Mathematical logic and set theory provide the foundational language for modern mathematics, articulating precise notions of proof, computability and the hierarchy of infinities. Central themes include ...

Algebraic structures form the backbone of many modern mathematical disciplines, providing abstract frameworks that capture the essence of operations and relations. Duality theory, in this context, ...

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. The Quanta Newsletter ...

By replacing the most fundamental concept in topology, Peter Scholze and Dustin Clausen are taking the first step in a far ...