Bolzano is a multi‑agent, open‑source system that employs parallel prover agents and a verifier agent to conduct proof search while maintaining a human‑readable research state. In initial manual trials on expert‑selected problems, it produced eight proofs verified by domain experts. When deployed without problem‑specific guidance on roughly 3,800 open problems from four paper sets, Bolzano solved about 200 of them, including four questions from papers accepted to the STOC 2026 conference, which were confirmed by the authors.
arXiv:2610.09769v1 Announce Type: cross Abstract: Large language models are increasingly contributing to mathematical research, where progress often depends on efficient proof search, incremental imp...
arXiv:2607. 09474v1 Announce Type: new Abstract: Large language models (LLMs) have shown increasing promise in solving open problems in mathematics.
Large language models (LLMs) have shown increasing promise in solving open problems in mathematics. However, their performance can be further improved through agentic workflows tailored to real-world mathematical practice.
arXiv:2604. 24021v4 Announce Type: replace Abstract: We present QED, an open-source multi-agent system that turns human-provided research questions into complete mathematical proofs without further human guidance.
Cogentic is a multi‑agent system designed to automate proof discovery for open research problems. It uses an iterative prove‑verify loop where an orchestrator assigns independent provers to different proof directions, verifies their outputs with specialized components, and records confirmed intermediate results in a persistent ledger for future rounds. Built on Gemini, Cogentic has produced novel results on five open problems in online learning, auction theory, and mechanism design, each verified by domain experts and detailed in companion papers.
arXiv:2608.28433v2 Announce Type: replace Abstract: Proof assistants such as Lean 4 promise the paradigm of formally verified mathematics, but large-scale formalization projects have faced major barr...
OpenFrontiers is a cross‑disciplinary resource that compiles 12,151 open research problems and a benchmark of 200 recently resolved mathematics problems, including 110 solved in 2026 and 90 still open. Each benchmark problem is formally stated in Lean 4, verified by automated probes, and reviewed independently. The evaluation protocol tests LLM agents under closed‑book, frozen‑retrieval, and live‑web conditions, revealing that closed‑book rediscovery is rare while live‑web success largely reflects retrieval of published solutions.
arXiv:2607. 09217v1 Announce Type: new Abstract: In this system paper, we present OpenProver, an open-source system for LLM-driven automated theorem proving (ATP) with integrated Lean 4 formal verification.
arXiv:2605. 22763v2 Announce Type: replace Abstract: Large language models (LLMs) increasingly excel at mathematical reasoning, but their unreliability limits their utility in mathematics research.
The paper introduces HorizonMath, a benchmark of 113 largely unsolved mathematical problems across eight domains, paired with an open-source framework for automated verification. It focuses on the generator‑verifier gap, targeting problems that are hard to discover but easy to verify computationally, thereby avoiding costly formal proof verification or manual review. Using this framework, the authors found six novel solutions—three each from GPT‑5.4 Pro and GPT‑5.6 Sol—demonstrating that current models can contribute to mathematical research, while most state‑of‑the‑art models score below 10%.
arXiv:2607. 27705v1 Announce Type: cross Abstract: Large language models can contribute useful ideas to mathematical research, yet long-horizon proof attempts remain difficult to coordinate, evaluate, and reproduce.
arXiv:2603. 02668v2 Announce Type: replace Abstract: We present SorryDB, a dynamically-updating benchmark of open Lean tasks drawn from 78 real world formalization projects on GitHub.