Gordon Whyburn, a student of Robert Lee Moore, supervised his thesis, entitled A Study of Hyperspaces.

He held visiting appointments at Cambridge University and the Indian Institute of Technology in Kanpur, India.

In 1950, Kelley was one of 29 tenured Berkeley faculty (3 of whom were members of the Mathematics Department) dismissed for refusing to sign a McCarthy-era loyalty oath mandated by the UC Board of Regents.

He was an active member of the School Mathematics Study Group (SMSG), which played an important role in designing and promulgating the "new math" of that era.

His doctoral students include Vashishtha Narayan Singh, James Michael Gardner Fell, Isaac Namioka, and Reese Prosser.