Abstract: We survey a collection of proofs towards equality, inequality, or independence of the relation of P to NP. Since the problem has attracted much attention from experts, amateurs, and ...

Abstract: Recently, a novel equality equivalency originating from Zhang neurodynamics (ZN) has been proposed and thoroughly investigated from order 0 to high order. Inspired by that concept, we ...

Uncover the root causes of inequality in the world. Gain the skills to combat social injustice through research, policymaking or international development. In an age of rapid economic and social ...

Large language models (LLMs) can prove mathematical theorems formally by generating proof steps (\textit{a.k.a.} tactics) within a proof system. However, the space of possible tactics is vast and ...

Historically, the minimization of the first eigenvalue of the Dirichlet Laplacian is probably the first such problem which appeared in the scientific literature. In Rayleigh’s famous book “Theory of ...

A Supreme Court case that could potentially undo and restrict citizenship rights shows that the border is everywhere.

London's magnificent hidden gems, from a globe-maker in Stoke Newington to our Roman amphitheatre - London is a city of ...

On a hill in north London, about 100 metres above sea level, is the capital’s only commercial scale vineyard, Forty Hall. It ...