A NOTE TO READERS
This is a book about the edge of what mathematics knows, written for the reader who has no special training and needs none. If you can picture a tile, a knot in a shoelace, a stack of oranges, or a box, you are already equipped for everything that follows. I have assumed curiosity and nothing else.
A few conventions will make the journey smoother. The mathematics in these pages is meant to be read, not worked: there are no exercises, no prerequisites, and no moments where you are expected to pick up a pencil. Where a formula appears, it is there because a sentence could not do its job as well, and you are free to glide over it without losing the thread. The diagrams — there are well over a hundred — are not technical figures to be decoded but illustrations to be enjoyed, each placed beside the words it illuminates.
I have tried throughout to be scrupulously honest about the difference between what is proven and what is merely believed. When a problem is solved, I say so and name the person who solved it; when it is open, I say that plainly, even when the answer seems obvious. A handful of results described here were, as I wrote, brand-new and still being checked by the mathematical community; I have flagged these as provisional rather than dress them up as settled. The frontier moves, and a book about the frontier is necessarily a photograph of a moving thing. Some of the open problems in these pages may be solved by the time you read about them — and if you are the one who solves them, I will consider this book to have more than served its purpose.
You may read straight through or wander as you please. The five parts move from the flat plane outward and upward, into knots and packings and dimensions we cannot see, and back down to objects you could hold in your hand; but each chapter stands on its own, and the shapes will be waiting wherever you choose to begin.
Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.
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