TechPrufer
Get started
Anthropic
Anthropic logoAnthropic · Feature trail

AI-assisted Mathematical Formalization

3 posts · Mar 2026 – Oct 2026

What this trail covers

Anthropic is developing and refining methods for AI-assisted scientific discovery, including protein design and analytical chemistry. Recent work has focused on leveraging large language models like Claude to autonomously design protein binders against multiple targets with high success rates, and to accelerate chemical analysis by processing raw NMR and LC-MS data. This demonstrates Claude's ability to significantly reduce the time and computational expertise required for complex scientific tasks. This post extends this work to the development of 'BootLoops', a toolkit for exact calculations in quantitative science, enabling Claude to find and solve 'Claude-shaped' problems across diverse scientific fields like ecology, population genetics, and linguistics by leveraging its broad knowledge, coding skills, and mathematical/statistical capabilities. The focus is on resolving the 'impedance mismatch' between human scientists and current LLMs by building harnesses that suit LLM strengths, leading to novel scientific insights and computations.

All Anthropic trails
  1. Claude-shaped scienceThis post introduces 'BootLoops', a toolkit designed to harness LLM capabilities for exact calculations in quantitative science. It details how the author collaborated with Claude to identify and solve 'Claude-shaped' problems, which are problems well-suited to LLM strengths like broad knowledge, coding proficiency, and mathematical/statistical abilities. The work demonstrates the application of BootLoops to diverse fields beyond physics, including ecology and population genetics, by mapping mathematical and computational techniques across disciplines. The post highlights the iterative process of tool development and problem-solving, emphasizing the need for domain experts to steer LLM-generated insights towards scientifically significant questions. It also discusses the 'impedance mismatch' between human scientific workflows and current LLM capabilities, and proposes BootLoops as a solution to bridge this gap.
  2. How Claude is uplifting biomolecular modelingThis post details how Anthropic used Claude to optimize over 30 deep learning models for biomolecular tasks (structure prediction, protein design, genomics, protein language models), achieving an average speedup of ~4x with minimal precision loss, and nearly 2x with identical outputs. It also describes the creation of a low-memory 'Big' mode enabling accurate modeling of systems larger than 10,000 tokens on a single GPU node. The post highlights the development of custom kernels (FlashPairformer) to accelerate triangle attention and multiplication operations in structure prediction models, outperforming existing standards. The optimized code for these models is open-sourced.
  3. Formalizing Fermat's Last TheoremThis post details the first end-to-end, computer-checked proof of Fermat's Last Theorem (FLT) generated by Claude autonomously over 11 days. It involved writing 13 million lines of Lean code and proving 29,500 intermediate theorems. The process leveraged a multi-agent harness and the Prove2Me platform for managing theorem DAGs, optimizing Lean compilation, and enabling search/reuse. This work demonstrates AI's capability to formalize complex mathematical proofs, significantly reducing the time and effort compared to human efforts, and highlights the potential for AI to assist in verifying mathematical literature and AI-generated mathematics.
  4. How Claude is accelerating protein design and analytical chemistryThis post details Anthropic's advancements in using Claude for protein design and analytical chemistry. For protein design, Claude (Mythos Preview and Opus 4.8) achieved hit rates of 22-35% against 14 out of 15 targets, with some designs binding significantly tighter than existing benchmarks. This involved Claude orchestrating specialized protein design and folding models, performing optimization, and computational screening. For analytical chemistry, Claude Opus 5 processed NMR and LC-MS data, delivering finished results in 19-23 minutes, matching lab analysis for hydrogen counts and purity. The work highlights Claude's ability to autonomously execute complex scientific tasks with minimal human intervention, reducing the time and expertise required.
  5. Learning more about Claude's mathematical capabilitiesThis post details how an unreleased research version of Claude improved a longstanding lower bound for the fraction of zeros of the Riemann zeta function satisfying the Riemann hypothesis, increasing it from 41.6% to 67.2%. The method involved combining existing mathematical techniques (Aryan, Baluyot, Goldston, Suriajaya, Turnage-Butterbaugh, Bombieri) and leveraging Claude's ability to explore a suitable space of functions with quadratic forms. The process involved Claude subagents coordinating, running numerical checks, and independently re-proving the finding, culminating in a Lean formalization. This showcases AI's potential to extend mathematicians' ideas and accelerate scientific discovery.
  7. Making Claude a chemistThis post details Anthropic's initial work in making Claude proficient in chemistry, specifically focusing on its performance in analyzing NMR spectra. It benchmarks Claude Opus 4.7, Opus 4.6, and Sonnet 4.6 against dedicated software (ChemDraw, MestReNova) for both forward prediction (structure to spectrum) and inverse prediction (spectrum to structure). Opus 4.7 demonstrated competitive or superior performance to existing tools in predicting peak positions, matching splitting patterns, and accurately elucidating structures from spectra alone, even for complex molecules with hints. The post also identifies limitations and future research directions, such as evaluating a wider range of chemical scaffolds, solvents, and 2D NMR experiments.
  8. Evaluating Claude’s bioinformatics research capabilities with BioMysteryBenchThis post introduces BioMysteryBench, a new benchmark designed to evaluate AI capabilities in bioinformatics research. It details the challenges of evaluating scientific research (method subjectivity, data noise, lack of canonical tests) and how BioMysteryBench addresses them by using messy, real-world data with objective, ground-truth answers derived from controllable data properties. The benchmark allows for method-agnostic evaluation, enabling creative problem-solving by the AI, and can generate 'superhuman' questions. The post presents results showing Claude's rapid improvement in scientific capabilities and its ability to solve problems that human experts found difficult, sometimes using novel strategies.
  9. Vibe physics: The AI grad studentThis post details a guest professor's experience using Claude Opus 4.5 to conduct a theoretical physics research calculation, resulting in a high-energy theoretical physics paper in two weeks. The process involved extensive prompting (over 110 drafts, 36M tokens) and demonstrated Claude's capabilities in speed, indefatigability, and eagerness, while also highlighting the essential role of domain expertise for accuracy evaluation. The experiment suggests that while AI is not yet performing end-to-end science autonomously, it can be guided to perform frontier science through carefully crafted prompts, marking a significant methodological advancement.