Inference by Turing Post What AI Is Missing for Real Reasoning? Axiom Math’s Carina Hong on how to build an AI mathematician
13 snips
Dec 4, 2025 
Carina Hong, co-founder and CEO of Axiom Math, is on a mission to enhance AI's reasoning through machine-checkable mathematics. She discusses why current AI models struggle with complex math and presents three pillars essential for an AI mathematician. Carina emphasizes the need for a hybrid approach, combining formal verification and neural networks. She explores the limits of intuition in math, critiques existing benchmarks, and advises on practical paths for using AI in mathematics, all while navigating the intriguing landscape between AGI and superintelligence.
AI Snips
Chapters
Books
Transcript
Episode notes
Why LLMs Struggle With True Math
- Current LLMs excel at retrieval but fail at de novo mathematical reasoning because they train on next-token prediction.
- Deep multi-step proofs break LLMs since they don't verify intermediate logical steps.
The Three Pillars Of An AI Mathematician
- An AI mathematician needs three pillars: a prover, a knowledge base, and a conjecturer that interact.
- Auto-formalization and auto-informalization glue these pieces to turn human math into machine-checkable proofs.
AlphaGeometry Generated New Geometry
- DeepMind's AlphaGeometry converted Euclidean figures into symbolic vectors and generated creative geometry problems synthetically.
- That machine-generated content guided human intuition and produced novel, interesting problems.
