A new preprint on arXiv offers a detailed case study of something the AI research community has been promising for years: a human and an AI working together to make a genuine mathematical discovery, rather than the AI simply solving a problem the human already defined.
The paper, from researchers Yanqiao Wang, Jin-Peng Liu, Peng Li, and Yang Liu, documents the collaborative process that led to sign-embedding quantum algorithms, foundational primitives for quantum linear algebra and operator-output quantum algorithms. The work was conducted using AIM, an agentic AI-mathematician system that later integrated the workflows developed during this project.
From vague idea to concrete result
The project began with a human-originated intuition: rational approximation works especially well for jump-type functions such as the sign function, and could serve as a design principle for quantum algorithms. Rather than using AI simply to solve a predefined problem, the researchers deployed it at the earliest, most open-ended stage of discovery.
AI-assisted exploration expanded the initial intuition into a route map, compared candidate formulations, and converged toward sign embedding as the central framework. AIM then connected a known matrix-sign identity to wider classes of matrix equations and matrix functions, and drafted proof and complexity calculations.
But the decisive scientific judgments remained human. The researchers selected which expanded routes were worth pursuing, rejected a Cayley-trapezoidal approximation when its validity required a hidden condition, and refined a Sylvester implementation from a coarse quadratic-gap query route to a factorised and scaled analysis.
A model for human-AI collaboration
The paper argues that human-AI co-discovery workflows are most valuable not as standalone theorem provers, but as research partners for problem formation, connection discovery, derivation, and skeptical review within a human-gated research loop.
This contrasts with typical AI-mathematics evaluations, which test models on already-formulated problems. The authors’ focus on the formative stage, where problems are still being shaped, suggests a different and potentially more impactful role for AI in research than the benchmark-chasing that dominates the field today.
The preprint has not yet been peer-reviewed.
Source: From Meta Idea to Advanced Mathematical Discovery, Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms (arXiv, June 2026)