Mathematics Department Chair Shing-Tung Yau hopes to make analytic geometry and string theory accessible to a wider audience with his new book, “The Shape of Inner Space,” which he co-wrote with science author Steven J. Nadis.

The book, released this month, explores how Yau mathematically proved the existence of a theoretical structure known as a Calabi-Yau manifold, in which dimensions other than the three spatial dimensions and time could be contained.

Yau and Nadis began writing nearly four years ago, and crafted the book to be a blend of first-person narrative, mathematical history, and scientific explanation.

“Once you start getting into the details of the geometry and topology developed here, it gets pretty complicated,” said Nadis, who was recruited by Yau to help make the book more accessible to lay readers. “It’s the first book that is trying to reach a broad audience that is about [these topics].”

Yau said that he wrote the book not only to share his research with others, but also to explain the ways in which mathematicians help contribute to the understanding of the universe.

“We [mathematicians] are just normal scientists, sometimes more quiet than physicists and biologists,” Yau said, adding that he wanted to explore “how mathematicians think about nature [and] how we contribute to understanding nature.”

The book also focuses heavily on the importance of collaborations between mathematics and other disciplines. Yau and Nadis trace the history of how physicists used the idea of Calabi-Yau manifolds to develop string theory, which posits that the universe is composed of single-dimensional strings vibrating in higher-dimensional spaces. Calabi-Yau manifolds help account for the extra dimensions.

“I think it’s an inspiring story about how progress in science is made by breaking traditional boundaries in disciplines,” said Physics Professor Andrew Strominger, who has used Yau’s work in his own string theory research. “I think it’s really the only book of its kind—and, of course, written by someone who not only witnessed but also inspired and produced some of the major developments [in this field],” Strominger said.

Following this book, Yau said that he intends to continue writing with Nadis in the future. They have already completed several chapters of a book on the history of Harvard’s Department of Mathematics.

—Staff writer Gautam S. Kumar can be reached at gkumar@college.harvard.edu.—Staff writer Evan T.R. Rosenman can be reached at erosenm@fas.harvard.edu.