[16] He was the PhD advisor for Frank Adams, Max Kelly, Crispin Nash-Williams, William Tutte and Christopher Zeeman.

[5] In July 1969, he was sent a draft paper by James H. Ellis, another GCHQ mathematician, about the possibility of what was termed "non-secret encryption", or what is now more commonly known as public-key cryptography, on which Wylie commented "unfortunately, I can't see anything wrong with this".

[17] He retired in 1973, and taught at Cambridgeshire High School for Boys (later Hills Road Sixth Form College) in Cambridge for seven years.

[5] In addition he influenced the intellectual development of generations of pupils at the Cambridgeshire High School for Boys/Hills Road Sixth Form College where he taught maths (particularly statistics, with his beloved chi-squared distribution) and classical Greek and where he also produced plays (such as Chekhov's The Cherry Orchard) and supervised the school chess team.

After retirement from teaching, Wylie was instrumental in the founding of the Liberal Democrats and in the Cambridge-based University of the Third Age and at the time of his death was preparing to read in the next Cambridge Greek Play, Aeschylus' Agamemnon.

His eldest son, the late Keith Wylie (1945–1999), a barrister, was a croquet international and open champion of Great Britain.