William Ross does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond their ...

A new proof illuminates the hidden patterns that emerge when addition becomes impossible. The simplest ideas in mathematics can also be the most perplexing. Take addition. It’s a straightforward ...

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 ...