Gale grew up in a family of modest means, but his parents valued education and encouraged his intellectual pursuits from an early age. He attended New York City public schools, where he demonstrated a prodigious talent for mathematics. After graduating from high school, Gale enrolled at Cornell University, where he earned his Bachelor's degree in mathematics in 1942. His academic excellence earned him a scholarship to study at the University of Cambridge, where he earned his Ph.D. in mathematics in 1949.