James Eells (October 25, 1926 – February 14, 2007) was an American mathematician, who specialized in mathematical analysis.

[1] Eells studied mathematics at Bowdoin College in Maine and earned his undergraduate degree in 1947.

Next he undertook graduate study at Harvard University, where in 1954 he received his Ph.D under Hassler Whitney with thesis Geometric Aspects of Integration Theory.

Eells did research on global analysis, especially, harmonic maps on Riemannian manifolds, which are important in the theory of minimal surfaces and theoretical physics.

In 1970 he was an invited speaker at the International Mathematical Congress in Nice (On Fredholm manifolds with K. D. Elworthy).