The original version of this story appeared in Quanta Magazine.
The simplest ideas in mathematics can also be the most perplexing.
Take addition. It’s a straightforward operation: One of the first mathematical truths we learn is that 1 plus 1 equals 2. But mathematicians still have many unanswered questions about the kinds of patterns that addition can give rise to. “This is one of the most basic things you can do,” said Benjamin Bedert, a graduate student at the University of Oxford. “Somehow, it’s still very mysterious in a lot of ways.”
In probing this mystery, mathematicians also hope to understand the limits of addition’s power. Since the early 20th century, they’ve