Anthony was born in Rhodesia (now Zimbabwe) and was raised on a farm where they had a large general purpose workshop. His father was a keen woodworker, and Anthony spent a lot of his youth working in the shop honing his woodworking skills for use later in life. In addition to learning many of his woodworking skills from his father, he attended a high school that had a large modern woodworking shop. During woodworking classes he made a wooden propeller for a life-sized hovercraft that he and a school friend built for a science exhibition.

After graduating from high school he attended college in Durban, South Africa, where he attained a PhD in physics. While at college he met his wife, Colleen, and they have three children. In 1980 they spent a year at MIT in Boston where Anthony did post doctoral studies in the plasma fusion laboratory. The Hayzens moved to the USA in 1995 after Anthony was offered a position at a high tech company in Knoxville, Tennessee.