The AI Why with Liam Lawson podcast

Formal Verification, AI Hallucinations, and Mathematical Truth | Tudor Achim, Co-Founder, Harmonic

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In this episode, Tudor Achim, Co-Founder and CEO of Harmonic, the AI lab behind Aristotle, a mathematical reasoning system that won gold at the International Math Olympiad, makes the case that AI hallucinations aren't the problem with today's models. The real problem is that nobody can verify whether a hallucination is right or wrong. Tudor explains why his team bakes formal, computer-checkable verification (using a language called Lean) directly into how Aristotle reasons, so instead of trusting an AI's word, you can mathematically prove it's correct. Liam and Tudor go deep on what "truth" actually means in mathematics versus the real world, why Andrew Wiles's famous proof of Fermat's Last Theorem had a two-year hidden flaw, and why Tudor believes math is in the middle of its first fundamental shift in 4,000 years, moving from proofs written in English to proofs written in verifiable code. They also get into a spirited debate about the U.S. education system, what Harmonic actually looks for when hiring (hint: it's not the résumé), and why Tudor thinks AI will never be trusted to grade its own homework. Key Topics Covered What "truth" means in mathematics versus science, and why logical reasoning is really just a simple form of math Why the proof of Fermat's Last Theorem had a hidden flaw for two years, even after being announced Why hallucinations are actually necessary for AI reasoning, and what separates a good hallucination from a bad one How Harmonic uses Lean and formal verification to make Aristotle's math proofs checkable step by step, like reviewing code Why Tudor doesn't think any AI will ever be trusted to fully verify its own output Why Harmonic gives away the Aristotle API for free right now, and where the business model is headed The "phase transition" Tudor believes is happening in math for the first time in 4,000 years: from English proofs to machine-verified code Why open-sourcing formal math matters more to Harmonic than keeping a competitive edge Harmonic's five-year goal: contributing to solving a Millennium Prize Problem by 2028 A debate on whether the U.S. education system actually teaches critical thinking, and what AI should (and shouldn't) change about how kids learn What Harmonic actually looks for when hiring, and why résumés carry almost no signal anymore Tudor's take on inequality, taxation, and what a healthy AI-driven economy could look like Episode Timestamps 00:00 Intro and welcome 00:33 What is truth, and is logic just math? 07:59 Why the company is called harmonic.fun 08:48 The real problem with LLMs and truth 12:57 How formal verification works inside Aristotle 16:43 Who else is building in this space 19:48 Can AI ever be verified with 100% accuracy? 23:10 Why AI can't fully verify its own answers 26:46 Open-source math vs a venture-backed business 29:39 The five-year goal: a Millennium Prize Problem by 2028 31:51 Has Harmonic's vision changed? 34:28 AI, formal verification and the future of education 44:34 Debating the US education system 45:09 How Harmonic hires and what they look for 50:21 Testing for trust and honesty in interviews 54:14 Harmonic's biggest challenge right now 58:19 The future of working with AI 59:55 Family, kids and optimism about the future 1:01:38 Inequality, capitalism and AI's role in the economy 1:04:19 Why Tudor does what he does 1:05:19 Where to find Tudor Connect with Tudor on LinkedIn: https://www.linkedin.com/in/tudorachim/ Partner Links Upgrade your AI toolkit: https://www.theaireport.ai/ai-executive-pass Subscribe to our free newsletter: https://newsletter.theaireport.ai/subscribe Join the community: https://community.theaireport.ai/checkout/the-ai-report-welcome-gift?coupon_code=WRTH Learn more about your ad choices. Visit megaphone.fm/adchoices

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