Pate was born in Pender, Nebraska to Richard E. Pate and Rachel Davis Pate, of Welsh and Irish ancestry respectively. He was the oldest of seven children, three of whom died in infancy. His family moved to Denver, Colorado, when he was three years old. He graduated from East Denver High School in Denver, Colorado in 1911, then left Denver for Princeton University. At Princeton he was a member of Phi Beta Kappa, worked on the undergraduate Red Cross Committee, and earned a bachelor of science degree in mathematics and physics in 1915, with high honors.