame has written a poignant and beautiful book. . . . Treat yourself to the wisdom of this sweet, gentle soul."
— Steven Strogatz
"Frame's new book, Geometry of Grief, suggests that thinking about fractals—and thinking geometrically, in general—can help us process life's most difficult moments... Zooming out instead of in, we might see our individual griefs as small versions of other tragedies in the world. Maybe, Frame says, thinking of grief as a fractal can inspire empathy and lead us to channel our sadness into helping others."
— Boston Globe
"This brief, intriguing personal meditation is inspired by mathematician Michael Frame’s lifelong love of geometry — including 20 years’ collaboration with fractal geometer Benoit Mandelbrot — and the childhood loss of his aunt, who set him on his career path. He writes: 'Grief informs geometry and geometry informs grief.' How so? His epiphany on first understanding any beautiful mathematical idea is always tinged with sadness, because it is unrepeatable. With quirky illustrations, he integrates the lives of his Mom and Dad."
"The word fractal, from the Latin fractus meaning 'broken glass,' was coined by Benoît Mandelbrot, who brought mathematics closer to nature by showing that iterating a simple geometric pattern can result in complex, rough-edged, and beautiful shapes. In Geometry of Grief, Frame, a former colleague of Mandelbrot’s at Yale, aims to unite maths with our lived experience still further by showing how fractals both inform and can help us cope with the experience of irreversible loss. . . . Ambitious and moving.”
— Times Literary Supplement
"Frame has written a wonderful memoir. Combining his passion for mathematics and his mastery of the geometry of fractals, in this text he seeks to educate, encourage, and inspire readers in a personal way. Identifying grief as irreversible, Frame makes surprising connections to foundational mathematical concepts such as continuity and self-similarity. . . . Here, he elucidates the foundational intertwining of science and grief in his own life through deeply and surprisingly personal stories from lived experience. Weaving together references from literature, art, popular culture, and mathematics, Frame clarifies the transcendence found through grief as a universal human experience. The text offers a wealth of resources for curious readers and is a must have for the bookshelf of any mathematics teacher who wants to inspire curiosity in students or relate with empathy to a student suffering loss. This book will be a wonderful addition to any advanced or graduate-level seminar, and preprofessionals in mathematics education will certainly benefit from exploring the book's diverse fields of discourse. Highly recommended."
"Frame writes: ‘Times folds up. So many ghosts crowd into my head. Parents, grandparents, aunts and uncles, dear friends, students… And far too many cats.’ Live long enough oneself and one realizes that half or more of one’s friends and relatives have departed the planet, ‘summoned,’ as the poet Robert Southey had it, ‘on the grand tour of the universe,’ before one. One lives with it, saddened yet grateful oneself still to be in the game. Yet some holes never successfully fill up."
“With poignancy and audacity, Frame builds an unexpected bridge between mathematical beauty and human sorrow, illuminating both.”
— Francis Su, author of "Mathematics for Human Flourishing"
“I expected to enjoy the experience of thinking in fresh ways with Frame about grief—and encountering his love of cats, really of all nature, made manifest on the page. What blew me away were the exciting new connections among love, grief, beauty, and resilience that flowered in my mind as I read. Immersed in Frame’s world of geometry, including fractals, and its applications to real-world emotions, I sometimes felt afloat in a mysterious, and always inviting, dream. It’s a beautiful place for all of us to spend time.”
— Barbara J. King, author of "How Animals Grieve"
“With concision and compassion, Frame shows how a mathematical mind makes sense of a grieving heart. The result is a peculiar, wise, and beautiful book.”
— Ben Orlin, author of "Math with Bad Drawings" and "Change Is the Only Constant"
“A unique, meaningful, and moving work that connects the irreversibility of loss that comes with grief and the irreversibility of first deeply understanding something—particularly something mathematical.”
— Susan Jane Colley, Oberlin College, editor of "American Mathematical Monthly"
“Captured perfectly an experience that I've long tried to put into words but couldn't—the nostalgic sense that comes immediately after a discovery. It's astonishing how so many important ideas come to us in an almost dream-like state, fully formed and with a hazy beauty that somehow falls away when we more fully work out to implications of that idea and put it into words and onto paper; the whole process makes the idea more real but somehow less charming."
— Christina Stankey, medical student and former student of Michael Frame
“Frame believes everyone can fall in love with math if it’s presented with empathy and humor and clarity and context. He portrays math as math-lovers know it: a beautiful garden, a place of curiosity and delight, a tribute to human creativity and the wonders of nature.”
— Steven Strogatz, from the foreword to "Fractal Worlds"