Claude-shaped science

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. Below, we share more about these projects and how BootLoops came about.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. And for many of us researchers and students, the distance between those headlines and what happens when we use these models can leave us frustrated and anxious.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. Here, the mismatch is between what scientists want and what AI does well. So how can we fix it?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. Below, I share how BootLoops came about, describe some early findings in areas where I have been applying it, and share some of my thinking on how to resolve the impedance mismatch between human and AI scientists today.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. I had to correct every sentence it wrote, steer it away from irrelevant threads, and pull it back from dead ends.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.Scattering amplitudes are how we interpret data from the Large Hadron Collider: smash two protons at 13 trillion electron volts, and the amplitude is the theoretical bridge between the debris and whatever new particle, a Higgs boson or something unknown, the collision produced. At their core are Feynman diagrams, multidimensional integrals of a particular form. The ones we are struggling with now can each be a PhD thesis, or occupy a group for years.Over the past 20 years an alternative has grown up: the S-matrix bootstrap. In the bootstrap approach, instead of grinding out the integral, you impose physical constraints until only one answer is possible. Knowing where the amplitude is infinite (its “singularities”) might narrow it to 20,000 options; a symmetry cuts that to 500; and so on down to one. The traditional bootstrap is purely analytic and has gone furthest in the most symmetric theories, where the constraints reach all the way to a single option (the nine-loop amplitude in N=4 super-Yang–Mills is an example). Closer to the real world you often run out of constraints before the end. A newer pivot, the semi-numerical bootstrap, closes the gap when you can also compute the amplitude at a handful of points to absurd precision (sometimes 1,000 digits): if few enough options remain, those numbers pin down the remaining coefficients exactly.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. The community's expertise is also unevenly distributed: good ideas sit in Wolfram Language, C++, Python, or Julia, and many more sit in papers with no code at all. So my first assignment for Fable 5 was to port all of it to a common framework, and to write the code the papers never provided.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. It turns out that problems that are simple enough for the S-matrix bootstrap are also simple enough for humans to do—and, indeed, most have been done. It nevertheless found a few unsolved problems. After some discussion with the model, it became clear that Claude was limiting itself to amplitudes with the simplest family of functions: logarithms. So I asked, could it do the same thing for the next simplest family, elliptic functions?Elliptic integrals are really hard, even for people like me who spend a lot of their time computing integrals. Only a handful of elliptic Feynman integrals have ever been computed, and none completely by the bootstrap, at least to my or Claude’s knowledge. The issue is not that the methods wouldn’t work, but rather that nobody had tried, since the expertise needed to do so is distributed among many humans. Claude, by contrast, easily generalized all of the machinery it had ported and built for the logarithmic case to these other integral classes. This time it wrote most of the software itself, or borrowed it from mathematics rather than physics. As the toolkit grew, it started to land one integral after another. 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.That was all after only a few weeks. Initially, I thought I would be satisfied just to do a write-up on that, but I was too tempted to see what else we (that is, me and Claude with BootLoops) could do.“I know Kung Fu”A serendipitous feature of science is that the same equations often appear over and over again in different contexts. In physics, for example, the diffusion equation, Fokker-Planck equation, and Schrödinger equation all have the same mathematical form, so if you develop a method to solve one problem, you can often apply it to many others. I knew that computations BootLoops was good at were relevant elsewhere: in cosmology and string theory, for example. What I didn’t know, but Claude was happy to tell me, was 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