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Formal Verification, AI Hallucinations, and Mathematical Truth | Tudor Achim, Co-Founder, Harmonic
23-07-2026 | 1 u. 9 Min.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/
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Learn more about your ad choices. Visit megaphone.fm/adchoices- Every answer an AI gives you sounds equally confident, whether it's true or completely made up. That's not a bug. It's how the technology was built.
Dan Klein is CTO and co-founder of Scaled Cognition, and a professor of computer science at UC Berkeley. In this conversation with Liam, Dan breaks down what a language model actually is, why it was never designed to know the truth in the first place, and why today's AI systems have no "smells," the subtle warning signs humans usually rely on to tell good information from bad.
They get into why reinforcement learning from human feedback quietly trains models to tell people what they want to hear, how that can tip into outright deception, and why Dan believes reliability, not raw intelligence, is the biggest unsolved problem in AI today.
Key Topics Covered:
What a language model actually does at its core: next token prediction
Why LLMs are plausibility engines, not truth engines
The difference between a hallucination and a lie
Why AI mistakes have no warning signs the way bad translations or sketchy websites do
How RLHF can train models to be sycophantic instead of accurate
The "package delivery" thought experiment: when reward signals diverge from truth
Why bolting reliability onto LLMs after the fact doesn't work
How Scaled Cognition architects models around verified actions instead of raw text generation
Why bigger models aren't automatically better models
The difference between disruptive technology and scaled technology
Why startups, not incumbents, tend to drive technical breakthroughs
What metacognition is and why today's AI systems don't have it
Why Dan believes reliability is the next major frontier in AI
Episode Timestamps:
00:00 Intro
00:15 What a language model actually is
06:31 From well-formed sentences to general knowledge
08:27 Why LLMs are plausibility engines, not truth engines
12:06 How Perplexity approaches verifiable answers
12:40 Dan's background and Scaled Cognition's mission
15:16 The two anti-patterns companies use to control LLMs today
21:16 How Scaled Cognition architects models differently
23:28 Does every client need a custom-trained model?
29:12 Why prompting alone can't guarantee reliability
30:55 Modularity, contracts, and building reliable systems
34:40 Why trust and digital literacy matter beyond the enterprise
39:12 Code smells and why AI mistakes have no warning signs
41:14 Are AI companies incentivized to tell the truth?
42:55 How reinforcement learning actually works
44:35 The package delivery thought experiment
48:44 Why models are trained to be sycophantic
51:01 Where this incentive is mechanically baked into the model
53:43 Does responsibility fall back on humans?
58:10 Just be more reliable than a human, not perfectly true
1:02:59 The last major technique shift in AI
1:10:55 Why frontier labs keep scaling despite the risk of disruption
1:17:15 The future of hyper-specialized models vs. one broad model
1:19:47 Is there anything uniquely human AI can't replicate?
1:25:45 Wearing three hats: professor, researcher, and CTO
1:29:47 Why Dan does what he does
Connect with Dan on LinkedIn:https://www.linkedin.com/in/dan-klein/
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Learn more about your ad choices. Visit megaphone.fm/adchoices - The volume problem in AI is solved. Now it's all about data quality, and who gets to define it.
Enzo Blindow is VP of Data & AI at Prolific, a platform that connects hundreds of thousands of people worldwide to the frontier labs and enterprises training and evaluating AI models. In this conversation with Liam, Enzo breaks down what actually goes into building high-quality training data, why models lean too hard into stereotypes, and the research Prolific published showing how easily AI can be nudged toward commercially motivated, and sometimes harmful, suggestions.
They discuss why synthetic data hits a ceiling that only human data can break through, how a single mistranslated instruction can quietly corrupt an entire dataset, and why "good taste" might be one of the hardest things for AI to ever replicate.
Key Topics Covered:
Why data volume is a solved problem and quality is everything now
How RLHF actually shaped early versions of ChatGPT
Why AI models lean too heavily into stereotypes
The asymmetry and hidden bias baked into internet-sourced training data
Prolific's ICLR research on commercial pressure in AI models
Who's responsible when AI models cause harm: labs vs. data providers
Synthetic data's ceiling, and why humans still have to validate it
What actually defines "taste" and why it's nearly impossible to model
The risk of AI flattening nuance and marginalized perspectives
Why human data is one of the most defensible moats in AI
Enzo's own definition of what "data" really means
Episode Timestamps:
00:00 Intro
00:21 What Prolific actually does
02:48 MCP vs. API vs. CLI access
04:19 How frontier labs started working with Prolific
06:40 Data volume vs. quality, and the role of RLHF
10:58 Who Prolific's biggest customers are
13:12 Why labs choose Prolific over other data vendors
16:13 Fact vs. opinion in AI training
19:02 Stereotypes and bias in AI models
21:15 Prolific's ICLR research on commercial pressure
23:36 Who's responsible: labs, governments, or data companies
27:22 How Prolific's data collection actually works
31:59 Synthetic data vs. human data
36:04 What defines "taste" in AI-generated content
39:33 Good taste vs. bad taste, and the risk of AI regression to the mean
42:36 Why Enzo joined Prolific
45:56 Blind spots most people have about training data
47:22 The "SaaSpocalypse" and data as a business moat
51:38 How Enzo visualizes "data" in his own mind
54:22 Why Enzo does what he does
57:16 Where to find Enzo and Prolific
Connect with Enzo on LinkedIn:
https://www.linkedin.com/in/enzoblindow/
Partner Links
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Learn more about your ad choices. Visit megaphone.fm/adchoices How to Successfully Roll Out AI Across Your Organization | Scott Likens, Global Chief AI Engineer, PwC
02-07-2026 | 50 Min.AI isn't replacing jobs. It's changing the way work gets done.
Scott Likens, Global Chief AI Engineer at PwC, spends his days helping organizations navigate one of the biggest technological shifts in history. In this conversation with Arturo Ferreira, Scott shares what he's seeing inside some of the world's largest companies as they race to adopt AI, transform workflows, and prepare for a future that's arriving faster than most people expect.
They discuss why many AI projects fail, the "frozen middle" preventing organizations from scaling AI, how education needs to evolve, and why the biggest challenge isn't the technology itself; it's helping people adapt to it.
Key Topics Covered:
Why most organizations are approaching AI the wrong way
The "frozen middle" slowing down enterprise AI adoption
How PwC is scaling AI across a global workforce
Why AI is different from every technology wave before it
The future of software engineering in the age of AI
Which industries are moving fastest with AI adoption
Why AI won't just replace jobs, it will reshape them
The role education must play in an AI-powered future
China's AI strategy versus the United States
Why curiosity may become the most important skill of the next decade
Episode Timestamps:
00:00 Intro and the story behind Scott's LinkedIn profile
03:20 What a Chief AI Engineer actually does
06:15 Why AI is different from previous technology revolutions
10:00 The "frozen middle" problem inside organizations
15:25 Why AI adoption is more about people than technology
18:45 PwC's partnership with Anthropic and enterprise AI
22:00 Which industries are moving fastest with AI
27:00 AI, jobs, and workforce transformation
33:00 Why education needs to change
35:30 China, the U.S., and the global AI race
40:00 The questions CEOs are asking about AI today
44:00 Why most AI projects fail
47:30 Advice for leaders trying to scale AI
50:00 Books, learning, and final thoughts
Connect with Scott on LinkedIn:
https://www.linkedin.com/in/scottlikens/
Connect with Arturo on LinkedIn:
https://www.linkedin.com/in/arturoferreira/
Partner Links
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Learn more about your ad choices. Visit megaphone.fm/adchoicesThe Internet Is Becoming More Centralized. Here's Why It Matters | Ajit Varma, Firefox
25-06-2026 | 58 Min.Most people don't think about their browser. Ajit Varma thinks they should.
As Head of Firefox, Ajit sits at the intersection of AI, privacy, open-source software and the future of the internet. In this conversation with Liam Lawson, he explains why browser competition matters more than ever, how AI is changing the way we interact with the web, and why user choice could become one of the most important issues of the next decade.
Key Topics Covered:
- Why Firefox believes the future of AI should be built on open standards
- How AI is changing browsers and the way people access information online
- Why browser competition matters more than most people realize
- The hidden risks of relying on a single AI model or platform
- How Firefox approaches privacy differently from Chrome and Safari
- Why most users choose convenience over customization
- The role open source software plays in preserving an open internet
- Why AI could create more builders, creators and entrepreneurs
- Ajit's vision for a future where AI works for humanity, not just corporations
Episode Timestamps:
00:00 Intro and the mission behind Firefox
02:09 Browser engines and why they matter
04:48 AI, browsers and the future of the web
05:58 Why Firefox takes a different approach to AI
11:15 User choice, AI models and customization
16:40 Why Ajit joined Mozilla
21:13 AI competition, consolidation and the future of tech
25:07 Does open source have a branding problem?
28:07 Privacy, customization and Firefox users
34:26 Product design, simplicity and consumer behavior
39:40 How Ajit uses AI personally
41:53 AI, entrepreneurship and the future of work
53:07 Why do you do what you do?
Connect with Ajit on LinkedIn: https://www.linkedin.com/in/ajitvarma/
Partner Links:
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