“We Believe in the Real Numbers”

On my first day of college, my honors calculus professor, Galen Shorack, strode into the classroom, picked up a piece of chalk, and wrote on the blackboard, “We believe in the real numbers.” His message integrated profound insights. Mathematics resides in the realm of metaphysics. Mathematics is a belief system built upon discovery, upon revelation, not invention or manufacture. The fruits of mathematical labor are verified by agreement with real world facts, but in and of themselves the manipulation of numbers and symbols are representational, not real.