Harvard physicist Matthew Schwartz’s Anthropic guest post on BootLoops: an open-source harness that steers LLMs toward checkable, quantitative “Claude-shaped” problems across physics, ecology, genetics, and more—with human experts supplying scientific taste.

Claude-shaped science

Guest post by Prof. Matthew Schwartz — Oct 1, 2026 — Anthropic

Summary

In this guest post, Prof. Matthew Schwartz returns to describe a new approach to AI-accelerated science. In Vibe Physics, Schwartz discussed similarities in capability between Claude and a physics graduate student. Here, he describes what happened when he stopped fighting Claude and allowed Claude to find “Claude-shaped” problems: ones best suited to the capabilities of the current generation of LLM tools. This led him to build BootLoops, a toolkit for exact calculations in quantitative science. Because similar calculations often turn up across very disparate areas of science, Claude found connections to ecology, population genetics, and a dozen other fields. These connections were often technically correct but scientifically unremarkable at first, so Schwartz worked with domain experts to steer BootLoops toward questions those fields care about.

Impedance mismatch

Agentic AI is improving rapidly. Everyone notices the models seem smarter: they know more, make fewer mistakes, and have better ideas. If you follow the trend lines, it is easy to speak confidently about the potential of AI to revolutionize science. However, academic scientists trying to use the models today in their own work often feel a disconnect. The models may be solving challenging and longstanding problems, but so far these have mostly been well-scoped applications of existing techniques. Many of the headlines seem to be in mathematics, the one part of science where a problem can be stated completely and an answer checked absolutely. But most of science is not like that.

The core conflict, as I see it, is that although these models are brilliant, working like a human scientist is not what current LLMs do best. Claude and GPT are good at science, but they are not scientists: yes, they are smart, but it can take a lot of hand-holding to get them to produce anything of scientific value. Physicists would call this an “impedance mismatch”: two systems that each work fine but are poorly matched, so most of what one puts in never gets through to the other.

BootLoops

I started looking for examples where the impedance mismatches are less acute. I began by having Claude build an accessible suite of tools for mathematical physics. Before long, the tools found uses for other problems. This iterative process generated a set of software and scientific protocols, which I call BootLoops. BootLoops functions as a kind of harness for the LLM, much like Claude Code or Claude Science is a harness for Claude, or Codex is a harness for GPT. I’ve found BootLoops especially well-suited for a class of quantitative problems in science. It is also open-source, so it can be used with whatever model you like.

The current generation of AI tools is not capable of solving most problems in science. However, they are astonishingly good at certain “agentic-AI-shaped” problems.

Once Claude had BootLoops, it kept noticing the same pattern: many fields have problems that a technique from mathematics, physics, or computer science would solve outright if anyone knew it existed. I started calling these “Claude-shaped” problems, and followed them outside high-energy theoretical physics—my home turf—into geology, biology, economics, and linguistics. In these other areas, I could not rely on my own expertise to know whether what Claude found was interesting. So I found some experts and asked. With their guidance, BootLoops was able to make substantive advances in many research areas.

Claude, take the wheel!

Last December, I tried using Claude as a research assistant, and found that Claude Opus 4.5 performed like a strong graduate student at 20 times the speed. Despite Claude producing a high-quality paper at the end of the experiment, it was a slog to get there.

This summer, I tried doing something different: instead of treating Claude like the collaborator I wanted it to be, I started to treat it like the collaborator it actually is. This required looking for problems suited to its strengths. Right now, Claude is just not able to help me with deep conceptual questions—but it does have a virtually unlimited breadth of knowledge across all domains, incredible coding skills, leading-edge knowledge of mathematics and statistics, and the ability to parse papers, appendices, and data at machine speed.

A natural place to start looking for Claude-shaped problems was in areas where coding could help. When Anthropic released Claude Fable 5 in Summer 2026, I wanted to see whether its cyber capabilities would translate to scientific computing. So I sought to test it by having it port, code up, and improve various methods from a handful of my papers and the adjacent literature on scattering amplitudes.

The semi-numerical bootstrap seemed ideal for agentic AI. It draws on mathematics, physics, and computer science that no one person has mastered; it needs a great deal of coding and algorithm development; and it is checkable, since the same numerics let anyone, expert or not, verify the final answer against the integral to as many digits as they like by running two scripts.

Claude did this effortlessly. I was surprised when it reproduced the results from my paper in around 20 minutes, while the code I wrote to do it took me weeks. However, I was not surprised when it informed me that I was doing something very inefficiently and that there was a better algorithm I was unaware of.

Then, I asked Claude to search for unsolved amplitudes it could compute… and later to generalize to elliptic functions. Soon we had 30 integrals BootLooped from end to end, comprising 15 reproductions of known results by this new method and 15 that had never before been computed.

Cross-field applications

A serendipitous feature of science is that the same equations often appear over and over again in different contexts. Claude was happy to tell me that these integrals could also map onto Bayesian evidence integrals in population genetics, or that the finite-field methods used for Feynman integral reduction could also apply to problems in evolutionary biology.

As projects drifted from my professional comfort zone, I brought in experts. In almost all cases, Claude was technically correct, but the result was not all that interesting until the expert helped steer us.

Highlights described in the post include:

Ecology / neutral biodiversity theory — solving Etienne’s equation at scale with James O’Dwyer, then subtracting the neutral prediction to study selection/competition.
Population genetics — with Michael Desai, analyzing billions of mutation pairs for gene conversion evidence.
Economics — an AI data editor porting replication packages of 4,452 papers.
Linguistics — AccStack stress database covering 6,072 languages.
Additional work in phylogenetics, earth science, genomics, sunspots, mathematical physics, cosmology, and statistics.

Overall: iterative improvement of BootLoops, searching for Claude-shaped applications, and pushing to the scientific frontier with experts. More at bootloops.ai.

Outlook

No matter how smart the models become, most scientific progress comes from real-world data that has to be acquired, understood, and checked, with each round informing the next question. AI can sit inside that loop, and that is genuinely valuable, but it does not collapse the loop to a point.

Schwartz argues BootLoops shows that if you find the right problem, much of the technical work of solving it can now be automated—but humans are still needed for the conceptual part and for scientific taste.

Disclosure

During this project, Schwartz has been working as a visiting researcher at Anthropic. BootLoops is not an Anthropic project; it is owned and maintained by Matthew Schwartz.

*Original: https://www.anthropic.com/research/claude-shaped-science*