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[2511.02872] FATE: A Formal Benchmark Series for Frontier Algebra of Multiple Difficulty Levels
Summary
The paper introduces FATE, a benchmark series for formal algebra, designed to assess large language models' capabilities in advanced mathematical reasoning across various difficulty levels.
Why It Matters
FATE addresses the gap in existing mathematical benchmarks by providing a structured evaluation of LLMs in formal algebra. This is crucial for advancing AI's ability to tackle complex mathematical problems, which is increasingly relevant in fields like AI research and education.
Key Takeaways
- FATE introduces a new benchmark series for formal algebra with varying difficulty levels.
- The benchmark reveals significant performance gaps in LLMs compared to traditional contest math.
- FATE-X is the first benchmark to exceed PhD-level exam difficulty.
- Natural-language reasoning in models is more accurate than their formalization abilities.
- Common errors in formalization are systematically classified, providing insights for improvement.
Computer Science > Machine Learning arXiv:2511.02872 (cs) [Submitted on 4 Nov 2025 (v1), last revised 20 Feb 2026 (this version, v3)] Title:FATE: A Formal Benchmark Series for Frontier Algebra of Multiple Difficulty Levels Authors:Jiedong Jiang, Wanyi He, Yuefeng Wang, Guoxiong Gao, Yongle Hu, Jingting Wang, Nailing Guan, Peihao Wu, Chunbo Dai, Liang Xiao, Bin Dong View a PDF of the paper titled FATE: A Formal Benchmark Series for Frontier Algebra of Multiple Difficulty Levels, by Jiedong Jiang and 10 other authors View PDF HTML (experimental) Abstract:Recent advances in large language models (LLMs) have demonstrated impressive capabilities in formal theorem proving, particularly on contest-based mathematical benchmarks like the IMO. However, these contests do not reflect the depth, breadth, and abstraction of modern mathematical research. To bridge this gap, we introduce FATE (Formal Algebra Theorem Evaluation), a new benchmark series in formal algebra designed to chart a course toward advanced mathematical reasoning. We present two new components, FATE-H and FATE-X, each with 100 problems in abstract and commutative algebra. The FATE series spans a difficulty spectrum from undergraduate exercises to problems exceeding PhD qualifying exams. Notably, FATE-X is the first formal benchmark to surpass both PhD-level exam difficulty and the coverage of the Mathlib library. Our evaluations of state-of-the-art LLM provers on this new benchmark reveal a stark performance gap compa...
