A new Hacker News thread reports that GPT-5.6 closed a 30-year gap in convex optimization after a single, carefully engineered prompt. The post accumulated 483 points and 314 comments within days.
The Core Claim
The model produced a proof that resolved an open question in convex optimization first posed in the mid-1990s. The result concerns the existence of a polynomial-time algorithm for a specific class of semidefinite programs previously considered intractable.
No fine-tuning or external tools were used. The output consisted of a formal argument that community members are now verifying against existing literature.
How the Prompt Was Constructed
The prompt combined three elements: a precise statement of the open problem, a request for a proof in the style of Boyd and Vandenberghe, and an instruction to flag any unproven steps. Early reproductions on the thread show that removing any of these components caused the model to revert to known partial results rather than the new claim.
Researchers on the thread note that the prompt ran to roughly 1,200 tokens and required two clarification rounds before the final proof appeared.
Verification Status
As of the latest comments, two independent groups have confirmed the key lemma using computer algebra systems. One verification used CVXPY; the second used a custom SDP solver in Julia. No counterexamples have surfaced.
The original poster has not released the exact prompt text, citing ongoing peer review.
Comparison with Prior AI Math Tools
| Tool | Problem Type | Human Input Required | Verification Rate | Public Proofs |
|---|---|---|---|---|
| GPT-5.6 | Convex optimization | 1,200-token prompt | 2/2 lemmas | 1 |
| AlphaProof | IMO problems | Formal statement | 4/6 problems | 4 |
| Lean + GPT-4o | Number theory | Tactic guidance | 70% auto-checked | 12 |
GPT-5.6 required the least scaffolding but currently has the smallest verified output set.
Who Should Test This Approach
Math researchers working on open problems in optimization or semidefinite programming can replicate the method immediately. Teams without access to formal verification software should first run the output through existing solvers such as MOSEK or SDPT3.
Practitioners focused on applied ML or prompt engineering for code should skip this workflow; the technique adds little value outside theoretical mathematics.
Practical Next Steps
Reproduce the result by stating the original 1990s conjecture verbatim, then append the three prompt components described above. Run the output through CVXPY or a similar library before claiming novelty.
The thread contains several partial prompt templates posted by commenters that have already produced consistent lemmas on smaller instances.
Bottom line: One verified proof does not yet prove general capability, but the workflow is now reproducible by any researcher with GPT-5.6 access.
Early results suggest that targeted prompting can surface new proofs in narrow mathematical domains where formal verification tools already exist.
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