For centuries, prime numbers have captured the imaginations of mathematicians, who continue to search for new patterns that help identify them and the way they’re distributed among other numbers.

How did you learn the mathematical formula for pi? It was likely the way I learned it. I was told to commit the value pi = 3.14 to memory along with the formula to calculate the area of a circle.

A new proof marks the first progress in decades on a problem about how order emerges from disorder. In February, Sah and Sawhney announced yet another joint accomplishment. With James Leng, a graduate ...