Mathematicians have shown that strangely twisted shapes exist in dimensions 2, 6, 14, 30 and 62, and that such shapes cannot exist in any other dimensions — save one.
For decades, no one could determine the status of dimension 126.
Now, three mathematicians have settled this final problem using a combination of computer calculations and theoretical insights.
The proof helps explain why these strangely twisted shapes are restricted to such a small number of dimensions.
And it may help mathematicians understand other, similarly strange behaviors that occur in other dimensions.
Excavating the history of this story, which spans more than half a century, reveals an epic tale of mathematical ingenuity and computer virtuosity.
