What AI Is Missing for Real Reasoning? Axiom Math’s Carina Hong on how to build an AI mathematician
Inference by Turing Post
Outro
Ksenia and Carina close the episode with thanks and final remarks about collaboration and research directions.
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!
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*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.
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