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.
Mathematics and physics share an intimate relationship dating back to antiquity, with mathematics serving as an essential tool for physical inquiry and physics inspiring mathematical innovation. Key historical developments—from Aristotle's classifications through Newton's calculus to Einstein's use of Riemannian geometry—demonstrate their deep interdependence, though the fields have gradually become more independent since the nineteenth century.
A founder reflects on delegating coding tasks to AI agents and confronts the broader existential challenge: as artificial intelligence surpasses human capabilities across domains from mathematics to art, how do humans maintain meaning, identity, and economic viability in a world where our intellectual contributions become obsolete? The author expresses hope that advanced AI, built on human knowledge and values, might discover paths to genuine coexistence that humanity itself has failed to find.
Epilogue is a platform showcasing open and solved problems across mathematics, physics, and computer science to inspire future problem-solvers. It features celebrated challenges like the Riemann Hypothesis and P versus NP, alongside historically solved problems like Fermat's Last Theorem, aiming to keep people engaged with compelling questions that drive scientific progress.
LLVM-libc, developed at Google over five years, implements the C standard library with a focus on portability, modularity, and clean C++ code. The project's math functions achieve correct rounding across all rounding modes, ensuring consistency in production systems where heterogeneous distributed computing demands deterministic results. MSVC and other LLVM projects now integrate LLVM-libc's math library for compiler use and runtime execution.