Beginning in 1983, he was a National Science Foundation postdoctoral fellow, lastly at the Courant Institute under Peter Lax.

These are numerical algorithms for tracking moving interfaces in complex situations, and have proved instrumental in a wide collection of applications, including semiconductor processing, fluid mechanics, medical imaging, computer graphics, and materials science.

Together with Alexander Vladimirsky, Sethian developed a class of Dijkstra-like ordered upwind methods for solving static Hamilton–Jacobi equations.

Examples include informing engineers how to design more precise ink jet plotters, allowing physicians to analyze brain and cardiac images, aiding oil companies in locating petroleum reserves, and telling process engineers how to build reliable computer chips.

Sethian was elected member of the National Academy of Engineering in 2008 for the development of efficient methods of tracking moving interfaces.

Previous recipients include Richard Bellman, Peter Lax, Alexandre Chorin, Jerrold Marsden, Tosio Kato, Gerald Whitham, Arthur Winfree, and Harold Widom.