Axiom is a mathematics and technology organization developing formal foundations and tools for machine-assisted reasoning and proof verification. Its work aims to give both computers and mathematicians reliable ways to reason about logic and establish mathematical results. A central offering is AXLE, an interactive proof environment designed to support this work. Axiom also conducts research and shares its findings through publications, engineering updates, and a blog, making its technical progress and ideas accessible to a wider audience.

The organization’s research spans topics in number theory, algebra, geometry, and related areas. Its published work includes studies of Rogers–Ramanujan identities, random hypersurfaces, and partition functions. Axiom also highlights the Bounded Gaps Project and reports on formalizing mathematical results in Lean: its AxiomProver has formalized the BGP246 bounded prime-gap theorem. Through its research, software, and technical communication, Axiom contributes to the development of tools and methods that connect mathematical practice with formal verification. Its work is aimed at advancing how proofs are expressed, checked, and explored.