# Mathematical Digest

### Short Summaries of Articles about Mathematics

in the Popular Press

"The First Digit Phenomenon," by T. P. Hill. *AmericanScientist*, July - August 1998 .

The government has recently discovered a new tool for identifying fraudulent tax returns, based on a strange statistical phenomenon. It turns out that on tax returns based on true data, 1 shows up as the first digit of a number more often than 2 does, and 2 shows up more often than 3 etc. This is a manifestation of Benford's law, a theory described by physicist Frank Benford in 1938, Benford noticed and described this pattern, which holds for data sets ranging from the areas of rivers, to American League baseball statistics. When people fill in a tax form with made-up numbers, however, the numbers do not follow the same pattern. This article describes the history and theory behind Benford's law, and explains some interesting applications beyond detecting tax fraud.

*---Elizabeth Veomett*