[edited on January 18, 2021] tl;dr Sometimes a mathematical result is strikingly contrary to generally held belief even though an obviously valid proof is given. Charles Stein of Stanford University discovered such a paradox in statistics in 1955. His result undermined a century and a half of work on estimation theory. ( Efron & Morris, 1977, p. 119) The James-Stein estimator leads to better predictions than simple means. Though I don’t recommend you actually use the James-Stein estimator i...
