Claude helped a physicist draft 36 manuscripts in 18 fields

At one point Claude told physicist Matthew Schwartz that its proof was finished apart from "one unproven lemma," and that lemma turned out to be the whole proof. Schwartz tells the story in a guest post on Anthropic's blog, next to a tally of 36 manuscripts in 18 fields with 19 coauthors over three months.

At a glance

• Schwartz stopped treating Claude as the scientist he wanted and went looking for "Claude-shaped" problems, where a known technique from math, physics or computer science would solve another field's question outright.
• His engine is BootLoops, an open-source harness for exact calculations that Claude built under his direction; with it, Claude solved an ecology equation nobody had handled at scale for 20 years.
• The catch, by his own account: results were usually technically correct but scientifically unremarkable until experts steered them, and one ecologist predicted his field would meet a result with a shrug.

If you missed the first installment: last December, in an Anthropic post called Vibe Physics, Schwartz used Claude Opus 4.5 as a research assistant. It performed like a strong graduate student working 20 times faster, but he had to correct every sentence it wrote. This summer, with Claude Fable 5, he changed tactics and treated Claude as the collaborator it actually is.

Claude reproduced in about 20 minutes results that took Schwartz weeks to code

Schwartz's home field is scattering amplitudes, the theory linking debris from Large Hadron Collider collisions to the particles those collisions produced. The hardest Feynman integrals here can each fill a PhD thesis. The S-matrix bootstrap avoids grinding them out: you impose physical constraints until only one answer remains.

Think of a game of twenty questions. Knowing where the amplitude goes infinite might leave 20,000 candidates, and a symmetry cuts that to 500. When the constraints run out, the semi-numerical variant computes the amplitude at a few points to absurd precision, sometimes 1,000 digits, and the remaining coefficients come out exactly.

Fable 5's first job was porting the field's methods, scattered across Wolfram Language, C++, Python and Julia, into one framework, plus writing the code papers never provided. It reproduced the results of Schwartz's paper in around 20 minutes; his own code had taken weeks. He then pushed it from logarithms to elliptic functions, and within a few weeks 30 integrals were solved end to end: 15 reproductions of known results and 15 never computed before.

A 20-year-old ecology equation fell, and the ecologist shrugged

Neutral biodiversity theory asks how much of an ecosystem's history comes down to chance. In 2001 Stephen Hubbell suggested, provocatively, that perhaps all of it does. In 2005 Rampal Etienne gave the idea a precisely testable equation, but for 20 years nobody could solve it at scale. Claude recognized it as BootLoops-shaped and solved it.

Applied to Barro Colorado Island in the Panama Canal, ecology's most studied forest, the result showed the mix of tree species changing 4.5 times faster than neutral theory allows. Plant biologist James O'Dwyer said it would likely "be met with a shrug by many ecologists," who already knew qualitatively that neutral theory can't keep up with real forests.

His better idea was to subtract the neutral prediction and study the remainder: selection, competition and differences between species. Working with Claude, Schwartz and O'Dwyer built a minimal predictive model of life histories that Schwartz says is in excellent agreement with data.

5.7 billion mutation pairs turned up evidence for gene conversion

Population genetics followed the same arc. Claude used methods from mathematical physics to solve a 30-year-old integral for how natural selection shapes rare mutations, and applied it to gnomAD, the largest public catalog of human genetic variation. Michael Desai, the colleague Schwartz recruited, was impressed by the technique but not by the science.

At Desai's suggestion, the team looked at correlations between pairs of mutations on a single chromosome. Claude added inequality certificates from computer-assisted proofs to the kit, and an analysis of 5.7 billion nearby pairs from the 1000 Genomes Project found evidence for gene conversion, a mechanism nearly every analysis of linked genetic variation ignores.

Other projects drifted toward more general Claude-shaped work. With two economists, an AI data editor ported the replication packages of 4,452 papers in five leading journals to open-source code, some 30,000 routines, and checked essentially every validatable number; the results appear in an NBER working paper. With three linguists, Claude built AccStack, a word-stress database covering 6,072 languages, plus a bibliography of 160,000 phonology works.

Each project runs in its own Claude Code session, with a master session on top

The 36 manuscripts came out of some 400 candidate problems. Claude Code sessions run in terminals on Google Cloud virtual machines, one per project, and a master session coordinates them, allocates compute and validates results. Subagents run the computations in the background and keep intermediate results in markdown files.

The subagents serve a mundane purpose: Schwartz regularly runs into Fable 5's classifiers, and a block then shuts down one agent rather than the whole session. Think of circuit breakers in a house, where one tripped breaker leaves the other lights on. Because compaction made Claude lose context, he has it consolidate its files so the latest plan stays within reach.

Supervision never goes away. After three days of work Claude announced that "the formula is solved. Two years of campaign, four deep marches." Its time estimates were far too long or far too short, and it would rather grind through a multiday calculation than build a tool that does the job in minutes. Schwartz's rule of thumb: "Done, with one asterisk" is often "not done at all."

All of these results are Schwartz's own report, several projects are still under exploration and verification, and he warns that automated checks can't be trusted. He worked as a visiting researcher at Anthropic during the project, though BootLoops is owned by him, not Anthropic. In our view, the 19 coauthors are the most honest number in the post: in almost every case Schwartz describes, Claude's result became interesting only after an expert steered it.

Whether the forest model travels

The next concrete test is in ecology. Schwartz and O'Dwyer are extending their model from Panama to other global forest plots, using datasets Claude helped curate, and no date has been given for those results. The BootLoops harness is on GitHub for anyone to use with whatever model they like, so how well it performs in other hands remains an open question.