As a teenager, Gordon studied piano intensively and performed extensively in public, including solo concerts for charity and with the Badger Symphony Orchestra. He received a BS degree from Princeton University and a PhD from the University of Wisconsin. His professional career has been in academic science and he has been a faculty member at MIT, Cornell University, University of California at Santa Barbara, and Duke University. He has carried out a multi-million dollar research program, mostly supported by the National Institutes of Health and has received a number of awards for his research, including election to the National Academy of Sciences, the American Academy of Arts and Sciences, the Eli Lilly Award (American Chemical Society), the Rose Award (American Society for Biochemistry and Molecular Biology). Recently, the American Chemical Society established a national award in his name, the Gordon Hammes Lecture. His work has resulted in more than 250 publications, including six books. He also has served as an  university administrator. At Cornell, he was Chair of the Department of Chemistry and co-founder and first Director of the Biotechnology Program. At UC Santa Barbara he served as Vice Chancellor for Academic Affairs. At Duke, he was Vice Chancellor for Medical Center Academic Affairs with oversight of the academic and research aspects of the Medical Center and a budget of several hundred million dollars.

Gordon and his wife Judy have three children, one of whom is a professional violinist. They moved permanently to Naples in the spring of 2010. In Naples, Gordon has served on the Board of the Valencia at Pelican Bay Condominium Association, has been involved in a relationship with Florida Gulf Coast University, and has participated in various tennis activities. He is currently ranked number 5 nationally in his age group in tennis and has been selected for the USA International Team.

He has retained his interest in music, still playing the piano, and served on the Board of the North Carolina Opera Association. As a member of the board of the Naples Music Club, he looks forward to helping young people develop their talents.