Dimension 126 Contains Twisted Shapes, Mathematicians Prove

It can be tempting to assume that your intuitions about three-dimensional space carry over to higher-dimensional realms. After all, adding another dimension simply creates a new direction to move around in. It doesn’t change the defining features of space: its endlessness and its uniformity. But different dimensions have decidedly different personalities. In dimensions 8 and 24, it’s possible to pack balls together especially tightly. In other dimensions, there are “exotic” spheres that look irremediably crumpled. And dimension 3 is the only one that can contain knots — in any higher dimension, you can untangle a knot even while holding its ends fast. Now, mathematicians have put the finishing touches on a story of dimensional weirdness that has been 65 years in the making. For many decades, researchers have wanted to know which dimensions can host particularly strange shapes — ones so twisted that they cannot be converted into a sphere through a simple procedure called surgery. The ... Read full article.