GPT-5.6 Pro Solves a 20-Year-Old Statistics Problem

OpenAI’s new GPT-5.6 Pro (Sol) has helped solve a 20-year-old open problem in statistics by producing a proof that overturns a long-held belief about one of the field’s most widely used statistical methods.

The result appears in a paper by University of Pennsylvania statistician Edgar Dobriban, who said GPT-5.6 Pro generated the proof after being asked to prove or disprove an open question involving the Benjamini-Hochberg procedure, a statistical technique used to reduce false positives when researchers run thousands or even millions of hypothesis tests. 

The method is widely used in genomics, biology, medicine, economics and other data-intensive fields.

For nearly two decades, many statisticians believed the method would continue to work even when the underlying tests were correlated.

Dobriban’s paper shows that this is not always true. It presents a mathematical counterexample demonstrating that, under specific conditions, the procedure can produce slightly more false discoveries than its theoretical limit permits.

According to the paper, GPT-5.6 Pro was given only the mathematical definition of the procedure and asked to prove or disprove the claim. 

After about 90 minutes of reasoning, the model produced a proof, a counterexample and code to verify the result. Dobriban said he independently checked the entire proof and the accompanying numerical calculations before publishing the work.

“The proof was obtained by GPT-5.6 Pro,” the paper states. It adds that the author “carefully checked the entire argument and the associated numerical certificate” before preparing the final manuscript.

The paper also includes computer simulations that support the theoretical result. While the failure is small, the finding overturns a widely accepted assumption in statistics and raises new questions about the limits of the Benjamini-Hochberg procedure under complex correlations.

The US government only recently lifted restrictions on the public release of OpenAI’s GPT-5.6, clearing the way for the company to make its latest AI model broadly available after weeks of limited access under a government review process.

The GPT-5.6 family consists of three models: the flagship GPT-5.6 Sol model, GPT-5.6 Terra as the mid-tier offering, and GPT-5.6 Luna as the lower-cost option.

The US government initially ordered OpenAI to restrict GPT-5.6 to a small group of government-approved partners while federal agencies evaluated the model’s capabilities and potential cybersecurity risks.