A researcher successfully solved six open Erdős problems in just five days using GPT-5.6 Sol, achieving a near 46% success rate after attempting a total of thirteen problems. The innovative approach involved crafting a detailed prompt that functioned like a contract, outlining necessary proof criteria and potential pitfalls, which aligns with emerging practices in prompt engineering that emphasize defining success metrics and edge cases. Additionally, he employed a multi-agent validation strategy, utilizing adversarial agents to rigorously test and challenge each draft solution before acceptance, thereby enhancing the reliability of the results generated by the AI model.
Codex: Codex refers to the AI component or system instance that maintained the full search state in memory across extended iterative sessions. It supported the ongoing loop of exploring, refining, and validating multiple proof strategies simultaneously. This memory and persistence capability enabled the multi-hour autonomous workflow described.
OpenAI: OpenAI develops and releases advanced AI models including iterations of the GPT series. Its GPT-5.6 Sol model was directly used by the researcher to generate solutions for open mathematical problems. The company’s tools continue to support complex reasoning workflows in scientific domains.
Qiaoqiao: Qiaoqiao is a researcher with a mathematics background who publicly shared a detailed workflow for applying AI to unsolved problems. He posted a thread documenting how he solved six open Erdős problems in five days using structured prompting with GPT-5.6 Sol. The approach emphasizes careful prompt design rather than requiring deep specialized knowledge.
Prompt Engineering: Researchers are using highly structured, contract-style prompts that explicitly define success criteria, list invalid weaker results, and incorporate known edge cases to guide AI models more reliably.
Multi-Agent Validation: Adversarial agent setups are being applied within AI workflows to systematically challenge and break draft solutions before final acceptance.