The Mathematical Intelligencer 33(1), 85-91.

**ISSN/ISBN:** Not available at this time.
**DOI:** 10.1007/ s00283-010-9182-3

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**Abstract:** The widely known phenomenon called Benford’s Law
continues to defy attempts at an easy derivation. This article briefly reviews recurring flaws in ‘‘back of the envelope’’ explanations of the law, and then analyzes in more detail some of the recently published attempts, many of which replicate an apparently unnoticed error in Feller’s classic 1966 text An Introduction to Probability Theory and Its Applications. Specifically, the claim by Feller and subsequent authors that ‘‘regularity and large spread implies Benford’s Law’’ is fallacious for any reasonable definitions of regularity and spread (measure of disper sion). The fallacy is brought to light by means of concrete examples and a new inequality. As for replacing the wrong assertions by an equally simple explanation which is valid, now that is a task for the future.

**Bibtex:**

```
@article {MR2774458,
AUTHOR = {Berger, Arno and Hill, Theodore P.},
TITLE = {Benford's law strikes back: no simple explanation in sight for
mathematical gem},
JOURNAL = {Math. Intelligencer},
FJOURNAL = {The Mathematical Intelligencer},
VOLUME = {33},
YEAR = {2011},
NUMBER = {1},
PAGES = {85--91},
ISSN = {0343-6993},
CODEN = {MAINDC},
MRCLASS = {62A99 (60E05)},
MRNUMBER = {2774458 (2012j:62006)},
DOI = {10.1007/s00283-010-9182-3},
URL = {http://dx.doi.org/10.1007/s00283-010-9182-3},
}
```

**Reference Type:** Journal Article

**Subject Area(s):** Probability Theory