AI just claimed three open problems in science. Revisit your too-hard list.

On 26 October OpenAI announced that its models had produced three new results at the frontier of science. In harmonic analysis, a proof of Sogge’s local smoothing conjecture in every spatial dimension — previously settled only in lower dimensions. In computer science, a claimed disproof of the Exponential Time Hypothesis, a conjecture an enormous body of complexity theory leans on. In physics, a claimed mathematically rigorous existence result for quantum chromodynamics. Rather than simply posting papers, OpenAI asked senior researchers in each field to act as “shepherds” for the release, and they chose different routes: the maths material went public straight away, while the physics group held its result back to write its own interpretation.

None of this has been independently verified yet. MIT’s Ryan Williams told reporters that researchers were “working to verify and examine their proof”, and noted that even a confirmed result would have no short-term practical applications. The University of Rochester’s Alex Iosevich, whose doctoral adviser formulated the smoothing conjecture, called it a “historic development”. Both reactions are worth holding at once. Whatever the final verdict on each proof, the announcement marks a shift that matters well outside universities: frontier models are now being pointed at problems nobody knows the answer to, and the claim on the table is that they are sometimes solving them.

Why a maths proof matters to a business

Most companies do not have a stalled conjecture on their roadmap. But nearly every company has a short list of problems it has quietly filed under “too hard”: a pricing model nobody has been able to make work, a forecasting problem that never got better than a spreadsheet, an engineering constraint that has been accepted for years, a dataset everyone suspects holds an answer nobody has had time to find. Those problems were deprioritised for a rational reason — the cost of the expert time needed to crack them was higher than the expected payoff.

What the last two years have shown, and what this announcement pushes further, is that the cost of serious analytical effort is collapsing. A model that can be pointed at an open problem in harmonic analysis can certainly be pointed at your gnarliest operational question, run hundreds of approaches in parallel, and come back with candidates for a human expert to test. The economics of “too hard” have changed, and most companies have not re-run the numbers.

The part that does not change: verification

The most instructive part of OpenAI’s announcement is not the results. It is the release process. The company did not just publish; it recruited domain experts to decide how each result should be checked and presented, and it acknowledged that choosing those experts created what it called an “asymmetry of information”. In other words, even the organisation that built the model treated its output as a claim to be verified, not a fact to be shipped.

That is the right instinct for any business using AI on hard problems. A model that can produce a novel proof can also produce a confident, elegant, wrong one. On a research problem, the cost of error is a retracted preprint. On a pricing model, a credit policy or a safety calculation, it is money or harm. The organisations that get value from AI-generated analysis will be the ones that build the checking in from the start:

• Every AI-generated finding gets a named human owner with the expertise to judge it, before anyone acts on it.
• Claims come with their working. The data used, the method, the assumptions — so a reviewer can check the reasoning, not just the conclusion.
• Results are tested against reality before they are trusted. Back-test the forecast, pilot the pricing change on a segment, run the engineering change in staging.
• Disagreement is expected. If two models, or two runs, reach different conclusions, that is information, not noise.

Re-running the “too hard” list

The practical response to this news is not to buy a research model. It is to revisit your roadmap with new assumptions about what analysis costs. We do this with clients as part of an AI Strategy engagement: we pull together the problems that were parked because they needed too much expert time, estimate what each would be worth if solved, and assess which ones are now tractable with AI doing the heavy exploratory work and your experts doing the judging. The output is a short, ranked list of bets, each with a defined verification step and a clear point at which you stop if it is not working.

The pattern we see is that the best candidates are rarely the most glamorous. They are problems where the company already holds good data and has an expert who can recognise a right answer when they see one, but has never had the hours to search the space properly. Those are exactly the conditions under which AI exploration plus human verification works — and exactly the conditions OpenAI chose for its own announcement.

The honest counter-argument

Scepticism is warranted. These are claims, not confirmed results, and the history of AI is full of breakthroughs that looked smaller once experts finished checking. Even confirmed, the maths result has no near-term commercial use, as the experts themselves say. And research mathematics is an unusually friendly domain for AI: the problems are precisely stated and a proof is either valid or not. Most business problems are messier, the data is worse, and “correct” is often a matter of judgement. It would be a mistake to read a proof in harmonic analysis as evidence that a model can fix your supply chain.

All true. Our point is narrower. The direction of travel is clear even if any individual claim falls over: the cost of exploring hard problems is dropping, and the bottleneck is moving to verification and judgement. Companies do not need to believe every headline to act on that. They need to know which of their parked problems are worth another look, and to have the expert review in place before they start.

What to do in the next 30 days

• Write down your “too hard” list. Five to ten problems that were parked because they needed more expert time than they seemed worth.
• Attach a value and an expert to each. What is it worth if solved, and who internally could tell a right answer from a plausible wrong one?
• Pick one with good data and run a time-boxed exploration. Let AI generate approaches; let your expert test them.
• Define the verification step before you start. Decide what evidence you would need to act on the result.

Whether or not the Exponential Time Hypothesis survives the next few months of scrutiny, the lesson for business is already here. Hard problems are getting cheaper to attack. The scarce resource is no longer the hours to explore; it is the expertise to know which answer is right. Companies that pair the two deliberately will find answers their competitors stopped looking for.

Got problems your team parked as too hard? Talk to Cravings about re-running your roadmap — we identify which parked problems AI now makes tractable, rank them by value, and design the expert verification that makes the results safe to act on.