Subvolts take AI that proves its answers right could unlock reliable reasoning and accelerate research. Feb 26, 2026 - Developers
- Learn about formal verification and Lean for building provably correct AI systems, differentiating from current large language models.
- Business
- Understand how verified AI can increase trust and reliability in high-stakes applications, potentially reducing risks and errors.
This interview explores a significant advancement in AI reliability, focusing on verifiable reasoning and its broad applications.
AI That Can Prove It’s Right: Verification as the Missing Layer in AI — Carina Hong
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Matt Turck interviews Carina Hong, founder of Axiom Math, on AI's potential for verified reasoning. Hong discusses AxiomProver's perfect score on the Putnam exam and how formal verification, using systems like Lean, can create AI that proves its correctness. The conversation explores how this approach could accelerate research, improve software reliability, and advance towards superintelligent reasoning.
Imagine AI that doesn't just guess, but can show its work like a math student proving a theorem. This episode explores how AI systems are being built to demonstrate their answers are correct, which could make them much more trustworthy for important tasks.
This episode offers insight into a novel approach to AI reliability through formal verification, moving beyond probabilistic outputs to provable correctness. It is for researchers, developers, and business leaders concerned with AI safety and trustworthiness. The discussion on verified reasoning connects to frontier labs' ongoing efforts to build more robust and dependable AI systems, particularly in areas requiring high accuracy like coding and complex problem-solving.
- HostMatt Turck
- GuestCarina Hongfounder/CEO, Axiom Math
- Guest: Carina Hong, founder/CEO of Axiom Math
- Show: The MAD Podcast
- Length: 64 minutes
- AxiomProver Score: Perfect 12/12 on the Putnam 2025
- Key Technology: Formal verification via Lean
What if AI didn’t just sound right — but could prove it? In this episode of the MAD Podcast, Matt Turck sits down with Carina Hong, a 24-year-old former math olympiad competitor and Rhodes Scholar, and the founder/CEO of Axiom Math, to unpack how AxiomProver earned a perfect 12/12 on the Putnam 2025 and why formal verification (via Lean) may be the missing layer for reliable reasoning. Carina argues we’re entering a “math renaissance” where verified reasoning systems can tackle problems that currently take researchers months — and potentially push beyond math into verified code, hardware, and high-stakes software. They go inside the “generation + verification” loop, what it means to build AI that can be trusted, and what this approach could unlock on the road to superintelligent reasoning.
(00:00) Intro
(01:25) Why the World Needs an AI Mathematician
(02:57) Scoring 12/12 on the World's Hardest Math Test (Putnam)
(04:05) The First AI to Solve Open Research Conjectures
(06:59) Does AI Solve Math in "Alien" Ways? (The Move 37 Effect)
(08:59) "Lean": The Programming Language of Proofs Explained
(10:51) How Axiom's Approach Differs from DeepMind & OpenAI
(16:06) Formal vs. Informal Reasoning (And Auto-Formalization)
(17:37) The AI "Reward Hacking" Problem
(20:18) Building an AI That is 100% Correct, 100% of the Time
(23:23) Beyond Math: Verified Code & Hardware Verification
(25:12) The Brutal Reality of Competitive Math Olympiads
(29:30) From Neuroscience to Stanford Law to Dropout Founder
(33:57) How Axiom Actually Works Under the Hood (The Architecture)
(37:51) The Secret to Generating Perfect Synthetic Data
(40:14) Tokens, Proof Length, and Inference Cost
(42:58) The "Everest" of Mathematics: Scaling Reasoning Trees
(46:32) Can an AI Win a Fields Medal?
(47:25) "Math Renaissance": What Changes if This Works
(55:47) How Mathematicians React to AI (And Why Proof Certificates Matter)
(57:30) Becoming a CEO: Dropping Ego and Building Culture
(1:00:42) Recruiting World-Class Talent & Building the Axiom "Tribe"
- Formal verification
- Carina Hong
- A method to mathematically prove that a system (like AI or software) works exactly as intended, with no errors.
- Lean
- Carina Hong
- A programming language used to write and verify mathematical proofs, enabling AI to demonstrate its reasoning is correct.
- Reward hacking
- Matt Turck
- When an AI finds unintended ways to achieve its goals or maximize its reward signal, often leading to undesirable outcomes.
Same guests, other shows
51 min
56 minBuilding an AI Mathematician with Carina Hong - #754
WithCarina Hong
48 min
1 h 05Questions people ask
- What is AxiomProver?
- AxiomProver is an AI system developed by Axiom Math that achieved a perfect score on the Putnam 2025 math competition, demonstrating its ability in verified reasoning.
- What is Lean?
- Lean is a programming language used for formal verification and writing mathematical proofs, which is central to building AI systems that can prove their correctness.
Page generated Oct 19, 2026. Summaries are Subvolts' own; the audio, artwork and notes belong to Matt Turck.