Human-AI Collaboration

We recently applied the AI Mathematician system AIM to a research project at the frontier of mathematics and quantum algorithms, leading to Sign-Embedding Quantum Algorithms for matrix equations and matrix functions. During this work, we combined general AI-assisted exploration with the AIM system to support route expansion, problem formation, candidate theorem and proof generation, complexity analysis, and result refinement. In this human-AI research loop, AI and AIM made nontrivial contributions from problem formation to problem solving. ...

Using the self-developed AI Mathematician system (AIM) as a research collaborator, we successfully solved a challenging problem in homogenization theory through a human–AI collaborative paradigm, resulting in a 17-page mathematical proof. This work systematically verifies the feasibility of upgrading AI from a mere mathematical problem-solving tool to a true research partner, opening a new path for breakthroughs in complex mathematical problems. ...