# EternalMath: A Living Benchmark of Frontier Mathematics that Evolves with Human Discovery

arXiv: https://arxiv.org/abs/2601.01400 · HTML: https://mlsanity.com/paper/2601.01400/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 12 of its 23 references that are in the map.
- First posted on arXiv 4 Jan 2026.

## Placed in

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

## Builds on (most cited first, 12 of 12)

- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [MiniF2F: a cross-system benchmark for formal Olympiad-level mathematics](https://mlsanity.com/paper/2109.00110/) (2021)
- [MathArena: Evaluating LLMs on Uncontaminated Math Competitions](https://mlsanity.com/paper/2505.23281/) (2025)
- [ProofNet: Autoformalizing and Formally Proving Undergraduate-Level Mathematics](https://mlsanity.com/paper/2302.12433/) (2023)
- [Evaluating the Performance of Large Language Models on GAOKAO Benchmark](https://mlsanity.com/paper/2305.12474/) (2023)
- [PutnamBench: Evaluating Neural Theorem-Provers on the Putnam Mathematical Competition](https://mlsanity.com/paper/2407.11214/) (2024)
- [MathScale: Scaling Instruction Tuning for Mathematical Reasoning](https://mlsanity.com/paper/2403.02884/) (2024)
- [Lean Workbook: A large-scale Lean problem set formalized from natural language math problems](https://mlsanity.com/paper/2406.03847/) (2024)
- [Are Your LLMs Capable of Stable Reasoning?](https://mlsanity.com/paper/2412.13147/) (2024)
- [MathSmith: Towards Extremely Hard Mathematical Reasoning by Forging Synthetic Problems with a Reinforced Policy](https://mlsanity.com/paper/2508.05592/) (2025)
- [VAR-MATH: Probing True Mathematical Reasoning in LLMS via Symbolic Multi-Instance Benchmarks](https://mlsanity.com/paper/2507.12885/) (2025)

## Built on by (most cited first, 4 of 4)

- [Beyond Benchmarks: MathArena as an Evaluation Platform for Mathematics with LLMs](https://mlsanity.com/paper/2605.00674/) (2026)
- [LemmaBench: A Live, Research-Level Benchmark to Evaluate LLM Capabilities in Mathematics](https://mlsanity.com/paper/2602.24173/) (2026)
- [Soohak: A Mathematician-Curated Benchmark for Evaluating Research-level Math Capabilities of LLMs](https://mlsanity.com/paper/2605.09063/) (2026)
- [Evaluating SageMath-Augmented LLM Agents for Computational and Experimental Mathematics](https://mlsanity.com/paper/2607.06820/) (2026)

## Abstract (arXiv)

Current evaluations of mathematical reasoning in large language models (LLMs) are dominated by static benchmarks, either derived from competition-style problems or curated through costly expert effort, resulting in limited coverage of research-level mathematics and rapid performance saturation. We propose a fully automated, theorem-grounded pipeline for evaluating frontier mathematical reasoning, which directly transforms recent peer-reviewed mathematical literature into executable and verifiable reasoning tasks. The pipeline identifies constructive or quantitative results, instantiates them into parameterized problem templates, and generates deterministic solutions through execution-based verification, enabling scalable, reproducible, and continuously updatable evaluation without reliance on large-scale expert authoring. By design, this approach supports temporal extensibility, intrinsic correctness checking, and domain-specific customization across mathematical subfields. Applying this pipeline yields EternalMath, an evolving evaluation suite derived from contemporary research papers. Experiments with state-of-the-art LLMs reveal substantial performance gaps, indicating that mathematical reasoning at the research frontier remains far from saturated and underscoring the need for evaluation methodologies that evolve in step with human mathematical discovery.