A Medium post flagged on Hacker News reports that GPT-5.6 Sol Pro produced a solution to a convex optimization problem that had remained open for 30 years.
The discussion thread received 19 points and 2 comments.
What the Solution Addresses
Convex optimization problems involve minimizing convex functions subject to convex constraints. The specific instance solved by the model dates back three decades and had resisted both analytical and numerical attacks by human researchers.
GPT-5.6 Sol Pro generated a candidate solution that satisfies the original problem constraints and optimality conditions.
How the AI Approach Worked
The model received the problem statement and supporting mathematical context. It then produced a formal derivation that meets the required verification criteria.
No new training run was reported; the result came from the existing model checkpoint.
Hacker News Community Reaction
The two comments focused on reproducibility and verification steps. One user asked whether the output had been checked with an independent solver. The second comment noted the 30-year timeline as the most notable detail.
No code repository or formal proof file was linked in the thread.
Comparison with Traditional Solvers
Standard convex optimization packages such as CVXPY and Gurobi rely on interior-point or first-order methods. They require explicit problem encoding and can struggle with certain non-standard formulations.
| Aspect | GPT-5.6 Sol Pro | CVXPY + SCS | Gurobi |
|---|---|---|---|
| Problem age handled | 30 years | Varies | Varies |
| Human encoding time | Low | High | High |
| Verification needed | Manual check | Built-in | Built-in |
| Open-source status | No | Yes | Commercial |
Practical Limitations
The result remains a single data point. No benchmark suite, runtime numbers, or scaling tests appear in the source. Independent reproduction is still required before the method can be considered reliable for new problems.
Who Should Test This
Researchers working on long-standing convex problems with limited progress may want to replicate the prompt structure. Teams needing guaranteed runtimes or certified optimality should continue using established solvers until further validation exists.
Verdict
The case shows that current large language models can surface candidate solutions to previously unsolved convex problems, but verification still rests with human experts and conventional tools.
Early experiments of this type will likely increase as model context windows grow.
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