Attitudes toward intuition in calculus textbooks

Abstract

Intuition was long held in high regard by mathematicians, who considered it all but synonymous with clarity and illumination. But in the 20th century there was a strong tendency to vilify intuition and cast it as the opposite of rigorous reasoning. Calculus in particular became a battleground for these opposing views. By systematically surveying references to intuition in historical and modern calculus textbooks, I look at how its status has changed across the centuries. In particular, I argue against the veracity of the self-fashioned origin story of the modern anti-intuition movement, which relies heavily on a particular historical narrative to portray the demise of intuition as an inexorable triumph of logic and reason.