Algorithms are a staple of modern life. People rely on algorithmic recommendations to wade through deep catalogs and find the best movies, routes, information, products, people and investments.

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.

New inventions — like the printing press, magnetic compasses, steam engines, calculators and the internet — can create radical shifts in our everyday lives. Many of these new technologies were met ...

You scrambled up a Rubik’s cube, and now you want to put it back in order. What sequence of moves should you make? Surprise: You can answer this question with modern algebra. You might remember ...