GPT-5.6 used a prompt to close a 30-year gap in convex optimization

TL;DR Highlight

A ten-page prompt got GPT-5.6 to return a claimed proof in 148 minutes

Who Should Read

A developer using LLM APIs who wants to hand hard problems to a model with a long, detailed prompt

Core Mechanics

The article body wasn't captured
- The provided text is only Reddit's landing text.
- Everything below comes from the author's post as quoted in comments.
A proof came back in 148 minutes
- Per the quoted author post, GPT-5.6 Sol Pro returned a proposed proof after 148 minutes.
- The author says it resolves quadratic dimension dependence at accuracy of order d⁻³.
The prompt was about ten pages
- The author wrote a much more elaborate prompt in the style of OpenAI's CDC prompt.
- It reportedly specified approaches to try and how the model should proceed.
The proof was checked in Lean
- The author says they checked it themselves and then formally verified it in Lean, a proof checker, and it passed.

Community Reactions

Opinion that the prompt already contained the technique
- A commenter says the author had worked on the problem for a year with GPT 5.4 and 5.5 and fed that into the prompt.
- They argue '148 minutes' really means 'a year plus 148 minutes'.
Author's reply as quoted in comments
- The prompt was also written with Sol's help, and the function class that worked (max of affine functions) was in the prompt.
- The author reportedly isn't sure how much previous-chat memory was used.
Comments note it isn't peer reviewed
- Several commenters stressed it hasn't been peer reviewed yet.
- One says the prompt is on page 27 and needed substantial domain expertise.
A field-literate commenter's take
- One commenter calls it niche but a real contribution.
- They explain the lower bound matches the complexity of a 30-year-old algorithm.

How to Apply

Build a long-prompt template for hard tasks
- Pick one problem you're stuck on and write out background, approaches to try, procedure, and success criteria.
- Compare the result against a short one-line question.
Put an approach list directly in the prompt
- List the methods to try, even without ranking them.
- Attach prior attempts as well.
Verify output with a separate checker
- Run model output through tests, a type checker, or a formal verifier.
- Trust only what passes.

Try It

copy & run

# Paste into Claude or ChatGPT (simplified version of the paper's method)

You are an expert in {{field}}. Solve the problem below.

[Problem]
{{problem definition}}

[What has been tried]
{{previous attempts and why they failed}}

[Approaches to try]
1. {{approach 1}}
2. {{approach 2}}
3. {{approach 3}}

[Procedure]
- Assess each approach, then develop the most promising one all the way.
- If stuck, state why and move to another approach.
- At the end, propose a way to verify the result.

Next to try: ask the same problem as a one-line question and compare results.

Terminology

Lower boundA limit saying no algorithm can solve the problem faster than this. Like a speed limit that applies to every algorithm.

LeanA tool that checks math proofs line by line. Think of it as a compiler for proofs.

Peer reviewOther experts vetting a paper before it's accepted. Code review for research.

OracleA hypothetical black box an algorithm can query for values. Like an API you call.