OpenAI的GPT-5.2Pro模型在研究员推动下，成功协助解决了数论领域的“埃尔德什难题”第281号，被数学家陶哲轩评价为AI解决开放性数学问题的重要案例。
人工智能在数学领域取得重大突破，GPT5.2模型仅用15分钟便证明了保罗·埃尔德什遗留的未解难题，并通过形式化工具验证。埃尔德什的千余猜想曾被视为人类智慧边界，但近期已有15个问题被解决，其中11个由AI完成。
瑞士数学家施密特宣布，GPT-5在无人类干预下首次独立解决了一个长期未解的数学难题。其解决方案展现出惊人的创造力，跨界借鉴了代数几何其他分支的技术，而非遵循常规逻辑。这一突破印证了陶哲轩对AI潜力的预判。
谷歌为Gemini应用推出Gemini3Deep Think模式，面向Ultra订阅用户。该模式大幅增强推理能力，专攻复杂数学、科学及逻辑难题，挑战当前顶尖模型。在多项基准测试中表现卓越，如在“人类最后的考试”中无工具得分41.0%，在ARC-AGI-2测试中使用代码执行时成绩领先。
Openai
$2.8
输入tokens/百万
$11.2
输出tokens/百万
1k
上下文长度
Xai
$1.4
$3.5
2k
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$30.8
200
-
Anthropic
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Google
$2.1
$17.5
$21
$105
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Alibaba
$4
$16
$1
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256
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Baidu
128
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Moonshot
Bytedance
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32
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