// reasoning models

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OpenAI's Reasoning Model Disproves 80-Year-Old Erdos Conjecture

OpenAI's unreleased reasoning model identified a counterexample to a discrete geometry conjecture that had resisted human mathematicians for decades. The achievement suggests specialized AI systems can now operate at the frontier of pure mathematics rather than merely assist with routine proofs. The gap between capabilities and deployment—the model remains unreleased—reveals how competition between labs may be decoupling breakthrough announcements from actual product availability. This makes it harder to assess whether these advances are reproducible or genuinely useful to working mathematicians. Mathematical progress has historically been driven by human intuition and collaboration. If AI can generate that intuition at scale, fields with those properties may see disruption sooner than others.

Reasoning Models Expose Aggregation Theory's Final Weakness

Ben Thompson's analysis identifies a critical inflection point: as AI reasoning models like OpenAI's o1 demand exponentially more compute per query, the unit economics that built Google's and Meta's advertising empires collapse. The margin compression isn't hypothetical—it's baked into the architecture. These companies face a choice: subsidize increasingly expensive inference or fragment their user base into tiered access. Raw intelligence becomes too costly to aggregate at scale, which means the business models that survive the next decade will differ materially from today's.