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 ...

Mathematicians are finding inevitable structures in sufficiently large sets of integers. Despite that, Furstenberg’s paper left a lasting imprint on mathematics. His new argument contained a kernel of ...

The original version of this story appeared in Quanta Magazine. The world of mathematics is full of unreachable corners, where unsolvable problems live. Now, yet another has been exposed. In 1900, the ...

Mathematicians rejoice when they prove that seemingly impossible things exist. Such is the case with a new proof posted online in March by Cédric Pilatte, a first-year graduate student at the ...

Mathematicians sometimes think of their research as a garden and unsolved problems as seeds waiting to sprout. Some problems are analogous to tulip bulbs. As mathematicians work to solve them, they ...