Jensen Inequality Reveals A Mathematical Shortcut

You can predict the outcome of a complex average just by looking at a curve. Jensen's inequality proves that the average of a curved function is always greater than or equal to the function of the average.

This rule is surprisingly powerful in fields like economics and machine learning. Instead of calculating every individual data point, you can estimate the final result by simply measuring the middle value. It shows that curved paths always favor the extremes rather than the center. Understanding this simple shift helps scientists quickly approximate complex systems without tedious manual calculations.