# ReverseMath: Answer Inversion for Scalable and Verifiable Mathematical Problem Generation

arXiv: https://arxiv.org/abs/2605.27709 · HTML: https://mlsanity.com/paper/2605.27709/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 17 of its 32 references that are in the map.
- First posted on arXiv 26 May 2026.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 17 of 17)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Large Language Models Can Be Easily Distracted by Irrelevant Context](https://mlsanity.com/paper/2302.00093/) (2023)
- [NLP Evaluation in trouble: On the Need to Measure LLM Data Contamination for each Benchmark](https://mlsanity.com/paper/2310.18018/) (2023)
- [Data Contamination: From Memorization to Exploitation](https://mlsanity.com/paper/2203.08242/) (2022)
- [A Careful Examination of Large Language Model Performance on Grade School Arithmetic](https://mlsanity.com/paper/2405.00332/) (2024)
- [AIMO-2 Winning Solution: Building State-of-the-Art Mathematical Reasoning Models with OpenMathReasoning dataset](https://mlsanity.com/paper/2504.16891/) (2025)
- [MATH-Perturb: Benchmarking LLMs' Math Reasoning Abilities against Hard Perturbations](https://mlsanity.com/paper/2502.06453/) (2025)
- [A Survey on Large Language Models for Mathematical Reasoning](https://mlsanity.com/paper/2506.08446/) (2025)
- [Evaluating Robustness of Large Language Models Against Multilingual Typographical Errors](https://mlsanity.com/paper/2510.09536/) (2025)
- [Do We Know What LLMs Don't Know? A Study of Consistency in Knowledge Probing](https://mlsanity.com/paper/2505.21701/) (2025)
- [SlimQwen: Exploring the Pruning and Distillation in Large MoE Model Pre-training](https://mlsanity.com/paper/2605.08738/) (2026)
- [SYNTHEVAL: Hybrid Behavioral Testing of NLP Models with Synthetic CheckLists](https://mlsanity.com/paper/2408.17437/) (2024)
- [Reason to Rote: Rethinking Memorization in Reasoning](https://mlsanity.com/paper/2507.04782/) (2025)
- [MGSM-Pro: A Simple Strategy for Robust Multilingual Mathematical Reasoning Evaluation](https://mlsanity.com/paper/2601.21225/) (2026)

## Abstract (arXiv)

Mathematical reasoning benchmarks are vital for evaluating large language models (LLMs), but many are static and repeatedly exposed through public evaluation and training pipelines, making it difficult to separate genuine reasoning from memorization. Meanwhile, manually constructing new math problems with reliable answers remains costly. We introduce ReverseMath, a scalable method for generating new math problems through answer inversion. Given a problem and its answer, ReverseMath masks a numerical value in the original problem, treats the original answer as a known condition, and rewrites the problem so that the masked value becomes the new answer. The generated problem reverses the original input-output relation, making its answer known by construction. We study ReverseMath for both evaluation and training. For evaluation, paired original/reversed problems reveal substantial behavioral shifts: models sometimes fail on reversed problems and even incorrectly output the original answer, suggesting memorization-like behavior. For training, ReverseMath provides automatically labeled reversed problems as data augmentation for reinforcement learning (RL). Experiments show that including ReverseMath-generated data improves mathematical reasoning performance across multiple benchmarks, demonstrating its value as both an analysis tool and a scalable source of verifiable training data.