When mathematician Georg Cantor first glimpsed the true nature of infinity, it changed mathematics forever. He demonstrated that infinity isn’t just endless; it exists in different sizes, each opening ...

Is there an infinity of infinities? The question sounds almost absurd, like a child’s riddle meant to twist your brain into knots. But for mathematicians, it’s a serious (and endlessly fascinating) ...

All of modern mathematics is built on the foundation of set theory, the study of how to organize abstract collections of objects. But in general, research mathematicians don’t need to think about it ...

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 ...