Paul Erdős posed over 1,200 problems across combinatorics, number theory, and graph theory, many with cash prizes, all marking the frontier where intuition must yield to rigorous proof. With roughly half resolved, the remainder includes some of the most structurally demanding open problems in discrete mathematics.

Qvanta® selects targeted problems from the authoritative Erdős Problems catalog and attacks them with AI-assisted formal proof infrastructure. Output is not conjecture and not informal argument: it is verified proof, with every claim compiled and machine-discharged where complete, and certified partial progress where the full statement remains open.

Our approach is neuro-symbolic: large language models propose proof paths, tactics, and candidate lemmas; formal proof assistants compile or reject every step. Generative reasoning and rigorous verification stay separated: research-grade output, not sophisticated guessing.

We operate across formalization, tactic search, bound verification, lemma extraction, and automated proof repair. Multiple AI systems collaborate across the pipeline, with a trusted formal kernel as the final arbiter. No proof is accepted that the verifier does not compile.

Combinatorial bounds, number-theoretic identities, and finite set mappings in our Erdős targets are the same structures that govern cryptographic hardness and post-quantum security arguments.

As NIST PQC standards introduce constructions whose security rests on mathematical hardness assumptions, the capacity to formally verify those foundations at depth becomes operationally relevant. The Erdős Problems Research Program is where Qvanta® builds that depth.