Can a Lightweight Automated AI Pipeline Solve Research-Level Mathematical Problems?

Large language models (LLMs) have recently achieved remarkable success in generating rigorous mathematical proofs, with “AI for Math” emerging as a vibrant field of research (Ju et al., 2026). While these models have mastered competition-level benchmarks like the International Mathematical Olympiad (Huang et al., 2025; Duan et al., 2025) and show promise in research applications through auto-formalization (Wang et al., 2025), their deployment via lightweight, natural-language pipelines for research problems remains underexplored. In this work, we demonstrate that next-generation models (e.g., Gemini 3 Pro, GPT-5.2 Pro), when integrated into a streamlined automated pipeline optimized for citation-based verification, can solve sophisticated research-grade problems. We evaluate our pipeline on two novel datasets: (1) the ICCM (2025) problem sets (comparable to the S.-T. Yau College Student Mathematics Contest) proposed by leading mathematicians (Shanghai Math Challenge, 2026), and (2) the “First Proof” problem set (Abouzaid et al., 2026), consisting of previously unpublished research questions. Our pipeline generated candidate proofs for all problems in the first two ICCM sets and the “First Proof” set. The solutions for the first two ICCM sets and Problem 4 of the “First Proof” set have been fully verified by our team. All generated proofs have been submitted to the official organization, and our generated results are publicly available at https://github.com/ml1301215/question_sets-test_results. We have open-sourced the code and developed a user-friendly UI for this workflow, accessible at https://github.com/ml1301215/research-math-assistant.

💡 Research Summary

The paper investigates whether a lightweight, natural‑language‑based AI pipeline can tackle genuine research‑level mathematics, rather than merely competition‑style problems. Building on the architecture originally proposed for IMO‑level tasks, the authors integrate state‑of‑the‑art large language models (Gemini 3 Pro and GPT‑5.2 Pro) and introduce two crucial enhancements: (1) domain‑specific prompt optimization that equips the models with graduate‑level terminology, definitions, and a structured “definition → assumption → proof” template; and (2) a citation‑augmented verification mechanism that forces the model to provide precise bibliographic references (including page or section numbers) for every non‑trivial claim. This citation requirement dramatically reduces hallucinations and gives human validators a concrete trail to follow.

The experimental evaluation uses two newly released benchmark suites that aim to reflect authentic research challenges. The first consists of three ICCM problem sets released by the International Congress of Chinese Mathematicians; the first two sets are comparable in difficulty to the S‑T Yau College Student Mathematics Contest, while the third contains open conjectures and Calabi‑Yau‑related questions. The second benchmark, called “First Proof,” comprises ten previously unpublished research‑level questions supplied directly by active mathematicians. The pipeline automatically generated candidate proofs for every problem in both suites within minutes.

Human experts verified all solutions in ICCM Sets 1 and 2 and Problem 4 of the First Proof suite. The verified proofs are fully rigorous, contain correct citations to sources such as Kashiwara & Schapira’s Categories and Sheaves and relevant nLab entries, and have been compiled into PDFs submitted to the ICCM organizers. For ICCM Set 3, the system correctly identified that the open conjectures are beyond current capability and, for the Calabi‑Yau sub‑problems, produced partial attempts that could not be fully validated due to a lack of domain specialists on the team. In the First Proof suite, the model claimed solutions for all ten problems; however, only Problem 4 was exhaustively checked, confirming the model’s ability to detect a false universal inequality by constructing a counterexample for the n = 1 case.

Three detailed case studies illustrate the pipeline’s breadth: (1) a combinatorial elimination problem where the AI proved that at most five “potential champions” can exist among eight students and three subjects, and the proof was later formalized in Lean 4 with over 5,000 lines of code; (2) an exercise in category theory (Exercise 3.5 from Kashiwara & Schapira) where the AI established the equivalence between left‑exactness of a functor and exactness of its Yoneda extension, citing the textbook’s definitions and nLab entries; (3) a problem from the First Proof set involving a novel polynomial operation ⊞ₙ and a functional Φₙ, where the AI demonstrated that the proposed inequality fails for n = 1 by a residue‑analysis argument and explicit counterexample.

A central finding is the “verification bottleneck”: while the pipeline can generate proofs in seconds to minutes, human verification of a single proof (including checking citations and logical coherence) typically requires 2–3 hours. This asymmetry underscores the urgent need for AI‑assisted verification tools, such as tighter integration with formal proof assistants, semi‑formal interactive interfaces, or explainable reasoning frameworks that can keep pace with rapid proof generation.

The discussion also highlights practical hurdles for large‑scale adoption: (i) usability gaps, as many mathematicians lack expertise in prompt engineering and AI toolchains; (ii) long‑context reasoning, where deep research problems demand sustained, coherent chains of thought that exceed current context windows; (iii) implicit knowledge handling, where AI struggles with unstated steps or notational shortcuts common in the literature, suggesting that merely scaling data is insufficient and that targeted processing of mathematical texts to reconstruct intermediate steps may be more effective.

In conclusion, the authors demonstrate that a lightweight, citation‑aware AI pipeline combined with next‑generation LLMs can indeed solve a non‑trivial subset of research‑level mathematical problems, achieving full human verification on several benchmarks. The work points toward a future where AI handles heavy computational and exploratory tasks, proposes conjectural patterns, and assists in the meticulous verification of sub‑steps, while human mathematicians focus on high‑level conceptual innovation. Advancing this vision will require improved verification automation, more intuitive user interfaces, and deeper model understanding of mathematical literature.