Failure Modes of Large Language Models on Research-Level Mathematics: A Taxonomy and an Empirical Characterisation
The "First Proof" benchmark [1] posed ten research-level mathematics questions to the strongest publicly available LLMs and found them consistently wrong-not silent, but confidently, fluently wrong. This paper asks why. Working from the per-question post-mortems in First Proof's Appendix A, I identify four failure modes: citation fabrication (F1), premise smuggling (F2), silent problem reformulation (F3), and local-to-global compatibility gaps (F4). I then audit eight one-shot proofs generated by Gemini 2.5 Flash on Questions 1, 2, and 5 of the benchmark, using two instruments built specifically to surface F1 and F2. The central finding is uncomfortable for anyone who sees retrieval-augme...
| Authors | Arnesh Banerjee, Ayushi Bhattacharjee |
|---|---|
| Primary category | cs.DL |
| Published | 12 June 2026 |
| Last updated at source | 12 June 2026 |
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