A team of four prominent mathematicians, including two Fields medalists, proved a conjecture described as a “holy grail of additive combinatorics.” Within a month, a loose collaboration verified it ...

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 ...

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 ...