Furman was born in the Lawrenceville section of Lawrence Township, Mercer County, New Jersey in 1892. He attended Lawrenceville School, where he was a model student, graduating with a Master's Prize from his high school in 1909. He enrolled in Princeton University, where he received Phi Beta Kappa honors and graduated in 1913. He received an M.S. in 1915 and a Ph.D. from Princeton in 1917. Furman served in World War I in the Army Chemical Warfare Service. He returned to Princeton in 1919 to become an assistant professor, gaining promotion and tenure in 1937, and finished his career in 1960 as the Russell Wellman Moore professor of chemistry.