[3] Burnham was in the U.S. Army Corps of Engineers during the Cold War from 1949 to 1952, stationed at Fort Belvoir, working in the drafting school.

[10][6] In 1970, he curated the exhibition at the Jewish Museum, "Software – Information Technology: Its New Meaning for Art".

The exhibition included work by Agnes Denes, Hans Haacke, Nam June Paik and others.

[3] In 1973, Burnham was awarded a fellowship from the John Simon Guggenheim Memorial Foundation to study the alchemical symbolism used in Marcel Duchamp's art.

[11] While he is best known as a theorist,[4] Burnham was trained as an artist;[12] the art he produced included alchemy-imspired diagramatic drawings, sculptures and works that incorporated light.

From 1955 through the 1960s he focused on sculpture, many of which incorporated light[3] or included viewer-activated technology and electro-luminous "ribbons".

[4] To support himself as an artist, he worked various jobs including architectural drafting, sign painter and fabricator, and later as an educator.