S Curve
Sigmoid Function · Logistic Curve
A mathematical curve shaped like the letter S — starting slow, accelerating through a rapid growth phase, then leveling off at a natural limit. It describes technology adoption, population growth, learning curves, and many other natural processes.
Origin
Belgian mathematician Pierre François Verhulst introduced the logistic function in 1838, modifying Thomas Malthus's exponential growth model to account for natural limits on population. His work was largely forgotten until Raymond Pearl and Lowell Reed of Johns Hopkins University independently rediscovered it in 1920. The characteristic S shape — from the Greek letter sigma — has since become one of the most widely recognized patterns in science, technology, and business.
Everyday Use
Every technology follows the same pattern: slow adoption, explosive growth, then saturation. Smartphones, social media, electric cars — they all trace an S curve. It also shows up in your own learning: frustrating early progress, a breakthrough phase, then diminishing returns as you approach mastery.