Eells was born on 25 October 1926, in Cleveland, Ohio.[1] Eells studied mathematics at Bowdoin College in Maine and earned his undergraduate degree in 1947. After graduation he spent one year teaching mathematics at Robert College in Istanbul and starting in 1948 was for two years an instructor at Amherst College in Amherst, Massachusetts. 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.
In the academic year 1955–1956 he was at the Institute for Advanced Study (and subsequently in 1962–1963, 1972–1973, 1977, and 1982).[2] He taught at Columbia University for several years. In 1964 he became a full professor at Cornell University. In 1963 and in 1966–1967 he was at the University of Cambridge, and after a visit to the new mathematics department developed by Erik Christopher Zeeman at the University of Warwick Eells became a professor of mathematical analysis there in 1969. Eells organized many of the University of Warwick Symposia in mathematics.
He was co-editor of the collected works of Hassler Whitney. Eells's doctoral students include Luc Lemaire, Peter Štefan (1941–1978), Giorgio Valli (1960–1999) and Pierre de la Harpe [de]. Eells was married since 1950 and had a son and three daughters.
with Luc Lemaire: Eells, J.; Lemaire, L. (1978). "A report on harmonic maps". Bulletin of the London Mathematical Society. 10: 1–68. doi:10.1112/blms/10.1.1.; re-published with a follow-up report in the books Harmonic Maps, 1992, and Two Reports on Harmonic Maps, 1994, by publisher World Scientific
with Luc Lemaire: Selected topics in harmonic maps, AMS 1983
with Andrea Ratto: Harmonic maps and minimal immersions with symmetries – methods of ordinary differential equations applied to elliptic variational problems, Princeton University Press 1993
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