Harkness was for a time a vice president of the American Mathematical Society and associate editor of its Transactions, was elected a member of the London Mathematical Society and in 1908 became a fellow of the Royal Society of Canada.
Harkness held various positions within the mathematical community, including vice president at the American Mathematical Society and associate editor for its Transactions. His election into the London Mathematical Society and fellowship with the Royal Society of Canada in 1908 further solidified his reputation.