AI is accelerating discovery but creating a verification bottleneck, making formal methods and mathematical rigor essential infrastructure for trusted AI-powered software at national scale.

Mathematical rigor should be treated as a national mission to build trust in AI-enabled software and prevent systemic failures as AI runs increasingly critical services.

Relying on reactive patching or bug bounties is insufficient for critical infrastructure; systems should be designed from the start with auditing and mathematical guarantees.

There should be a public infrastructure of verified software, including open libraries of verified components, standardized benchmarks, robust update-checking tools, and cross-disciplinary training across math, CS, engineering, and national security.

The shift is from discovery bottlenecks to verification bottlenecks, illustrated by AI helping refute a central geometry conjecture and a mathematician moving into AI safety work.

Formal verification and formal methods are essential to automatically validate AI outputs and reduce errors in critical domains like healthcare, finance, and infrastructure, while acknowledging they can't solve every problem.

The Leiden Declaration and the International Mathematical Union endorsement underscore integrating rigorous verification into AI development, with a push for national-scale investment in mathematics research and education.