Subvolts take AI is learning to do math, potentially discovering new theorems. Nov 4, 2025 - Developers
- Learn about the technical hurdles and potential of AI in formal mathematics and code generation for proofs.
- Business
- Understand how AI can be applied to formal verification for high-stakes software and hardware, ensuring reliability.
This interview explores a significant advancement in AI's reasoning and discovery capabilities, particularly in a complex field like mathematics.
Building an AI Mathematician with Carina Hong - #754
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From Subvolts
Summary and analysis by Subvolts editorial, AI-assisted.
Carina Hong, founder and CEO of Axiom, discusses building an "AI Mathematician" on The TWIML AI Podcast. She explains how modern LLMs, formal proof languages like Lean, and code generation breakthroughs enable this. The conversation covers technical hurdles such as data gaps and autoformalization, and Axiom's vision for AI discovering new math through self-play.
Imagine teaching a computer to not just solve math problems, but to invent new math. This episode explores how powerful AI, combined with special math languages, is being used to create an AI that can discover new mathematical ideas on its own.
This episode delves into the cutting edge of AI's application in formal mathematics. Listeners will learn about the convergence of LLMs and formal methods, the challenges in translating natural language proofs to machine-verifiable formats, and the potential for AI to discover novel mathematical knowledge. It's for researchers and developers interested in AI's reasoning capabilities and formal verification, connecting to frontier labs' work on advanced reasoning and AI-assisted discovery.
- HostSam Charrington
- GuestCarina Hongfounder and CEO, Axiom
- Guest: Carina Hong, founder and CEO of Axiom
- Episode Title: Building an AI Mathematician with Carina Hong - #754
- Show: The TWIML AI Podcast
- Length: 56 minutes
- Key Areas for AI Math: Advanced LLM reasoning, formal proof languages (e.g., Lean), code generation breakthroughs
- Technical Challenge: Data gap between general code and formal math code, autoformalization
In this episode, Carina Hong, founder and CEO of Axiom, joins us to discuss her work building an "AI Mathematician." Carina explains why this is a pivotal moment for AI in mathematics, citing a convergence of three key areas: the advanced reasoning capabilities of modern LLMs, the rise of formal proof languages like Lean, and breakthroughs in code generation. We explore the core technical challenges, including the massive data gap between general-purpose code and formal math code, and the difficult problem of "autoformalization," or translating natural language proofs into a machine-verifiable format. Carina also shares Axiom's vision for a self-improving system that uses a self-play loop of conjecturing and proving to discover new mathematical knowledge. Finally, we discuss the broader applications of this technology in areas like formal verification for high-stakes software and hardware.
The complete show notes for this episode can be found at https://twimlai.com/go/754.
- LLMs
- Sam Charrington
- Large Language Models, AI systems that understand and generate text, like ChatGPT.
- autoformalization
- Carina Hong
- Translating mathematical ideas written in everyday language into a format a computer can check for correctness.
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1 h 04
51 minQuestions people ask
- What is an AI Mathematician?
- It is an AI system designed to understand and generate mathematical proofs, with the potential to discover new mathematical knowledge.
- What are the main challenges in building an AI Mathematician?
- Key challenges include a data gap between general code and formal math code, and the difficulty of 'autoformalization' – translating natural language proofs into a machine-verifiable format.
Page generated Oct 19, 2026. Summaries are Subvolts' own; the audio, artwork and notes belong to Sam Charrington.