OpenAI's GPT-5.6 Sol Disproves 20-Year-Old Statistics Conjecture in 90 Minutes

OpenAI's GPT-5.6 Sol Pro disproved a 20-year-old statistics conjecture about the Benjamini-Hochberg false discovery rate procedure in 90 minutes, producing a proof, counterexample, and numerical certificate. University of Pennsylvania statistician Edgar Dobriban used the model to show the procedure fails for correlated two-sided Gaussian tests, a result posted to arXiv on July 13, 2026. The achievement highlights a stark capability gap from the predecessor GPT-5.5, which failed after 20 hours of work.

OpenAI's GPT-5.6 Sol Disproves 20-Year-Old Statistics Conjecture in 90 Minutes - GPT-5.6 Sol Pro disproved a conjecture about the Benjamini-Hochberg false discovery rate procedure in approximately 90 minutes, producing a proof, counterexample, and numerical certificate 1 https://the-decoder.com/gpt-5-6-sol-reportedly-disproves-a-30-year-old-statistics-conjecture-in-90-minutes-after-humans-couldnt-crack-it/ - The predecessor model GPT-5.5 failed to solve the same problem after more than 20 hours of work with multiple parallel agents 2 https://x.com/EdgarDobriban/status/2077082912021786660 - The counterexample shows the BH procedure's FDR exceeds 0.0104 at a nominal level of 0.01 for correlated two-sided Gaussian tests — a gap small but mathematically rigorous 3 https://arxiv.org/abs/2607.12208 - UC Berkeley statistician Will Fithian called the conjecture 'the most interesting open problem in my area of statistics' 4 https://x.com/wfithian/status/2077218361398964684 - The result was posted as an arXiv preprint on July 13, 2026, with Dobriban as sole author and explicit acknowledgment that the proof was obtained by GPT-5.6 Pro 3 https://arxiv.org/abs/2607.12208 Edgar Dobriban, an associate professor of statistics at the University of Pennsylvania's Wharton School, used OpenAI's GPT-5.6 Sol Pro to disprove a conjecture that had stood unchallenged for roughly two decades in the field of multiple hypothesis testing. The model produced a complete counterexample, proof, and machine-checkable numerical certificate in approximately 90 minutes 1 . The conjecture held that the Benjamini-Hochberg BH procedure — a foundational method for controlling false discovery rates introduced in a 1995 paper that has been cited more than 130,000 times — would reliably control FDR for correlated two-sided Gaussian tests regardless of correlation structure 3 . Dobriban's result, posted to arXiv on July 13, demonstrates that this is not the case . 3 https://arxiv.org/abs/2607.12208 The finding is notable not only for its mathematical significance but for the stark capability gap it illustrates between successive AI models. Dobriban reported that GPT-5.5 failed to solve the same problem even after iterating with multiple parallel agents for more than 20 hours. GPT-5.6 Sol Pro solved it in a single attempt 2 . The Conjecture and the Counterexample The Benjamini-Hochberg procedure, published in 1995, is among the most widely used statistical methods in science. It provides a way to control the false discovery rate — the expected proportion of false positives — when conducting many simultaneous statistical tests, a common scenario in genomics, neuroscience, and clinical trials 1 . While the original BH paper proved the method works when tests are independent, researchers widely believed it also held under correlation for continuous, normally distributed test statistics with two-sided tests. No one had proven or disproven this for roughly 20 years 3 . Dobriban's counterexample constructs a Gaussian factor model with three coordinate blocks of hypotheses. At a significance level of α = 0.01, the construction provably yields an FDR exceeding 0.0104 for sufficiently large numbers of hypotheses — a small but rigorously certified violation. Monte Carlo simulations at N=200 confirmed an FDR of approximately 0.01036 3 . The gap is narrow — an actual FDR of 0.0104 versus a target of 0.01 — but the mathematical certificate, verified using interval arithmetic via the Arb library, proves the violation is real and not a numerical artifact 3 . How GPT-5.6 Sol Found It Dobriban provided GPT-5.6 Sol Pro with the mathematical definition of the Benjamini-Hochberg procedure and asked it directly to prove or disprove the conjecture. After approximately 90 minutes of reasoning, the model returned a complete solution: a proof framework, an explicit counterexample, and code for the numerical certificate 1 . The approach combines known mathematical methods in a novel configuration — empirical CDF analysis with 'outward-rounded ball arithmetic' to certify strict inequalities. The arXiv paper explicitly states: 'The proof was obtained by GPT-5.6 Pro and carefully checked by the author' 3 . Dobriban noted the dramatic performance gap with the previous model generation. GPT-5.5, even with extended computation time and multiple parallel agents, could not find a valid solution 2 . Reactions from the Statistics Community The result drew immediate attention from leading statisticians. Will Fithian, a professor at UC Berkeley who works on multiple testing theory, described the conjecture as 'by far, the most interesting open problem in my area of statistics' 4 . Fithian's reaction also captured a growing ambivalence in academia about AI-generated mathematical results. 'Any statistician would have been excited to construct this counterexample, and I'd have been thrilled for them. GPT-5.6 solved it, but I wish a human had,' he wrote. He added: 'I can't help but mourn the bygone days when a key result always meant a colleague to celebrate' 4 . The result comes days after OpenAI claimed GPT-5.6 Sol Ultra produced a proof of the 50-year-old Cycle Double Cover Conjecture in under an hour using 64 parallel subagents — a separate and even more ambitious claim that remains under peer review 5 . Why It Matters The Benjamini-Hochberg procedure is embedded in the analysis pipelines of thousands of research labs worldwide. While the counterexample involves a specific correlation structure and a narrow FDR violation, it formally invalidates a safety assumption that researchers have relied on when applying the method to correlated data 1 . The practical implications remain a subject of debate. The FDR violation is marginal — roughly 4% above the nominal level — and may not change day-to-day research practice. But the theoretical guarantee is broken, which matters for fields where FDR control is a regulatory or methodological requirement 3 . The episode also extends a pattern of frontier AI models producing verifiable mathematical results that eluded human researchers. Whether such outputs constitute 'genuinely new knowledge' or sophisticated recombination of existing techniques remains an open question — one Dobriban's own paper does not attempt to answer 1 . What's Next Dobriban has released the full ChatGPT conversation log, the preprint, and associated code on GitHub, inviting the community to verify and build on the result 1 . The preprint has not yet undergone formal peer review, though the machine-checkable numerical certificate provides an unusual degree of independent verifiability. The broader question of AI-assisted proof production is moving rapidly. With both the BH counterexample and the Cycle Double Cover claim emerging in the same week of July 2026, the mathematical community faces an accelerating need to develop norms around attribution, verification, and credit when frontier models contribute to or produce results autonomously 5 . Companies mentioned Further sources 1 The Decoder, 'GPT-5.6 Sol reportedly disproves a 30-year-old statistics conject… ↗ https://the-decoder.com/gpt-5-6-sol-reportedly-disproves-a-30-year-old-statistics-conjecture-in-90-minutes-after-humans-couldnt-crack-it/ 2 Edgar Dobriban on X, thread on AI resolving Benjamini-Hochberg conjecture, July… ↗ https://x.com/EdgarDobriban/status/2077082912021786660 3 Edgar Dobriban, 'The Benjamini–Hochberg Procedure Can Fail to Control the FDR f… ↗ https://arxiv.org/abs/2607.12208 4 Will Fithian on X, reaction to Benjamini-Hochberg counterexample, July 2026 ↗ https://x.com/wfithian/status/2077218361398964684 5 The Decoder, 'OpenAI's GPT-5.6 Sol Ultra reportedly solves a 50-year-old math p… ↗ https://the-decoder.com/openais-gpt-5-6-sol-ultra-reportedly-solves-a-50-year-old-math-problem-in-under-an-hour/ The stories that matter, in one email. Free — unsubscribe anytime.