In September 2026, mathematician Kevin Buzzard published a post titled “FLT: Anthropic has beaten me to it”. He had been leading a project with a five-year grant to formalise the mathematics behind Fermat’s Last Theorem. Anthropic had just reported a complete computer-checkable proof produced during an 11-day Claude run. Buzzard compiled and checked it himself. Buzzard’s assessment .
The projects had different goals, and Claude built on existing mathematics and formalisation work. Even with those qualifications, this is a striking change in what a machine can help researchers accomplish, and how quickly.
A company can make the same timing mistake without ever publishing a forecast. It only has to assume that next year’s tools will be a slightly better version of the ones it tried last year. That assumption shapes budgets, hiring, software purchases and the projects a team decides are still too expensive to attempt. Decisions can be out of date before they are implemented.
We expect many AI predictions to keep underestimating the pace of change. The larger business risk is the comfortable amount of preparation time those predictions seem to offer.
We have already explored the operating consequences in Hyper-Agile : when implementation gets faster, the bottleneck moves toward deciding what to build and judging whether it works. The same shift applies to planning. Teams need to update their assumptions at something closer to the speed at which the tools are changing.
The next improvement starts from a higher base
Linear progress adds roughly the same amount each time. Exponential progress multiplies what is already there. A capability that doubles through six equal intervals goes from 1 to 64. Extending the first increase as a straight line would get you to 7.
METR’s March 2025 study provides evidence for a specific version of this pattern. It found an approximately seven-month doubling time in the human-duration of software and reasoning tasks frontier agents could complete with 50% reliability over its historical measurement period. That measures progress on a defined task suite, rather than intelligence as a whole. METR’s study .
The business effects appear when that progress crosses useful thresholds. Completing a function, implementing a feature and working through a substantial project are different propositions for the person assigning the work. An improvement that looks incremental on a benchmark can change which jobs are worth attempting with an agent.
The hockey-stick image captures how this feels. Early gains seem manageable; later gains start changing the assumptions behind ordinary decisions. An exponential has no single mathematical take-off point. Our view is that we are already in the phase where the practical consequences are becoming difficult to ignore.
Five examples from 2026
Two of these examples directly compare dated forecasts with measured results. The others show research advancing faster than experienced people expected, or a result arriving within a window experts considered unlikely. They support an argument about compressed timelines, with different strengths of evidence. FRI cautions that early-resolving milestones bias interim reviews toward underestimation; some forecasts also overestimated progress. These selected cases cannot establish overall forecast accuracy. FRI’s review .
September: an 11-day run reached a major mathematical milestone
Fermat’s Last Theorem was proved by Andrew Wiles in the 1990s. Formalising a proof means translating its reasoning into a form a computer can check, including intermediate steps that mathematicians normally leave implicit.
Anthropic reported that Claude produced a complete formal proof in Lean during an 11-day run, using existing mathematical literature, libraries and parts of earlier formalisation projects. Buzzard independently checked that the code compiled and established the intended result. His own funded project had a broader goal of building reusable, readable mathematical infrastructure, using a different proof approach. Its five-year grant was therefore not a prediction that this exact machine-generated output would take five years. Anthropic’s report , Buzzard’s assessment .
May: hard programming problems left the forecast behind
LEAP experts’ median forecast put LiveCodeBench Pro Hard performance at 14% by the end of 2026 and 33% by the end of 2030. By May 2026, FRI reported a score of 53.8%. That surpassed both central expectations, although it remains a result on a particular programming benchmark. Original forecasts , May result reported by FRI .
February: cybersecurity overtook a 2028 forecast
The Forecasting Research Institute reports that experts expected AI to solve at least 90% of Cybench challenges in 2028; superforecasters expected 2030. Claude Opus 4.6 crossed the reported threshold in February 2026, scoring 93% on a 37-problem subset. This is benchmark performance, with a subset-comparability caveat, rather than a claim about arbitrary real-world attacks. FRI’s forecast review .
September: a Millennium Prize Problem reached the review stage
In a 2025 LEAP survey, AI experts assigned a median probability of just 10% to AI solving or substantially assisting with a Millennium Prize Problem by 2027. The probability rose to 20% by 2030. These problems represent major unresolved questions in mathematics. Original forecast .
In September 2026, OpenAI announced a proof resolving the Navier–Stokes problem after an 88-hour AI research run. The Clay Mathematics Institute subsequently described the problem as apparently settled and pointed to its evaluation process. As of 11 October, the evidence cited here establishes an announced proof and that response, rather than a completed prize adjudication. OpenAI’s announcement , Clay’s statement .
If the result withstands scrutiny, a milestone experts considered unlikely within the forecast window will have arrived in 2026. A single low-probability event does not establish that a probability forecast was poorly calibrated. It does show why planning only around the most likely timeline can leave an organisation unprepared.
July: cryptographic research advanced in 60 hours
HAWK, a proposed post-quantum signature scheme, had been through two rounds of expert review over roughly two years. Anthropic reported that Mythos Preview found an improved attack after 60 hours, with human guidance and validation involved. HAWK was a candidate scheme; the result did not amount to breaking deployed encryption. Anthropic’s research .
There was no published prediction that the next advance would take another two years. This is a capability surprise: an AI system helped extend specialist research on a problem that experts had already examined closely. Together with the mathematical work, it broadens the story beyond performance on coding tests.
The business may become the slower part
The common thread is that important milestones can arrive before the people watching them expect. A forecast that places a capability several years away can quietly become permission to postpone learning. If the capability arrives early, the preparation time disappears.
Consider two small companies evaluating the same tool. Both find that it struggles with a particular workflow. One records that AI is not ready and leaves the subject until next year’s strategy review. The other records exactly where it failed, prepares a repeatable test and tries again after a meaningful model update.
If capability crosses the threshold in the meantime, the second company is positioned to notice. It also has the context, evaluation method and operating experience needed to put the improvement to use. That advantage can grow through repeated cycles of testing and adoption.
Physical infrastructure, regulation and organisational change still constrain adoption. Software benchmarks cannot tell us how quickly an entire economy will change. For work that can already be carried out digitally, however, a long internal decision cycle can itself become the limiting factor.
The singularity question becomes harder to ignore
There is a further possibility: AI could accelerate the work that produces better AI. If increasingly capable systems help researchers design experiments, implement ideas and evaluate results faster, the improvement cycle could shorten again.
That feedback is central to the singularity hypothesis: technological progress accelerating so strongly that what follows becomes exceptionally difficult to predict. The long-discussed idea becomes more relevant as AI takes on more substantial technical work.
The examples here do not establish self-sustaining recursive improvement or a date for a singularity. Missed predictions alone also cannot prove an exponential trend. They give us a reason to examine measured progress and to take faster scenarios seriously.
Give assumptions a review date
A useful response starts with a real piece of work. Choose something the team has wanted to automate or build, record the present constraint, and define what a successful result would look like. Measure usable output, review effort, cost and reliability. Revisit it when the tools materially improve.
Keep the working context, tests and lessons from each attempt. That is the practical value of workflows : the next iteration can start with what the team has already learned. Faster tools become more useful when the surrounding workflow can improve with them.
The companies that benefit will be able to recognise a useful change and put it to work while their competitors are still relying on an old assessment. Which decision in your business depends on AI staying roughly as capable as it is today?