Fable 5 vs. GPT-5.6 Sol on an NP-hard problem: does /goal help?

AI models are getting measurably better at hard maths, and that matters more to your business than you might think.

What's Actually Happening With These Models

There's a quiet but significant story developing around GPT-5.6 (one of OpenAI's more recent model variants) and its performance on problems that have historically defeated computers entirely. Specifically, researchers have been testing it against NP-hard problems. NP-hard is a category of computational problem so complex that even the fastest computers struggle to find optimal solutions in reasonable time; think scheduling hundreds of deliveries, optimising a supply chain, or cracking certain encryption methods.

The detail worth sitting with: a prompt-level adjustment apparently helped GPT-5.6 close a 30-year gap in a branch of mathematics called convex optimisation. Convex optimisation, in plain English, is the science of finding the best possible answer within a constrained set of options. It underpins everything from logistics routing to financial modelling. A 30-year-old open problem does not close itself. That is a meaningful result.

The Prompt Engineering Angle Nobody Talks About Enough

The comparison circulating right now pits different approaches to prompting these advanced models against each other, specifically looking at whether adding a simple goal-framing instruction changes model performance on hard problems. The finding appears to be: yes, it does. Meaningfully.

This is not a minor tweak. If the framing of your instruction to an AI model can be the difference between a mediocre answer and a mathematically significant one, that reframes what "knowing how to use AI" actually means. It is not just about which tool you pick. It is about how precisely you tell it what you want.

We have seen this in our own work at Thirty3 Labs. The gap between a vague prompt and a structured, goal-oriented one is routinely the difference between something usable and something you have to redo three times.

What This Means If You Run a Business

Most small business owners using AI tools are doing so casually. They type something in, get something out, decide whether it's good enough. What the current research keeps demonstrating is that this approach leaves a lot of value on the table.

If goal-oriented prompting improves performance on genuinely hard academic problems, it almost certainly improves performance on your specific business problems too. Drafting a client proposal, summarising a contract, writing product descriptions with a particular conversion goal in mind: all of these have a "correct" answer that varies depending on your objective. Telling the model what that objective is, precisely and explicitly, is not optional if you want good results.

The second implication is about competitive gap. As AI models improve rapidly (and they are improving rapidly, the pace right now is not normal), the businesses getting value from them are not necessarily the ones with the biggest budgets. They are the ones who have bothered to understand how to direct these tools properly. That gap is only going to widen.

What To Do About It

1. 1.Rewrite your standard AI prompts with explicit goals. Instead of "write me a product description," try "write a product description for a 45-year-old homeowner who prioritises reliability over price, with the goal of getting them to book a consultation call." Specificity is not pedantry; it is engineering.

1. 1.Test the same task with and without goal framing. Run your most common AI task both ways and compare outputs honestly. The difference will probably convince you faster than any article will.

1. 1.Stop treating AI tools as a single tier. GPT-5.6, Claude, Gemini and others are not interchangeable for every task. Start paying attention to which model performs better on your specific use cases, not just which one you have a subscription to.

1. 1.Invest time in prompting before investing money in tools. A better prompt on a free-tier model will often outperform a lazy prompt on a premium one. That is the lesson hiding inside all of this research.

1. 1.Follow the technical developments, even loosely. You do not need to read every paper. But knowing that prompt structure now demonstrably affects mathematical reasoning tells you something about how seriously to take your own AI instructions.