# What makes math problems hard for reinforcement learning: a case study

Source: [What makes math problems hard for reinforcement learning: a case study](<https://www.sota2.com/research/paper/68fa5cff1e209131ce9d60ba>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T17:59:20.361Z

Authors: Ali Shehper, Anibal M. Medina-Mardones, Lucas Fagan, Bart{\\l}omiej Lewandowski, Angus Gruen, Yang Qiu, Piotr Kucharski, Zhenghan Wang, Sergei Gukov

Published: 2024-08-27T18:00:06.000Z

## Abstract

Using a long-standing conjecture from combinatorial group theory, we explore, from multiple perspectives, the challenges of finding rare instances carrying disproportionately high rewards. Based on lessons learned in the context defined by the Andrews-Curtis conjecture, we propose algorithmic enhancements and a topological hardness measure with implications for a broad class of search problems. As part of our study, we also address several open mathematical questions. Notably, we demonstrate the length reducibility of all but two presentations in the Akbulut-Kirby series (1981), and resolve various potential counterexamples in the Miller-Schupp series (1991), including three infinite subfamilies.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Presentation Solving on Miller–Schupp benchmark 1190-presentation](<https://www.sota2.com/research/sota/presentation-solving-on-miller-schupp-benchmark-1190-presentation.md>): Presentation Solving; Miller–Schupp benchmark 1190-presentation; Presentations Solved: 533.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2408.15332>)

[PDF](<https://arxiv.org/pdf/2408.15332.pdf>)