Models Ace Math and Code. They Still Can't Write a Textbook.

Nathan Lambert has spent the last few years watching AI models get dramatically better at coding and math. Writing an AI textbook made him notice where they haven’t.

In his post “I wrote an AI textbook, how long until AI can do it better?” Lambert argues models have plateaued at long-form, non-fiction explanatory writing, the kind a textbook needs, even while their coding and math scores keep climbing. He writes that “organizing knowledge is a compression. This compression is needed to make insight,” and that current models instead “increase entropy in long-form non-fiction writing,” meaning their long explanations tend to add confusion rather than remove it.

Who Lambert is

Lambert writes Interconnects AI, a widely read newsletter on AI models and research. He was previously a senior research scientist and post-training lead (leading the fine-tuning stage that shapes a model’s behavior after its initial training) at the Allen Institute for AI (Ai2), where he worked on the open, publicly downloadable language model project Tülu, until leaving the organization in June 2026.

What he gets right, and where it’s more speculative

Lambert’s diagnosis of why long-form writing is hard is specific, not just a vibe. He argues models are good at checking small, self-contained units, whether a sentence reads well, whether an equation is correct, but struggle when many of those units have to build on each other across a long document without contradicting or repeating themselves. That matches a pattern builders using AI for documentation or reports will recognize: individual paragraphs read fine, but the whole document doesn’t hang together as one argument.

Where Lambert moves from diagnosis to prediction is his claim about what this means for AI doing real science. He argues that if models can’t yet organize “the most established science in their area” into a clear explanation, their ability to make genuinely new open-ended discoveries is limited too, predicting that “the progress of LLMs for science will look closer to solving low-hanging fruit” than to major breakthroughs. That’s a reasonable inference from his own writing experience, not something the post proves with a broader study. It’s his forecast, not a settled result.

Why it’s notable

Most public benchmarks (standardized tests used to score how good an AI model is) track coding and math because those are easy to score automatically: a program either passes its tests or it doesn’t. Long-form organizational quality is much harder to measure, so it gets less attention even though it’s exactly the skill needed for a model to explain its own reasoning, write documentation, or synthesize research findings into something a person can actually use.

What it means for builders

If you’re using AI to draft anything longer than a few paragraphs, a report, a spec, a set of docs, treat the output as a rough structure to edit, not a finished piece to publish. Read the whole document for whether it holds together as one argument, not just whether each paragraph reads smoothly on its own. That gap between sentence-level quality and document-level coherence is precisely the weakness Lambert is describing.

It’s also a reason to be skeptical of claims that AI agents can autonomously handle open-ended research or strategy work today. If a model still struggles to organize well-established facts into a clear explanation, treating it as capable of independent judgment on genuinely unresolved problems is premature.

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