Issuers tack it on so that the whole card number will satisfy a specific mathematical test—the Luhn algorithm. Here’s how the algorithm works: Write out all but the last digit of the card number.

Bias in algorithms doesn’t necessarily mean they’re useless. But Dressel and Farid—like many others in their field—are trying to warn against putting too much faith in these numbers.

Excerpted from Things to Make and Do in the Fourth Dimension: A Mathematician’s Journey Through Narcissistic Numbers, Optimal Dating Algorithms, at ...