Buckmire was born in 1968 in Grenville, Grenada. In 1969 his family moved to the United States while his father earned a Ph.D. degree at the University of Massachusetts at Amherst, and in 1978 they moved to Barbados. There Buckmire attended high school at the Combermere School. Buckmire returned to the United States in 1986 to attend the Rensselaer Polytechnic Institute (RPI), graduating with a B.S. degree in three years and earning his Ph.D. in 1994, both in mathematics. His dissertation was on transonic aerodynamic flow. In 1994 he joined Occidental College as a postdoctoral researcher, and in 1996 he gained an appointment there as an assistant professor. His research interests include computational fluid dynamics for aerodynamics, nonstandard finite difference schemes, and the application of mathematical models to unusual phenomena such as the financial performance of movies.
Buckmire is also known as an LGBT activist. He came out during college in 1988 or 1989, having gained information about homosexuality through the early Internet. He became active in several student organizations at RPI, including serving as president of the Rensselaer Gay/Lesbian/Bisexual Association and even co-founding the Women Students Association. In 1991 he began the Queer Resources Directory, an online resource that for information on issues relating to sexual minorities, and in the 1990s administered several queer electronic discussion groups. He was also active in outreach through radio, co-creating a queer local radio station while at RPI, and later becoming a contributing for This Way Out, a national radio newsmagazine show.
From his youth, Buckmire participated in competitive chess, becoming Barbados Junior Champion four times and National Champion three times, and as of 1997 was ranked as a senior master and one of the top 250 chess players in the United States.
- Greenblatt, R. Ellen (1997). "Ron Buckmire". In Bronski, Michael. Out-standing lives: profiles of lesbians and gay men. New York: Visible Ink Press. pp. 61–65. ISBN 1-57859-008-6.
- "Ron Buckmire". Occidental College. Retrieved June 6, 2015.
- "Ron Buckmire, Professor of Mathematics" (PDF). Math Alliance.
- "Ron Buckmire's Research Page". sites.oxy.edu. Retrieved June 6, 2015.
- Forde, Michael Bernadine. The History of Organized Chess in Barbados (1877 – 1985) (PDF) (Thesis). University of the West Indies, Cave Hill. Retrieved January 29, 2017.