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Rohan Paul· @rohanpaul_ai · X·· 2026-05-21AI 评分64
AI 导读

OpenAI的通用推理模型近期通过连接代数数论与平面几何,成功解决了保持数十年的平面单位距离猜想(Erdős猜想)。关键突破在于模型并非专用定理证明引擎,其成功依赖于延长和深化测试时计算过程,而非仅增加训练数据。这一进展表明前沿大模型已蕴含潜在的数学研究能力,当前瓶颈部分源于模型被允许“思考”的时间和方式。未来方向不是AI取代人类判断,而是在人类判断开始前拓宽思维的疆域,从而推动科学发现与创新。

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A general-purpose LLM can produce frontier research when given enough test-time compute.

Here, just a general-purpose OpenAI model has connected algebraic number theory to plane geometry and used that bridge to beat a decades-old conjecture.

Shows how frontier models may already contain useful latent mathematical competence, and the bottleneck is partly how long and how well they are allowed to think.

引用Rohan Paul@rohanpaul_ai
AI in math is creating history again, as OpenAI's general-purpose reasoning model has disproved a major Erdős conjecture from 1946. The important part is not that AI solved a hard math problem, but how little special machinery it needed. For decades, the planar unit distance problem looked almost embarrassingly simple: place points on a plane, then ask how many pairs can be exactly one unit apart. For decades, the best examples looked like stretched versions of a square grid, so mathematicians believed grids were almost the best possible design. OpenAI’s internal model broke that picture by finding an infinite family of constructions that gives a polynomial improvement, with the proof checked by external mathematicians. The point to note is that the model was not a bespoke theorem-proving engine trained only for this problem, and the official post says its success improved with more test-time compute, meaning more reasoning at inference rather than only more training. That matters so much, because research progress often comes from holding a fragile chain of ideas together long enough to cross from one field into another. In this case, the bridge ran from a plain geometric question into deep algebraic number theory, including machinery like infinite class field towers and Golod–Shafarevich theory. And now we see a general-purpose reasoning system appears able to search a conceptual space where human taste, field boundaries, and inherited guesses may have quietly narrowed the path. So future is not machines replacing judgment, but machines widening the map before judgment begins.
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来源:Rohan Paul · x.com