Kevin Buzzard runs an EPSRC-funded project at Imperial College to formalize Fermat’s Last Theorem in Lean, the language proof assistants use to check mathematics line by line. The grant is £1 million across five years. Last Friday Anthropic published a machine-checked formalization of the same theorem, produced by Claude in eleven days, and Buzzard posted his reaction on his own blog.

I was given £1M to run my project over 5 years; Anthropic took only 11 days but I do wonder if they spent more money…

The arithmetic is public, and it answers him.

Anthropic’s research write-up states the scale without decoration. Claude generated 13 million lines of Lean and proved 30,300 intermediate theorems, 29,500 of which the final proof uses. The artifact is more than five times the size of Mathlib, the community library every serious Lean project builds on. Lean verified the result using only its three standard axioms , and a comparator confirmed the theorem statement matches Mathlib’s own wording of it. The run consumed about six billion output tokens.

The model was an internal research version the company describes as roughly comparable to Claude Fable 5.1. Anthropic’s published output rate for that model is $50 per million tokens . Six billion output tokens at that rate invoice at roughly $300,000, and output is the cheaper half of a real bill. Input and cached context are billed separately, and what a company pays itself is not what it charges a customer. As an order of magnitude the figure holds: about a third of Buzzard’s five-year grant, spent in eleven days.

Human mathematical input was limited to occasional high-level direction from Tianyi Peng, the Columbia researcher whose Prove2Me platform coordinated the agents against a directed graph of theorem statements.

Anthropic is unusually plain about what this is not. The company writes that what is novel here is the verification, checking a proof the way you would check a calculation with a calculator. Andrew Wiles completed the proof in 1994. Nothing about the mathematics changed last week, and Buzzard, who has more standing on this than almost anyone, wrote that “mathematically this work of anthropic tells us essentially nothing.”

That is the whole point, and it is why the cost is interesting rather than embarrassing.

Five weeks ago OpenAI published new results on ten problems that specialists had not moved in at least a decade, with machine-checkable Lean certificates attached to every one. The company put the token cost at about $2,000.

Set the two numbers beside each other. Ten genuinely new mathematical results cost roughly two thousand dollars to produce. Mechanically confirming one result the field has accepted for thirty years cost something on the order of three hundred thousand. The expensive part of the work is not finding the answer, it is putting the answer in a form that does not require trusting whoever produced it.

For a reader trying to make sense of those two figures at once: discovery is now close to free, and proof is where the money goes.

The Workload Nobody Forecasts

Compute demand estimates are built almost entirely on generation. Users asking questions, agents writing code, models producing text that a person eventually reads. The Fermat run measures the other workload, and it came in far above anything the generation side of the same problem would have cost.

Enterprise deployment stalls at exactly this seam. MIT’s NANDA researchers found that 95% of corporate generative AI pilots produced no measurable profit and loss impact, with most organizations still short of production. Model quality is rarely the binding constraint. A business cannot ship output it has no way to check, and human review stops scaling long before the output does.

Mathematics is the easy case. Lean will accept or reject an argument at no charge once the argument is written down, which is a free oracle most commercial work does not have. Everywhere else the checking apparatus has to be built first, and building it draws on the same infrastructure the generation does.

That reframes what the data center buildout is actually being underwritten against. The contracted capacity now being signed in multi-year blocks is priced off forecasts of how much people will ask models to do. The larger and far less modeled line is what it costs to establish that the models did it correctly. Chip design and cryptography sit at the visible edge of that demand because their proof obligations already existed. The rest of the economy has to construct the oracle before it can use one, and that construction is itself a compute purchase.

Six billion tokens bought no new knowledge. They bought certainty about knowledge that was already thirty years old, and certainty is the line item the demand forecasts leave out.