James Henle's fields of interest include set theory, logic, nonstandard analysis, combinatorial geometry, economics, mathematics education, philosophy of mathematics, music and gastronomy.

Henle was a Peace Corps volunteer in the Philippines and has made research trips to England and Venezuela. His current research takes him to flashing lights, tricky bounces, historic camera angles, economic inequality, tiling planes with squares and introducing mathematics as a fine art.

Henle is the author of The Proof and the Pudding: What Mathematicians, Cooks, and You Have in Common and An Outline of Set Theory, and he is the co-author of Sweet Reason (with Jay Garfield and the late Tom Tymoczko), Calculus: The Language of Change (with David Cohen) and Infinitesimal Calculus (with E. M. Kleinberg). He writes a column, “Cucina Matematica,” for  the Mathematical Intelligencer .

Henle plays clarinet in the Northampton Woodwind Quintet and recently retired from the pit orchestra of the Valley Light Opera.