AI Solves Erdős Problems and Discovers Novel Matrix Multiplication Algorithm — On the Same Day
GPT-5.2 Pro cracked multiple longstanding Erdős problems while a separate AI system independently discovered a new matrix multiplication algorithm, marking what may be the most consequential 24 hours for AI-driven mathematical research to date.
In a single day that is likely to be studied by historians of science, AI systems achieved two independent mathematical breakthroughs that would each, on their own, constitute major milestones. As @emollick documented, GPT-5.2 Pro has now solved multiple Erdős problems — open conjectures posed by the legendary Hungarian mathematician Paul Erdős, many of which have stood unsolved for decades. Ethan Mollick called this a "definite example of models breaching a threshold," and the framing is hard to argue with: these aren't textbook exercises or benchmark games. They are problems that professional mathematicians have struggled with for years.
Simultaneously, as @AISafetyMemes highlighted, a separate AI system developed a novel matrix multiplication algorithm — a domain where even marginal improvements have enormous downstream implications for compute efficiency across all of computing. The poster framed both events together as "another step towards dangerous full recursive self-improvement," a characterization that is alarmist but not entirely without basis. When AI can improve the fundamental mathematical operations that underpin AI training itself, the feedback loop starts to tighten.
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