The $64M Bet on an AI That Has to Be Right | Carina Hong, CEO of Axiom

What It Covers

Carina Hong, CEO of Axiom Math, explains how her company builds AI mathematicians that combine generation and verification using formal languages like Lean. Axiom scored nine out of twelve on the 2026 Putnam exam, surpassing last year's top human performer, demonstrating breakthrough capabilities in formal mathematical reasoning and proof verification.

Key Questions Answered

• •Formal Verification Architecture: Axiom combines three core components: a prover system that generates proofs, a conjecture system that proposes theorems, and a knowledge base that stores proven results. Auto-formalization converts natural language mathematics into Lean code, enabling deterministic verification of probabilistic AI outputs. This architecture achieves higher sample efficiency than pure language model approaches by grounding generation in verifiable formal systems.
• •Putnam Performance Breakthrough: Axiom Prover solved nine of twelve problems on the 2026 Putnam exam within time limits, matching the previous year's top human score. The median Putnam score among thousands of top undergraduate math students is zero, making any correct solution significant. This performance demonstrates AI can now compete with elite human mathematicians on novel, unseen competition problems requiring creative problem-solving.
• •Commercial Applications in Verification: Hardware verification teams are one-third to one-fourth the size of design teams, with verification taking up to three years in chip development. Formal verification can prove code equivalence during migrations, verify database consistency in Byzantine fault tolerance scenarios, and ensure safety-critical code correctness. AWS took five years to manually formalize memory isolation in their hypervisor, a task AI could accelerate significantly.
• •Auto-Formalization as Core Technology: Converting natural language mathematical statements into formal Lean code is harder than proving theorems because no solution exists yet to verify correctness. In code verification, test cases with input-output pairs provide grounding signals for formal specifications. Axiom treats auto-formalization as fundamental infrastructure, not just data generation, with statement formalization being more challenging than proof formalization due to lack of verification signals.
• •Future of Mathematical Research: Mathematicians will operate at higher abstraction levels, using AI as diligent graduate students to verify intuitions and handle technical lemmas. The system constructs counterexamples for sanity checking and generates interesting patterns for conjecture formation. Top mathematicians like Terence Tao can focus on theory-building and intuition while AI handles computational verification, similar to how LaTeX replaced typewriters without eliminating mathematical research.