A statistics professor at the University of Pennsylvania's Wharton School used OpenAI's GPT-5.6 Sol Pro to disprove a long-standing conjecture about a foundational statistical method in just 90 minutes. The problem had resisted human efforts for roughly 30 years.
Edgar Dobriban, an associate professor, employed the AI model to construct a statistical model that proves the Benjamini-Hochberg (BH) procedure can fail under certain conditions. The BH procedure, developed in 1995 by statisticians Yoav Benjamini and Yosef Hochberg, is a cornerstone of modern statistics. It controls the false discovery rate (FDR), which is the share of reported significant results that are false alarms. The original BH paper has received more than 130,000 citations, according to Dobriban.
The 30-year-old conjecture
Benjamini and Hochberg originally showed their procedure works reliably with independent data. But real-world data points are often linked—for example, genetic variants correlated due to inheritance. Experts assumed BH would work reliably with correlated, normally distributed data, specifically for two-sided tests. No one had ever proved it.
Will Fithian, a statistician at Berkeley, called the disproved conjecture "the most interesting open problem in my area of statistics." The finding does not mean BH is generally unusable. The gap above the target level in Dobriban's model is relatively small: an actual FDR of 0.104 versus a target of 0.1. The result mainly matters for theory; practical effects need further study.
How the AI solved it
Dobriban used GPT-5.6 Sol Pro to construct a statistical model where the actual FDR provably exceeds the target level. Simulations confirm the result, and Dobriban published the accompanying code. The solution combined existing approaches rather than inventing new ones. Dobriban said the combination was unusual but the result was "not especially surprising." The challenge was finding the right way to connect known methods.
The AI model took about 90 minutes to find the solution. By contrast, the previous model, GPT-5.5, could not find a solution even after roughly 20 hours of work with several agents. The full chat and prompt are available online.
Dobriban noted the improvement between models. "So the capability improvement is quite real. Exciting times to live in!" he said.
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Broader implications for AI and science
The result adds to a growing list of examples of AI usefulness in human workflows. Fithian said the result is "another marker of advancing AI capabilities whose consequences will reach far beyond math." But he also expressed a sense of loss. "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."
The article raises the broader question of whether models can reason to genuinely new knowledge or only recombine training data. Even if only recombination, they are useful as everyday tools. More ambitious goals, like building self-improving AI that can generalize, may demand beyond recombination. Deep learning pioneer Richard Sutton recently founded a startup to tackle that problem.
What this means for statistics
When testing thousands of hypotheses at once—for example, scanning the human genome for disease-linked genes—more tests increase false positives. The BH procedure limits false positives by controlling FDR. Correlated data can make the BH method miss its target. The disproved conjecture was that BH works reliably with correlated, normally distributed data for two-sided tests.
Dobriban's preprint shows that under certain conditions, the procedure can exceed its target FDR by a small margin. The result is more theoretical than practical for now, but it resolves a question that had puzzled statisticians for decades.
The article was published on Jul 15, 2026.