This article provides a concise overview of the main mathematical theory of Benford’s law in a form accessible to scientists and students who have had first courses in calculus and probability. In particular, one of the main objectives here is to aid researchers who are interested in applying Benford’s law, and need to understand general principles clarifying when to expect the appearance of Benford’s law in real-life data and when not to expect it. A second main target audience is students of statistics or mathematics, at all levels, who are curious about the mathematics underlying this surprising and robust phenomenon, and may wish to delve more deeply into the subject. This survey of the fundamental principles behind Benford’s law includes many basic examples and theorems, but does not include the proofs or the most general statements of the theorems; rather it provides precise references where both may be found.

本文以对微积分和概率论第一门课程的科学家和学生可用的形式，简要概述了本福德定律的主要数学理论。特别是，这里的主要目标之一是为有兴趣应用本福德定律的研究人员提供帮助，他们需要了解一些一般性原则，以阐明何时在实际数据中期望本福德定律的出现以及何时不期望本福德定律的出现。第二个主要目标受众是各个层次的统计或数学专业的学生，​​他们对这种令人惊讶且健壮的现象所基于的数学感到好奇，并可能希望更深入地研究该学科。这项对本福德定律背后基本原理的调查包括许多基本示例和定理，但不包括定理的证明或最一般的陈述；而是提供了可能同时找到两者的精确参考。