James Hoffman created software for scientific visualization, particularly of surface geometries studied in differential geometry. While a graduate student at the University of Massachusetts at Amherst, James was enlisted by Mathemetician David Hoffman to help prove an important result in minimal surface geometry, discovering the first new examples of complete embedded minimal surfaces in more than one hundred years. The first example, the Costa surface, was described in 1983 by Brazilian graduate student Celso Costa as an equation, but a proof that it was embedded (lacked self-intersections) was provided by David Hoffman and William Meeks, who used computer visualizations created by James to see that the surface was embedded and dissect it to prove that it was. This finding, followed by the discovery of scores of other surfaces and families of surfaces illustrated by Hoffman's computer graphics, overturned a century-old conjecture that the only examples of such minimal surfaces where the plane, catenoid, and helicoid.

Hoffman's work has been featured in articles in Science News, Scientific American, and Nature, and he has co-authored papers in Science and Macromolecules. He is credited with involvement in the discovery of new three-dimensional morphologies for modeling block co-polymers, such as the Split-P surface (a hybrid of the P and G triply periodic surfaces), and derived the first level set formulation for the Lidinoid surface.

Hoffman is the co-author of a patent for an internal combustion engine with increased thermal efficiency. He is also the inventor of a solar panel using concentrating photovoltaics for increased efficiency.