He earned a doctorate at Harvard University under Maxime Bôcher and William Fogg Osgood in 1903.

He then served as a professor at Northwestern University from 1905 to 1943, including 20 years as Chair of the Mathematics Department.

Curtiss authored textbooks on trigonometry and analytic geometry with Elton James Moulton.

He also published the second Carus Mathematical Monograph, Analytic Functions of a Complex Variable.

He and his wife, who was seriously ill, committed suicide by carbon monoxide poisoning in the garage of their home in Redlands, California.