# Towards Generating Controllable and Solvable Geometry Problem by Leveraging Symbolic Deduction Engine

arXiv: https://arxiv.org/abs/2506.02565 · HTML: https://mlsanity.com/paper/2506.02565/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 38 references that are in the map.
- First posted on arXiv 3 Jun 2025.

## Builds on (most cited first, 18 of 18)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Llemma: An Open Language Model For Mathematics](https://mlsanity.com/paper/2310.10631/) (2023)
- [Draft, Sketch, and Prove: Guiding Formal Theorem Provers with Informal Proofs](https://mlsanity.com/paper/2210.12283/) (2022)
- [HyperTree Proof Search for Neural Theorem Proving](https://mlsanity.com/paper/2205.11491/) (2022)
- [Lean Workbook: A large-scale Lean problem set formalized from natural language math problems](https://mlsanity.com/paper/2406.03847/) (2024)
- [LEGO-Prover: Neural Theorem Proving with Growing Libraries](https://mlsanity.com/paper/2310.00656/) (2023)
- [First Experiments with Neural Translation of Informal to Formal Mathematics](https://mlsanity.com/paper/1805.06502/) (2018)
- [Math Word Problem Generation with Mathematical Consistency and Problem Context Constraints](https://mlsanity.com/paper/2109.04546/) (2021)
- [Towards Autoformalization of Mathematics and Code Correctness: Experiments with Elementary Proofs](https://mlsanity.com/paper/2301.02195/) (2023)
- [Learning by Analogy: Diverse Questions Generation in Math Word Problem](https://mlsanity.com/paper/2306.09064/) (2023)
- [Mathematical Word Problem Generation from Commonsense Knowledge Graph and Equations](https://mlsanity.com/paper/2010.06196/) (2020)
- [SubgoalXL: Subgoal-based Expert Learning for Theorem Proving](https://mlsanity.com/paper/2408.11172/) (2024)
- [Training a First-Order Theorem Prover from Synthetic Data](https://mlsanity.com/paper/2103.03798/) (2021)
- [MATHWELL: Generating Educational Math Word Problems Using Teacher Annotations](https://mlsanity.com/paper/2402.15861/) (2024)
- [COMET: "Cone of experience" enhanced large multimodal model for mathematical problem generation](https://mlsanity.com/paper/2407.11315/) (2024)
- [DISK: Domain-constrained Instance Sketch for Math Word Problem Generation](https://mlsanity.com/paper/2204.04686/) (2022)

## Built on by (most cited first, 1 of 1)

- [Incentives Of EdTech: A Systematic Review Of EduNLP Research](https://mlsanity.com/paper/2606.13691/) (2026)

## Abstract (arXiv)

Generating high-quality geometry problems is both an important and challenging task in education. Compared to math word problems, geometry problems further emphasize multi-modal formats and the translation between informal and formal languages. In this paper, we introduce a novel task for geometry problem generation and propose a new pipeline method: the Symbolic Deduction Engine-based Geometry Problem Generation framework (SDE-GPG). The framework leverages a symbolic deduction engine and contains four main steps: (1) searching a predefined mapping table from knowledge points to extended definitions, (2) sampling extended definitions and performing symbolic deduction, (3) filtering out unqualified problems, and (4) generating textual problems and diagrams. Specifically, our method supports to avoid inherent biases in translating natural language into formal language by designing the mapping table, and guarantees to control the generated problems in terms of knowledge points and difficulties by an elaborate checking function. With obtained formal problems, they are translated to natural language and the accompanying diagrams are automatically drew by rule-based methods. We conduct experiments using real-world combinations of knowledge points from two public datasets. The results demonstrate that the SDE-GPG can effectively generate readable, solvable and controllable geometry problems.