Mathematical experiments are becoming more abundant due to human-machine teaming, enabling researchers to tackle complex problems with AI assistance. Over a single weekend, a researcher used a combination of AI models, including GPT-5.6 Sol, parallel agents, exact-arithmetic programs, and a proof assistant, to explore two challenging mathematical problems.

One problem involved the non-existence of a Hadamard matrix of order 668. The AI agents explored numerous avenues, closing off 44 precisely defined regions of the search space and auditing five standard routes to a non-existence proof. The second problem, related to a mathematical theorem, yielded a proof candidate. This candidate included a conventional argument, exact checks on selected inputs, a teaching guide, and a partial formalization in Lean. However, it awaits specialist review for novelty and comprehensive validation.

This approach mirrors a broader scientific research cycle: propose an experiment, implement and run it, evaluate the results, and use that evaluation to generate a better experiment. AI's role is to automate this entire loop, reducing iteration time and learning from every evaluation. The key development is the partial automability of the experimental cycle itself, dramatically reducing the cost of proposing, executing, and refining mathematical experiments once exact evaluators are available.