Beyond Benchmarks: MathArena as an Evaluation Platform for Mathematics with LLMs
Authors: Jasper Dekoninck, Nikola Jovanović, Tim Gehrunger, Kári Rögnvaldsson, Ivo Petrov, Chenhao Sun, Martin Vechev
Organizations: ETH Zurich · INSAIT · Sofia University "St. Kliment Ohridski"
Abstract
Large language models (LLMs) are becoming increasingly capable mathematical collaborators, but static benchmarks are no longer sufficient for evaluating progress: they are often narrow in scope, quickly saturated, and rarely updated. This makes it hard to compare models reliably and track progress over time. Instead, we need evaluation platforms: continuously maintained systems that run, aggregate, and analyze evaluations across many benchmarks to give a comprehensive picture of model performance within a broad domain. In this work, we build on the original MathArena benchmark by substantially broadening its scope from final-answer olympiad problems to a continuously maintained evaluation platform for mathematical reasoning with LLMs. MathArena now covers a much wider range of tasks, including proof-based competitions, research-level arXiv problems, and formal proof generation in Lean. Additionally, we maintain a clear evaluation protocol for all models and regularly design new benchmarks as model capabilities improve to ensure that MathArena remains challenging. Notably, the strongest model, GPT-5.5, now reaches 98% on the 2026 USA Math Olympiad and 74% on research-level questions, showing that frontier models can now comfortably solve extremely challenging mathematical problems. This highlights the importance of continuously maintained evaluation platforms like MathArena to track the rapid progress of LLMs in mathematical reasoning.
We present a new approach for benchmarking Large Language Model (LLM) capabilities on research-level mathematics. Existing benchmarks largely rely on static, hand-curated sets of contest or textbook-style problems as proxies for mathematical research. Instead, we establish an updatable benchmark evaluating models directly on the latest research results in mathematics. This consists of an automatic pipeline that extracts lemmas from arXiv and rewrites them into self-contained statements by making all assumptions and required definitions explicit. It results in a benchmark that can be updated regularly with new problems taken directly from human mathematical research, while previous instances can be used for training without compromising future evaluations. We benchmark current state-of-the-art LLMs, which obtain around 10-15% accuracy in theorem proving (pass@1) depending on the model, showing that there is currently a large margin of progression for LLMs to reach human-level proving capabilities in a research context.
Recent advancements in large language models have led to significant improvements across various tasks, including mathematical reasoning, which is used to assess models' intelligence in logical reasoning and problem-solving. Models are evaluated on mathematical reasoning benchmarks by verifying the correctness of the final answer against a ground truth answer. A common approach for this verification is based on symbolic mathematics comparison, which fails to generalize across diverse mathematical representations and solution formats. In this work, we offer a robust and flexible alternative to rule-based symbolic mathematics comparison. We propose an LLM-based evaluation framework for evaluating model-generated answers, enabling accurate evaluation across diverse mathematical representations and answer formats. We present failure cases of symbolic evaluation in two popular frameworks, Lighteval and SimpleRL, and compare them to our approach, demonstrating clear improvements over commonly used methods. Our framework enables more reliable evaluation and benchmarking, leading to more accurate performance monitoring, which is important for advancing mathematical problem-solving and intelligent systems.
As frontier language models attain near-ceiling performance on static mathematical benchmarks, existing evaluations are increasingly unable to differentiate model capabilities, largely because they cast models solely as solvers of fixed problem sets. We introduce MathDuels, a self-play benchmark in which models occupy dual roles: each authors math problems under adversarial prompting and solves problems authored by every other participant. Problems are produced through a three-stage generation pipeline (meta-prompting, problem generation, and difficulty amplification), and validated by an independent verifier that excludes ill-posed questions. A Rasch model (Rasch, 1993) jointly estimates solver abilities and problem difficulties; author quality is derived from the difficulties of each model's authored problems. Experiments across 19 frontier models reveal that authoring and solving capabilities are partially decoupled, and that dual-role evaluation reveals capability separations invisible in single-role benchmarks. As newer models enter the arena, they produce problems that defeat previously dominant solvers, so the benchmark's difficulty co-evolves with participant strength rather than saturating at a fixed ceiling. We host a public leaderboard that updates as new models are released.