Is math the ultimate test for AI reasoning? Or is next-token prediction fundamentally incapable of discovering new truths and discovering conjectures?

Carina Hong, co-founder and CEO of Axiom Math, argues that to build true reasoning capabilities, we need to move beyond "chatty" models to systems that can verify their own work using formal logic.

In this episode of Inference, we get into:

Why current LLMs are like secretaries (good at retrieval) but bad at de novo mathematics

The three pillars of an AI Mathematician

How AlphaGeometry proved that symbolic logic and neural networks must merge

The difference between AGI and Superintelligence

Why "Theory Building" is harder to benchmark than the International Math Olympiad (IMO)

The scarcity of formal math data (Lean) compared to Python code

We also discuss the bottlenecks: the "chicken and egg" problem of auto-formalization, why Axiom bets on specific superintelligence over general models, and how AI will serve as the algorithmic pillar for the future of hard science.

This is a conversation about the structure of truth, the limits of intuition, and what happens when machines start grading their own homework. Watch it!

Did you like the episode? You know the drill:

📌 Subscribe for more conversations with the builders shaping real-world AI.

💬 Leave a comment if this resonated.

👍 Like it if you liked it.

🫶 Thank you for watching and sharing!

*Guest:*

Carina Hong, co-founder and CEO of Axiom Math

https://www.axiom.xyz/

https://x.com/CarinaLHong

https://www.linkedin.com/in/carina-hong/

📰 The transcript and edited version at https://www.turingpost.com/carina/

Chapters:

0:53 Why LLMs Struggle with Basic Math

2:42 Building an AI Mathematician: The 3 Pillars (Prover, Knowledge Base, Conjecturer)

5:50 The Role of Human-AI Collaboration

6:34 Can AI Have Intuition? (Conjectures & AlphaGeometry)

10:16 A Hybrid Approach: LLMs + Formal Verification

11:24 Specialist Science Models vs. Generalist Giants

13:33 The Problem with Current AI Benchmarks

16:34 Practical Applications: Enterprise & Formal Verification

21:24 The Main Bottleneck: Data Scarcity

23:49 AGI vs. Superintelligence: The "Plate" Analogy

26:31 Book Recommendations (Math, Law, and Literature)

30:56 How to Use AI for Math Discovery Today

Turing Post is a newsletter about AI's past, present, and future. Ksenia Se explores how intelligent systems are built – and how they're changing how we think, work, and live.

Ksenia and Turing Post:

https://x.com/TheTuringPost

https://www.linkedin.com/in/ksenia-se

https://huggingface.co/Kseniase

#AI #FutureOfAI #MathAI #FormalVerification #Lean #AxiomMath #Superintelligence #Reasoning

What AI Is Missing for Real Reasoning? Axiom Math’s Carina Hong on how to build an AI mathematician

Inference by Turing Post