Automated computational science could accelerate discovery by selecting, adapting and developing numerical methods. This prospect requires mathematical knowledge that AI systems can interpret and reuse with explicit guarantees.

Here we present FARMS, a faithful and efficient foundation that transforms computational mathematics into AI-ready computing knowledge. FARMS connects formal statements to source context, algorithmic meaning and quantitative guarantees through source preparation, reusable representations and semantic review.

Across 171 targets in randomized numerical linear algebra and numerical partial differential equations, 157 were accepted by the pipeline, with mean estimated costs of US $0.85-2.29 per target across sources. Lean-checked implications from explicit source premises connect selected statements to computational skills, illustrated by a heat-flow solve and wave-response compression.

FARMS therefore supports an affordable, reusable knowledge foundation for trustworthy automated computational science.