Can GPT‑5.6 Sol Crack Fermat’s Last Theorem After 33 Hours of Continuous Running?

Experiment Setup

Michael P. Frank assigned GPT‑5.6 Sol the research goal of investigating whether a proof of Fermat’s Last Theorem simpler than the Wiles‑Taylor proof exists. The focus areas were Frey‑curve modularity, the uniform infinite‑descent method, arithmetic abc‑type inequalities, and uniform low‑genus quotients. The task required rigorous note‑taking, computational verification of candidate lemmas, and a clear separation between proven results and conjectures.

Run Duration and Termination

The session ran in the background for approximately 33 hours , consuming a large amount of compute resources before OpenAI’s system forcibly stopped it.

Model Self‑Analysis

In its post‑mortem report GPT‑5.6 Sol listed two possible reasons for the termination: (1) the system flagged the session for excessive resource usage; (2) OpenAI had previously attempted the same problem with similar models and chose not to repeat the compute expense.

The model also described the work performed during the run: it converted many apparently plausible shortcuts into precise statements, then falsified or discarded them, producing a “this path is dead” map rather than a complete proof, and recommended halting the effort.

Technical Interpretation of the Block

In codex‑cli the “goal blocked” message indicates that the model encountered the same blocker for three consecutive inference turns, which suggests a routine safety or dead‑lock prevention mechanism rather than a problem‑specific block.

Version 5.6 Bug and Workaround

Users reported a bug in version 5.6 of Sol that manifests during long‑running tasks. The temporary workaround is to switch to version 5.5, compress the context, run for a few minutes, and then switch back to version 5.6. Attempting to preserve the same session without this step can cause the session to become stuck.

Reference link: https://x.com/lu_sichu/status/2081367506468360495