a16z Infra Partner Lisha Li sits down with OpenAI mathematicians Mehtaab Sawhney and Mark Sellke to discuss how quickly AI’s mathematical capabilities are advancing, what recent results reveal about model reasoning, and what happens when AI begins making progress on problems mathematicians have struggled with for decades. Mehtaab and Mark unpack several recent results from OpenAI’s models, including advances in sphere packing and the construction of a non-sofic group. They explain why the surprising part isn’t simply that models can search more possibilities or work longer than humans: in many cases, the reasoning traces look remarkably similar to the work of an expert mathematician, including choosing promising approaches, backtracking when they fail, and combining ideas from across the literature. They also explore what this means for mathematics itself: how the role of human taste and judgment may change, whether AI could produce far more mathematics than humans can absorb, and why models that accelerate discovery may also make sophisticated results easier to understand. Timestamps: 00:00 - Intro 00:50 - From Practicing Mathematician to OpenAI: Meet Mark & Mehtaab 02:43 - Why GPT-5 Was the Conversion Moment 04:21 - Beyond Search & Connections: How Recent Progress Goes Deeper 09:51 - Reasoning Traces: Is It Lucky Sampling or Actual Backtracking? 11:44 - Why Math Papers Are a Bad Training Set for Real Mathematics 16:20 - The Astra 10-Problem Set: Favorites & Deep Dives 36:17 - The Harness vs the Model: What Actually Matters? 40:01 - What Even Is "Taste" in a Model? 57:32 - How Should the Math Community Adopt AI? 01:00:01 - Empirical vs Theoretical Math & the Positive Vision Resources: Follow Lisha Li on X: https://x.com/lishali88 Follow Mehtaab Sawhney on X: https://x.com/mehtaab_sawhney Follow Mark Sellke on X: https://x.com/MarkSellke Stay Updated: If you enjoyed this episode, be sure to like, subscribe, and share with your friends! Find a16z on X: https://twitter.com/a16z Find a16z on LinkedIn: https://www.linkedin.com/company/a16z Listen to the a16z Show on Spotify: https://open.spotify.com/show/5bC65RDvs3oxnLyqqvkUYX Listen to the a16z Show on Apple Podcasts: https://podcasts.apple.com/us/podcast/a16z-podcast/id842818711 Follow our host: https://x.com/eriktorenberg Please note that the content here is for informational purposes only; should NOT be taken as legal, business, tax, or investment advice or be used to evaluate any investment or security; and is not directed at any investors or potential investors in any a16z fund. a16z and its affiliates may maintain investments in the companies discussed. For more details please see http://a16z.com/disclosures.