Descriptive set theorists study the niche mathematics of infinity. Now, they’ve shown that their problems can be rewritten in the concrete language of algorithms. All of modern mathematics is built on ...

The original version of this story appeared in Quanta Magazine. In 2003, a German graduate student named Britta Späth encountered the McKay conjecture, one of the biggest open problems in the ...

A series of unsolved puzzles in number theory called Diophantine problems date back to 3,700 years ago. Over the years mathematicians have whittled away at them, and recent work has made significant ...

Giving birth to a conjecture — a proposition that is suspected to be true, but needs definitive proof — can feel to a mathematician like a moment of divine inspiration. Mathematical conjectures are ...

In 2003, a German graduate student named Britta Späth encountered the McKay conjecture, one of the biggest open problems in the mathematical realm known as group theory. At first her goals were ...

The original version of this story appeared in Quanta Magazine. All of modern mathematics is built on the foundation of set theory, the study of how to organize abstract collections of objects. But in ...