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LESSON 2 · Think Like a Mathematician

Run Benford Yourself

Grab any folder of receipts, a spreadsheet of populations, or a page of stock prices. Count the leading digit of each number — just the first nonzero digit. Tally how often 1 appears, how often 2, 3, and so on.

You should see 1 leading about 30% of the time, 2 about 17%, and 9 fewer than 5%. This is Benford's Law, and it emerges from any data spanning several orders of magnitude. Try it on river lengths, city populations, or first-page search counts — the shape holds. (Vote tallies are a famous exception: they cluster in too narrow a range, so the law breaks down and can flag fraud where none exists.) Run the experiment once, and you will not look at a spreadsheet the same way again.