New posts in Big Picture

What sorts of extra axioms might we add to ZFC to compute higher Busy Beaver numbers?

Axiomatic definition of quantum groups

Why is modular forms applicable to packing density bounds from linear programming at $n\in\{8,24\}$?

Why did Voevodsky consider categories "posets in the next dimension", and groupoids the correct generalisation of sets?

Concepts in topology successfully transferred to graph theory and combinatorics with non-trivial applications?

Measuring a presheaf's failure to be a sheaf?

Is algebraic geometry constructive?

Current status of Grothendieck's homotopy hypothesis and Whitehead's algebraic homotopy programme

Research directions in persistent homology

Locales as geometric objects