# Solving a Research Problem in Mathematical Statistics with AI Assistance

arXiv: https://arxiv.org/abs/2511.18828 · HTML: https://mlsanity.com/paper/2511.18828/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 42 references that are in the map.
- First posted on arXiv 24 Nov 2025.

## Builds on (most cited first, 11 of 11)

- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [Statistics of Robust Optimization: A Generalized Empirical Likelihood Approach](https://mlsanity.com/paper/1610.03425/) (2016)
- [Distributionally Robust Learning](https://mlsanity.com/paper/2108.08993/) (2021)
- [Generalized Resilience and Robust Statistics](https://mlsanity.com/paper/1909.08755/) (2019)
- [Minimax Confidence Intervals for the Sliced Wasserstein Distance](https://mlsanity.com/paper/1909.07862/) (2019)
- [Point Convergence of Nesterov's Accelerated Gradient Method: An AI-Assisted Proof](https://mlsanity.com/paper/2510.23513/) (2025)
- [Robust W-GAN-Based Estimation Under Wasserstein Contamination](https://mlsanity.com/paper/2101.07969/) (2021)
- [G"odel Test: Can Large Language Models Solve Easy Conjectures?](https://mlsanity.com/paper/2509.18383/) (2025)
- [Accelerating mathematical research with language models: A case study of an interaction with GPT-5-Pro on a convex analysis problem](https://mlsanity.com/paper/2510.26647/) (2025)
- [Counting Cycles with AI: Counting Cycles with AI: Computationally Efficient Equivalent Forms with Applications](https://mlsanity.com/paper/2505.17964/) (2025)

## Built on by (most cited first, 6 of 6)

- [Beyond Benchmarks: MathArena as an Evaluation Platform for Mathematics with LLMs](https://mlsanity.com/paper/2605.00674/) (2026)
- [The Agentic Researcher: A Practical Guide to AI-Assisted Research in Mathematics and Machine Learning](https://mlsanity.com/paper/2603.15914/) (2026)
- [QED-Nano: Teaching a Tiny Model to Prove Hard Theorems](https://mlsanity.com/paper/2604.04898/) (2026)
- [Judging What We Cannot Solve: A Consequence-Based Approach for Oracle-Free Evaluation of Research-Level Math](https://mlsanity.com/paper/2602.06291/) (2026)
- [k-server-bench: Automating Potential Discovery for the k-Server Conjecture](https://mlsanity.com/paper/2604.07240/) (2026)
- [The Benjamini--Hochberg Procedure Can Fail to Control the FDR for Correlated Two-Sided Gaussian Tests](https://mlsanity.com/paper/2607.12208/) (2026)

## Abstract (arXiv)

Over the last few months, AI models including large language models have improved greatly. There are now several documented examples where they have helped professional mathematical scientists prove new results, sometimes even helping resolve known open problems. In this short note, we add another example to the list, by documenting how we were able to solve a previously unsolved research problem in robust mathematical statistics with crucial help from GPT-5. Our problem concerns robust density estimation, where the observations are perturbed by Wasserstein-bounded contaminations. In a previous preprint (Chao and Dobriban, 2023, arxiv:2308.01853v2), we have obtained upper and lower bounds on the minimax optimal estimation error; which were, however, not sharp. Starting in October 2025, making significant use of GPT-5 Pro, we were able to derive the minimax optimal error rate (reported in version 3 of the above arxiv preprint). GPT-5 provided crucial help along the way, including by suggesting calculations that we did not think of, and techniques that were not familiar to us, such as the dynamic Benamou-Brenier formulation, for key steps in the analysis. Working with GPT-5 took a few weeks of effort, and we estimate that it could have taken several months to get the same results otherwise. At the same time, there are still areas where working with GPT-5 was challenging: it sometimes provided incorrect references, and glossed over details that sometimes took days of work to fill in. We outline our workflow and steps taken to mitigate issues. Overall, our work can serve as additional documentation for a new age of human-AI collaborative work in mathematical science.