In 1923, he entered the Royal College of Science at Imperial College London.

Martyn was awarded a Bachelor of Science degree in 1926; a PhD in 1929; and a Doctor of Science degree in 1936.

Martyn moved to Australia in 1927 to take up one of the first posts in radio research there.

He was awarded the Thomas Ranken Lyle Medal of the Australian National Research Council in 1947 for his discovery of atmospheric tides, and received the T. K. Sidey Medal from the Royal Society of New Zealand in the same year, an award set up for outstanding scientific research.

Martyn was one of the then 12 Fellows of the Royal Society resident in Australia, and it was largely through his patient negotiation that the various scientific bodies in Australia agreed that 11 of these 12 Fellows were independent enough to form a credible Australian Academy of Science (AAS), which they did in 1954.

As well as being a Foundation Fellow of the AAS, he was elected its Secretary for Physical Sciences for 1954-5 and its president for 1969 until his death in 1970.

In 1959, Martyn delivered the first four of the annual series of ABC lectures (subsequently named the Boyer Lectures) on "Society in the Space Age".

He married Margot Adams, from Sydney in 1944.

He died in Camden, New South Wales on 5 March 1970.