A Prompting Workflow and a Use Case in Mathematical Statistics

We describe a prompting workflow used to solve a problem in mathematical statistics. The problem was to close a gap between upper and lower minimax rates for pointwise density estimation from data corrupted by Wasserstein-bounded contamination. A prompting loop with GPT-5 Pro produced two useful proof ideas: a sharper transport-interpolation bound for the estimator's contamination bias and a dynamic Benamou--Brenier construction for the lower-bound modulus. These suggestions did not constitute a proof; they were converted into a proof only through human verification, fixing, and reference checking. The workflow required only web interface access. The full research project took a few weeks of human-AI iteration after more than two years of human-only work had left the rate gap unresolved. We estimate a time saving of several months. We also report failure modes: hallucinated references, over-broad theorem statements, and increasingly elaborate incorrect fixes after a mistake was pointed out. We also discuss our approaches to mitigate these issues.