He was born in Binghamton, New York, in 1947. In 1974, Thompson received his Ph.D. in mathematics from Cornell University. He specialized in probability theory and statistical mechanics. Later, he conducted research in quantum physics and mathematical biology at the La Jolla Institute in San Diego, the State University of New York at Binghamton, and Cambridge University in the United Kingdom. He authored seven books on science and philosophy, and wrote many articles for scientific journals and for Back To Godhead, the official magazine of ISKCON.

In 1993 Thompson co-wrote Forbidden Archeology. The book claims that humans have lived on the earth for millions, or billions, of years, and that the scientific establishment has suppressed the fossil evidence for extreme human antiquity. The authors speak about a knowledge filter (confirmation bias) as the reason for this suppression. Forbidden Archeology has attracted attention from creationists and paranormalists, but has been labeled as "pseudoscience" and "antievolutionism" by representatives of the mainstream archaelogical and paleoanthropologist community. Meera Nanda in the Indian magazine Frontline called Cremo and Thompson "the intellectual force driving Vedic creationism".

In 1996 Thompson and Cremo appeared on the widely criticized by the scientific community NBC special The Mysterious Origins of Man. The book Forbidden Archeology provided much of the content for the program.

He died on September 18, 2008.