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

TL;DR

EternalMath is a dynamic, automated benchmark derived from recent mathematical literature, designed to evaluate and track the evolving capabilities of large language models in frontier mathematics.

Contribution

The paper introduces a fully automated, theorem-grounded pipeline for creating an evolving, verifiable mathematical reasoning benchmark directly from research papers.

Findings

State-of-the-art LLMs show significant gaps in frontier mathematical reasoning.

EternalMath enables scalable, reproducible, and continuously updatable evaluation.

The approach supports domain-specific customization and temporal extensibility.

Abstract

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 \textbf{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.