AI models may need confidence to make discoveries

LLMs have moved from occasional claims of mathematical breakthroughs in 2024 and 2025 to a much faster pace in 2026, with new model-produced results appearing frequently. The prompting behind some reported discoveries appears simple: ask for a hard breakthrough, then repeatedly encourage the model to keep searching rather than settle for easier work.

The central issue is less prompt wording than model self-belief. Claude Mythos reportedly tried to stop while looking for a cryptographic breakthrough, and DeepSeek-R1 declined to generate Tower of Hanoi solutions beyond eight disks because it judged the task impossible. Similar behavior appeared in older coding agents, which would refuse exhaustive manual tasks even when they were capable of completing them.

The refusal problem has improved for routine tasks, including counting and code review, but scientific and mathematical discovery may require models trained to believe they can attempt unsolved problems. Future training data could include AI-generated discoveries, creating a feedback loop that makes models more willing to pursue ambitious results. Until then, persistence, clear expectations and reassurance may help models continue working on difficult problems.