With inspiration coming from computational biology, computer science, and theoretical physics, much of the work revolves around discrete structures and their underlying topology and geometry. The fascination is not in the study of one object, but the space of all ways an object can deform and evolve.
Underneath this framework lies a strong desire for the proper visualization of data, from drawings to graphics to photography. Conveying results with visual clarity, accuracy, and simplicity is as important as the discovery of the ideas themselves.
These ideas should also be made incarnate, for the physical matters. Humans care about how things look, taste, feel, and sound. And mathematics is part of this tapestry, dealing not just with the mind, but the body as well, extending to our tangible world.
Some works and thoughts have appeared in venues such as NPR, The Times of London, and Forbes, with generous support over the years by the National Science Foundation, DARPA, the Mellon Foundation, the Whiting Fellowship, and the Templeton Foundation.
A 36-lecture DVD course on the shape of nature, covering some of the most beautiful ideas in math, aimed at the general public, published by The Great Courses.
A textbook on geometry in the discrete setting, written for math and computer science students, coauthored with Joseph O'Rourke, published by Princeton University Press.
A visualization of the impact of choosing a major on career paths for 15600 Williams alums, laying the foundation for CereusData, a company aimed at producing beautiful and comprehensible images.
The Unfolding Humanity artwork alludes to Dürer's 500-year-old problem on the outside, whereas the walls of mirrors on the inside points to the shape of our universe.
The centerpiece of the 2018 redesign of USD math is the new Studio, serving as an incubator and promoter of a radical, physical experience in mathematics research.