Mathematicians proved in 2025 that any sufficiently large graph can be sandwiched between two simpler graphs, a conjecture posed in 2004 that connects two different types of random graph structures. This breakthrough demonstrates that random binomial graphs and random regular graphs are related in a deeper way, allowing difficult properties of regular graphs to be proven through their simpler counterparts.
A programmer used Claude to help formalize a proof of Conway's refinement conjecture about surreal numbers, a mathematical system invented by John Conway. The proof was written in Lean and passed mechanical verification, though it remains unverified by professional mathematicians.