宾大教授用 GPT-5.6 Sol Pro 在 90 分钟内推翻统计学 30 年未解猜想

宾夕法尼亚大学的一位统计学教授使用 OpenAI 的 GPT-5.6 解决了他研究领域中的一个核心未解问题。

当研究人员同时检验成千上万个假设时，比如扫描人类基因组寻找与疾病相关的基因，他们会遇到一个问题：检验的次数越多，漏掉的假阳性就越多。

1995 年，统计学家 Yoav Benjamini 和 Yosef Hochberg 发展了一种方法来限制这些假阳性。它控制假发现率（False Discovery Rate, FDR），即报告为显著结果中实际上是错误警报的比例。

Benjamini-Hochberg 方法（https://en.wikipedia.org/wiki/False_discovery_rate，简称 BH）现在被广泛应用于现代统计学及许多科学领域。根据宾夕法尼亚大学沃顿商学院副教授 Edgar Dobriban（https://x.com/EdgarDobriban）的说法，原始论文已被引用超过 13 万次。

Benjamini 和 Hochberg 最初表明他们的方法在独立数据上有效。然而，现实世界的数据点往往是相关的。例如，当基因组中某些位置经常共同遗传时，基因变异可能是相关的。

多年来，专家们假设 BH 方法在相关的、正态分布的数据上也能可靠工作，特别是在检验双向偏差时。但之前没有人证明过这一点。

an 现在使用 OpenAI 的 GPT-5.6 Sol Pro（https://the-decoder.com/openai-staffer-maps-out-which-of-gpt-5-6-sols-five-reasoning-levels-fits-which-task-complexity/）推翻了这一假设。在他的预印本中（https://faculty.wharton.upenn.edu/wp-content/uploads/2017/06/bh.pdf），他利用 AI 构建了一个统计模型，其中实际假发现率可证明超过了目标水平。模拟也证实了这一结果。Dobriban 还发布了相关的代码（https://github.com/dobriban/BH）。

Dobriban 写道，超过目标水平的差距“相对较小（0.104 对比 0.1）”，因此目前这一结果主要具有理论意义。实际影响仍需进一步研究，这一发现并不意味着 BH 方法通常不可用。

这个结果对统计学家仍然具有重要意义，因为在人工未能解决问题后，人工智能快速地解决了它。多布里班（Dobriban）表示，GPT-5.6 Sol Pro 大约用了 90 分钟，而 GPT-5.5 即使在几个代理共同工作约 20 小时后也无法找到解答。“所以能力的提升是真实存在的。生活在这样激动人心的时代！”他写道。完整的聊天记录和提示可在此查看：https://chatgpt.com/share/6a541c6f-a2d0-83ea-bb2f-782271a103ca。

伯克利统计学家威尔·菲希安（Will Fithian）：https://x.com/wfithian/status/2077218361398964684 称这个被推翻的猜想是“我所在统计学领域中最有趣的未解问题”，并且这个结果是“AI 能力进步的又一个标志，其影响将远远超出数学领域。”

菲希安还暗示了这些结果对专家自身工作的冲击。“我忍不住怀念那些过去的日子，当一个关键结果总意味着可以庆祝的同事、值得欣赏的人类洞察力以及激励人心的人类成就。”

与数学中的类似案例一样：https://the-decoder.com/openais-gpt-5-6-sol-ultra-reportedly-solves-a-50-year-old-math-problem-in-under-an-hour/，这个解法似乎是结合了已有的方法，而不是完全产生全新的东西。多布里班说，这种组合不寻常，但结果最终“并不特别令人惊讶”。挑战在于找到正确的方法来连接已知的方法，而较新的模型成功做到了这一点。

这仍然留下一个更广泛的问题未解。基于人类数据训练的模型能否推理出真正的新知识，或者它们“只能”重新组合在训练中学到的内容：https://the-decoder.com/so-called-reasoning-models-are-more-efficient-but-not-more-capable-than-regular-llms-study-finds/? 即便重新组合是这些系统唯一能做的事情，它们作为内置于人类工作流程的日常工具已经证明很有用。多布里班的结果增加了一个不断扩大的例子列表：https://the-decoder.com/terence-tao-argues-ai-could-bring-division-of-labor-to-math-for-the-first-time-in-history/。

但更宏大的目标，比如构建能够自我改进且具备泛化能力的人工智能：https://the-decoder.com/deepmind-ceo-hassabis-says-nobody-in-the-world-knows-what-happens-next-so-cautious-optimism-means-building-guardrails-now/，可能需要超越简单重组的方法。深度学习先驱理查德·萨顿（Richard Sutton）也是持这种观点的人之一，他最近创办了一家初创公司，正是为了应对这一问题：https://the-decoder.com/turing-award-winner-rich-sutton-founds-oak-lab-to-build-ai-agents-that-learn-on-their-own/。

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A University of Pennsylvania statistics professor used OpenAI's GPT-5.6 to solve one of the central open questions in his field.

When researchers test thousands of hypotheses at once, like scanning the human genome for disease-linked genes, they run into a problem: The more tests you run, the more false positives slip through.

In 1995, statisticians Yoav Benjamini and Yosef Hochberg developed a method to limit these false positives. It controls the false discovery rate, or FDR, which is the share of reported significant results that are actually false alarms.

The Benjamini-Hochberg procedure：https://en.wikipedia.org/wiki/False_discovery_rate, or BH, is now widely used in modern statistics and across many scientific fields. According to Edgar Dobriban：https://x.com/EdgarDobriban, an associate professor at the University of Pennsylvania's Wharton School, the original paper has received more than 130,000 citations.

Benjamini and Hochberg originally showed that their method works with independent data. Real-world data points, however, are often linked. Genetic variants can be correlated, for example, when certain locations in the genome are frequently inherited together.

For years, experts assumed the BH procedure would also work reliably with correlated, normally distributed data, specifically when testing for deviations in both directions. But nobody had ever proved it.

an has now disproven that assumption using OpenAI's GPT-5.6 Sol Pro：https://the-decoder.com/openai-staffer-maps-out-which-of-gpt-5-6-sols-five-reasoning-levels-fits-which-task-complexity/. In his preprint：https://faculty.wharton.upenn.edu/wp-content/uploads/2017/06/bh.pdf, he uses the AI to construct a statistical model where the actual false discovery rate provably exceeds the target level. Simulations confirm the result. Dobriban also published the accompanying code：https://github.com/dobriban/BH.

Dobriban writes that the gap above the target level is "relatively small (0.104 vs 0.1)," so the result mainly matters for theory at this point. Practical effects still need further study, and the finding doesn't mean the BH procedure is generally unusable.

The result is still significant for statisticians because AI solved the problem quickly after humans had failed. Dobriban says GPT-5.6 Sol Pro took about 90 minutes. GPT-5.5 couldn't find a solution even after roughly 20 hours of work with several agents. "So the capability improvement is quite real. Exciting times to live in!" he writes. The full chat and prompt are available here：https://chatgpt.com/share/6a541c6f-a2d0-83ea-bb2f-782271a103ca.

Berkeley statistician Will Fithian：https://x.com/wfithian/status/2077218361398964684 called the disproved conjecture "the most interesting open problem in my area of statistics" and the result "another marker of advancing AI capabilities whose consequences will reach far beyond math."

Fithian also hinted at how much these results are shaking experts' sense of their own work. "I can't help but mourn the bygone days when a key result always meant a colleague to celebrate; a human insight to admire; a human achievement to be inspired by."

As with similar cases in mathematics：https://the-decoder.com/openais-gpt-5-6-sol-ultra-reportedly-solves-a-50-year-old-math-problem-in-under-an-hour/, the solution appears to combine existing approaches rather than produce something entirely new. Dobriban said the combination was unusual, but the result was ultimately "not especially surprising." The challenge was finding the right way to connect known methods, and the newer model managed to do that.

This leaves a broader question unanswered. Can models trained on human data reason their way to genuinely new knowledge, or can they "only" recombine what they learned during training：https://the-decoder.com/so-called-reasoning-models-are-more-efficient-but-not-more-capable-than-regular-llms-study-finds/? Even if recombination is all these systems can do, they already prove useful as everyday tools built into human workflows. Dobriban's result adds to a growing list of examples：https://the-decoder.com/terence-tao-argues-ai-could-bring-division-of-labor-to-math-for-the-first-time-in-history/.

But more ambitious goals, like building self-improving AI that can generalize：https://the-decoder.com/deepmind-ceo-hassabis-says-nobody-in-the-world-knows-what-happens-next-so-cautious-optimism-means-building-guardrails-now/, may demand something beyond recombination. Deep learning pioneer Richard Sutton is among those who think so, having recently founded a startup to tackle exactly that problem：https://the-decoder.com/turing-award-winner-rich-sutton-founds-oak-lab-to-build-ai-agents-that-learn-on-their-own/.

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