The book Flatland: A Romance of Many Dimensions by Edwin A. Abbott explores the concept of physical dimensions through characters who encounter higher-dimensional beings. The protagonist, “A. Square,” ...

Michael Freedman’s momentous 1981 proof of the four-dimensional Poincaré conjecture was on the verge of being lost. The editors of a new book are trying to save it. One of the most important pieces of ...

Watanabe invented a new way of distinguishing shapes on his way to solving the last open case of the Smale conjecture, a central question in topology about symmetries of the sphere. In a burst of work ...

The nature of what the universe is expanding into is complicated, say our readers, and may be beyond our comprehension It is all too easy to think of the big bang and the resulting expanding universe ...