# MathConstruct: Challenging LLM Reasoning with Constructive Proofs

arXiv: https://arxiv.org/abs/2502.10197 · HTML: https://mlsanity.com/paper/2502.10197/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 4 of its 32 references that are in the map.
- First posted on arXiv 14 Feb 2025.

## Placed in

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

## Builds on (most cited first, 4 of 4)

- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [ConStat: Performance-Based Contamination Detection in Large Language Models](https://mlsanity.com/paper/2405.16281/) (2024)

## Built on by (most cited first, 16 of 16)

- [MathArena: Evaluating LLMs on Uncontaminated Math Competitions](https://mlsanity.com/paper/2505.23281/) (2025)
- [Proof or Bluff? Evaluating LLMs on 2025 USA Math Olympiad](https://mlsanity.com/paper/2503.21934/) (2025)
- [RealMath: A Continuous Benchmark for Evaluating Language Models on Research-Level Mathematics](https://mlsanity.com/paper/2505.12575/) (2025)
- [Mathematical Proof as a Litmus Test: Revealing Failure Modes of Advanced Large Reasoning Models](https://mlsanity.com/paper/2506.17114/) (2025)
- [ASyMOB: Algebraic Symbolic Mathematical Operations Benchmark](https://mlsanity.com/paper/2505.23851/) (2025)
- [Learning to Disprove: Formal Counterexample Generation with Large Language Models](https://mlsanity.com/paper/2603.19514/) (2026)
- [LeanTutor: Towards a Verified AI Mathematical Proof Tutor](https://mlsanity.com/paper/2506.08321/) (2025)
- [A Survey of Deep Learning for Geometry Problem Solving](https://mlsanity.com/paper/2507.11936/) (2025)
- [TCS-BENCH: Benchmarking State-of-the-Art Generative AI Theoretical Computer Science Research Ability](https://mlsanity.com/paper/2608.09538/) (2026)
- [PBEBench: A Multi-Step Programming by Examples Reasoning Benchmark inspired by Historical Linguistics](https://mlsanity.com/paper/2505.23126/) (2025)
- [ProofVerifier: A Scalable, Diversity-Driven Framework for Natural-Language Proof Verification](https://mlsanity.com/paper/2602.02377/) (2026)
- [Can LLMs subtract numbers?](https://mlsanity.com/paper/2511.02795/) (2025)
- [LLM Swiss Round: Aggregating Multi-Benchmark Performance via Competitive Swiss-System Dynamics](https://mlsanity.com/paper/2512.21010/) (2025)
- [LeanTutor: Towards a Verified AI Mathematical Proof Tutor](https://mlsanity.com/paper/2601.17473/) (2026)
- [MathConstraint: Automated Generation of Verified Combinatorial Reasoning Instances for LLMs](https://mlsanity.com/paper/2605.08498/) (2026)
- [RamseyGadgets: A Graph Construction Dataset for LLMs](https://mlsanity.com/paper/2608.14999/) (2026)

## Abstract (arXiv)

While Large Language Models (LLMs) demonstrate impressive performance in mathematics, existing math benchmarks come with significant limitations. Many focus on problems with fixed ground-truth answers, and are often saturated due to problem simplicity or the viability of guessing or memorization. Crucially, they capture only a narrow subset of relevant math problems. To address this research gap, we introduce MathConstruct, a new benchmark of 121 challenging problems sourced from various math competitions, which targets constructive proofs, a widely encountered problem type requiring the construction of mathematical objects with specific properties. These proofs are particularly suitable for LLM evaluation, as solution correctness can be easily verified. Our automated verifiers also enable MathConstruct to generate problem variations, used to evaluate robustness. State-of-the-art LLMs solve only 60% of MathConstruct problems, highlighting its complexity and importance for LLM evaluation.