[3] After study at Phoenix College, Royden transferred in 1946 to Stanford University, where he received his bachelor's degree in 1948 and his master's degree in 1949, with a master's thesis written under the supervision of Donald Spencer.
Royden received his Ph.D. in 1951 at Harvard University under the supervision of Lars Ahlfors with thesis Harmonic functions on open Riemann surfaces.
[8] In 1974 he was an Invited Speaker (Intrinsic metrics on Teichmüller space) at the International Mathematical Congress in Vancouver.
Upon his death he was survived by his wife (the mathematician Virginia "Jinx" Voegeli), two daughters (one, Leigh Royden, a noted geologist), a son, and several grandchildren.
[2] His doctoral students include Alan Huckleberry, Peter A. Loeb and John Wetzel.