The First Digit Phenomenon

Dr. Ted Hill

School of Mathematics
Georgia Institute of Technology

February 27, 1998

Abstract

Discovered over a century ago, the First Digit Phenomenon predicts that in "random data sets" of real numbers, the leading (non-zero) significant digit is not uniformly distributed, as would be expected, but rather follows a specific logarithmic distribution now known as Benford's Law. This survey talk will mention some of the colorful history of the problem, empirical evidence, classical "proofs" of various sorts, and modern applications such as detection of tax fraud, and will present a new probability limit law based on invariance properties, ergodic theory and random measures.