The false discovery rate (FDR) is a statistical framework designed to manage the proportion of incorrect "discoveries" when conducting multiple hypothesis tests simultaneously. Historically, researchers relied on the Benjamini-Hochberg (BH) procedure, which was widely believed to guarantee that the rate of false positives remained below a target threshold across all scenarios. However, a recent mathematical breakthrough by Edgar Dobriban utilizes an AI-assisted proof to demonstrate that this standard method can fail under specific conditions involving correlated two-sided Gaussian tests. By constructing a complex factor model, the research proves that dependencies between variables can cause the actual error rate to exceed the intended limit. This discovery refutes a long-standing statistical conjecture and suggests that traditional FDR controls may require adjustment for high-throughput data analysis. 

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