Inside Openai’s Breakthroughs In Mathematical Reasoning

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

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