What if you were told that we actually live in a 10-dimensional universethat the leading theory of nature posits only 4 out of 10 are accessible to our everyday senses? How do we account for the other 6 dimensions? What do they look like, where are they hiding, and what, if anything at all, do they do? In The Shape of Inner Space, geometer and leading string theorist Shing-Tung Yau unpacks the widely-held belief that these undetected dimensions are tightly curled in elaborate, twisted shapes called Calabi-Yau manifolds. Yau explains that these spaces are so miniscule that humans will probably never see any of them directly. Amazingly, however, this hidden realm may hold the answers to some of the most profound questions we have about our universe.