https://ai-mathematician.net/en/Recent content on AIM BlogHugoenMon, 22 Jun 2026 00:00:00 +0000https://ai-mathematician.net/en/posts/sign-embedding-quantum-algorithms/Mon, 22 Jun 2026 00:00:00 +0000https://ai-mathematician.net/en/posts/sign-embedding-quantum-algorithms/Human-AI collaboration advances quantum algorithm research and proposes Sign-Embedding Quantum Algorithms.https://ai-mathematician.net/en/posts/pessimistic-verification/Sun, 17 May 2026 00:00:00 +0000https://ai-mathematician.net/en/posts/pessimistic-verification/We present Pessimistic Verification, a simple and efficient way to improve LLM-based verification for open-ended mathematical proofs.https://ai-mathematician.net/en/posts/homogenization.theory/Fri, 07 Nov 2025 00:00:00 +0000https://ai-mathematician.net/en/posts/homogenization.theory/A human–AI collaboration successfully completed a 17-page mathematical proof in homogenization theory.https://ai-mathematician.net/en/posts/aim/Thu, 05 Jun 2025 00:00:00 +0000https://ai-mathematician.net/en/posts/aim/We present AIM, a multi-agent framework powered by large language models, advancing from "solving problems" to "conducting research".https://arxiv.org/abs/2505.22451Wed, 28 May 2025 00:00:00 +0000https://arxiv.org/abs/2505.22451PublicationsIntroduces AIM, a large-reasoning-model agent framework for frontier mathematical research, combining longer exploration trajectories with verification-oriented mechanisms for research-level proof tasks.https://arxiv.org/abs/2606.24899Fri, 12 Jun 2026 00:00:00 +0000https://arxiv.org/abs/2606.24899PublicationsPresents a human-AI co-discovery case study in which AIM-supported exploration, theorem formation, derivation, and audit workflows contributed to sign-embedding quantum algorithms for matrix equations and matrix functions.https://arxiv.org/abs/2511.21522Wed, 26 Nov 2025 00:00:00 +0000https://arxiv.org/abs/2511.21522PublicationsStudies pessimistic verification workflows for open-ended mathematical proofs, where a proof is rejected when any verifier finds a critical error.https://arxiv.org/abs/2510.26380Thu, 30 Oct 2025 00:00:00 +0000https://arxiv.org/abs/2510.26380PublicationsPresents a homogenization-theory case study showing how AIM-assisted reasoning and targeted human intervention can support the development of a complete mathematical proof.https://arxiv.org/abs/2508.18914Tue, 26 Aug 2025 00:00:00 +0000https://arxiv.org/abs/2508.18914PublicationsProposes FormaRL, a reinforcement-learning framework for autoformalization that uses unlabeled data, Lean syntax checks, and LLM consistency checks to improve formalization accuracy.https://arxiv.org/abs/2609.03549https://arxiv.org/abs/2609.03549DiscoveriesFiltering estimates a hidden system's state from noisy measurements. This work gives conditions ensuring that three central filtering equations have unique solutions even when model coefficients grow without bound. AIM helped explore mathematical tools and draft arguments, with the final results checked by the researchers.https://arxiv.org/abs/2608.22756https://arxiv.org/abs/2608.22756DiscoveriesThis work compares two algebraic measurements of the infinitesimal symmetries of an isolated hypersurface singularity. It shows that their dimensions are usually equal, with a precise one-dimensional exception controlled by the degeneracy of the Hessian, and thereby resolves a previously proposed conjecture.https://arxiv.org/abs/2604.25333https://arxiv.org/abs/2604.25333DiscoveriesThis work explores quantum algorithms for difficult matrix computations that appear in scientific computing and applied mathematics. Its main contribution is a reusable framework that may help quantum computers solve several families of matrix problems more systematically.https://arxiv.org/abs/2510.26380https://arxiv.org/abs/2510.26380DiscoveriesThis case study shows how AIM can support mathematicians on a long and technical proof. AIM helps propose reasoning steps and organize the search, while human researchers guide, check, and refine the proof to maintain mathematical rigor.