Zermelo-Fraenkel set theory is so widely accepted that modern mathematicians hardly think about it. But believing in its core principles didn’t come easily. How do mathematicians decide that something ...

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 ...

Set theory provides the fundamental language and axiomatic basis for virtually all modern mathematics. At its core lies the Zermelo–Fraenkel system (ZF), often augmented by the Axiom of Choice (AC) to ...