Discover how the Luhn Algorithm verifies credit card accuracy, supports secure transactions, and helps prevent errors in inputting Social Security numbers.

The original version of this story appeared in Quanta Magazine. Imagine a town with two widget merchants. Customers prefer cheaper widgets, so the merchants must compete to set the lowest price.

Abstract: The role of differential equations (DEs) in science and engineering is of paramount importance, as they provide the mathematical framework for a multitude of natural phenomena. Since quantum ...