A statistics professor at the University of Pennsylvania has used OpenAI's GPT-5.6 Sol Pro to disprove a 30-year-old conjecture in statistics, solving a problem that had stumped human researchers for decades.
The Benjamini-Hochberg procedure and its limits
When scientists test thousands of hypotheses at once, such as scanning the human genome for genes linked to diseases, they face a common problem: the more tests they run, the more false positives appear.
In 1995, statisticians Yoav Benjamini and Yosef Hochberg developed a method to control these false positives. Their procedure manages the false discovery rate, or FDR, which measures the proportion of reported significant results that are actually false alarms.
The Benjamini-Hochberg method, often called BH, is now widely used in modern statistics and across many scientific fields. Edgar Dobriban, an associate professor at the University of Pennsylvania's Wharton School, noted that the original paper has received more than 130,000 citations.
Benjamini and Hochberg originally showed that their method works with independent data. But real-world data points are often linked. Genetic variants can be correlated, for instance, 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.
AI cracks the problem in 90 minutes
Dobriban has now disproven that assumption using OpenAI's GPT-5.6 Sol Pro. In his preprint, he describes how the AI constructed a statistical model where the actual false discovery rate provably exceeds the target level. Simulations confirm the result. Dobriban also published the accompanying code.
The finding matters more in theory than in practice for now. 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 does not mean the BH procedure is generally unusable.
Stay ahead of the AI curve
The most important updates, news, and content — delivered weekly.
No spam. Unsubscribe anytime.
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 could not 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 online.
Reactions from the statistics community
Berkeley statistician Will Fithian 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."
How the model solved it
As with similar cases in mathematics, 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? 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.
But more ambitious goals, like building self-improving AI that can generalize, 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.