Harpur was born in Ballybay, County Monaghan, Ireland. He was a graduate of the University of Glasgow and taught in Ireland for 7 years before coming to the Colony of New York in 1760. Three days after his arrival in 1761 he was installed as professor of mathematics at King's College, renamed Columbia College after U.S. independence (today Columbia University). One of his prized pupils was Alexander Hamilton while he studied there in 1774.[1]: 33 During his tenure, he was hired by the university to catalog the collections of the Columbia library, making him the first librarian of the university.[2]
Harpur served in various capacities in the New York government during the American Revolution. He was a member of the New York State Assembly from 1777 to 1784. He was Deputy Secretary of State under John Morin Scott and Lewis Allaire Scott from 1778 to 1795. In the spring of 1795, after the American Revolutionary War, Robert Harpur, with his 2nd wife Myra and family, moved west along the upper Susquehanna River. He settled near Belden Brook on his Warren Patent, which is near present-day Harpursville, NY.[1]: 97
The New York State Library, in Albany, New York, holds the following materials of Harpur, according to its online catalog: "This collection contains material created by Harpur and material collected about him. Among Harpur's papers are his personal account books, 1768-1814, which include house expenses and tuition accounts for students he tutored; and a photostat of a land grant to Harpur for lands in Kingsbury and Queensbury townships. Among the items collected about Harpur are several biographies, postcards of the Senate House in Kingston, N.Y. and Clinton's mansion, and a photostat of a 1790 print of Columbia College, where Harpur taught."
Herbert, Anne T. (2003). Robert Harpur's New York: his role in its growth from province to state. Broome County Historical Society. ISBN 1930484054.