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Fermat's Last Theorem Shows Which Work AI Takes Over First

By , Senior AI ConsultantPublished

Claude Fable 5.2 formalized Fermat's Last Theorem in 30 hours because a computer could check every step, which shows which kinds of work AI agent teams will take over first.

Anthropic has released Claude Fable 5.2, an upgrade to its top model that costs less than the version before and is open to every user. It is made for long jobs, where one model hands pieces of the work to hundreds of copies of itself and collects what they produce. The best demonstration of what it can do also shows which jobs those agent teams can finish and which they cannot.

A proof that a program checks, not a person

Formalizing a proof means writing it so a program can accept or reject each step. That is why it suits agents. When a team of 1,000 Fable 5.2 agents formalized Fermat's Last Theorem, they started from short prompts and worked out their own way of dividing the work. Their only guide was a list of intermediate results, and the checker told them how many of those they had proved so far. It did two jobs: it caught every error, and it told the team how far along it was.

The September run took 11 days and needed a purpose-built setup and a human researcher's guidance. This one took 30 hours with minimal human help, used a third of the tokens and produced a proof seven times shorter. The same setup run on the cheaper Opus 5.5 reached 26% of the proof after 18 hours and barely moved after that.

There is one fair caution. The September run built on groundwork that Buzzard's team had already published, so the human effort did matter. But the part that was slow and expensive, writing and checking tens of thousands of steps, went to the agents.

Most office work has a smaller version of the same check

You already have checkers in your own work. A column of regional sales must add up to the company total. A salary deposit must match the bank statement. An invoice must match a purchase order and a delivery note. In Anthropic's tests the model caught exactly these kinds of mismatches, such as regional figures that did not sum to the reported total.

For example, a distributor that receives 2,000 supplier invoices a month might spend five minutes matching each one by hand. That is about 165 hours, more than a month of one person's time. An agent team could match every invoice against its order and delivery note, while a simple script confirms that the totals tie. Say one invoice in ten does not match. The clerk then reviews 200 invoices, each with the mismatch already named, which is about 17 hours. The clerk's judgment still decides what to do about a short delivery, but the clerk no longer spends time on the 1,800 that match.

Work without a checker will move more slowly

A hiring decision, a pricing strategy or a letter to an unhappy customer has no program that says whether it is right. A person has to read all of it, so the speed of the work is the speed of the reading, and a faster model does not change that. Agents will still help with this work, but a human will stay in the loop much longer.

This also tells you where to put your effort. The teams that gain most will turn their judgment into checks a computer can run: a rule that every refund over a set amount has a reason code, or a test that every customer reply names the order number. Writing those rules is cheap and does not need AI.

Fable is not the model for most of this. For everyday work, the cheaper Opus 5.5 is still the better place to start, and Fable earns its price of $8 per million input tokens and $40 per million output tokens on jobs that run for hours. On a coding test, Fable 5.2 at High effort matched Opus 5.5's best result for roughly half the cost per task. Mythos 5.2, the same model without the cybersecurity and biology safeguards, is open only to vetted security and biomedical organizations.

Before you hand any job to an agent, write down how you would know it was done right. If you can turn that answer into a check a program runs, the job is ready to hand over.

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