Reasoning training helps math but can hurt medicine — because some domains need new facts, not sharper thinking.

This is really a question about matching the training method to what a domain is missing — new facts, or better handling of existing facts. The sharpest anchor in the corpus is the finding that LLMs store knowledge in their lower layers and do reasoning in their higher layers Why does reasoning training help math but hurt medical tasks?. That physical separation is the whole answer in miniature: reasoning-focused training (long chains of thought, RLVR) tunes the upper layers and reliably helps math, where the facts are trivial and the work is all inference. But the same training can *degrade* knowledge-heavy domains like medicine, because it doesn't add the facts those domains actually lack — and can disturb the retrieval that was working.

So the dividing line is: does the domain fail because the model can't reason, or because it doesn't know? Math, logic, and code puzzles are reasoning-bound — and strikingly, base models often already contain the reasoning latent, so 'training' there is really *elicitation*, selecting a capability that's present rather than installing one Do base models already contain hidden reasoning ability?. Medicine, law, and niche technical fields are knowledge-bound: no amount of reasoning polish substitutes for facts absent from pretraining. The hardest evidence of that ceiling is prompt optimization — it can only reorganize what a model already knows and cannot inject anything new Can prompt optimization teach models knowledge they lack?. If clever prompting fixes your domain, it was a reasoning/activation problem all along.

For genuinely knowledge-bound domains, the corpus is opinionated about *how* to inject. Structure beats volume: StructTuning hits half of full-corpus performance on 0.3% of the data by teaching where a fact sits in a domain taxonomy rather than drilling raw text Can organizing knowledge structures beat raw training data volume?, and medical knowledge-graph curricula compose primitive facts into domain 'superintelligence' the same way Can knowledge graphs teach models deep domain expertise?. There's a menu of injection mechanisms — RAG for flexibility, fine-tuned weights for speed, adapters for swappability — each optimizing a different deployment constraint, and combining them beats any single route How do knowledge injection methods trade off flexibility and cost?. And purely tacit, data-only learning without any explicit structure leaves gaps in interpretability and out-of-distribution robustness that a little structured knowledge cheaply closes Does refusing explicit knowledge harm AI system performance?.

Here's the part you didn't know you wanted to know: the two goals interfere, and the standard trap is injecting knowledge with the wrong tool and silently wrecking reasoning. Plain supervised fine-tuning is the culprit — it raises benchmark accuracy while cutting the quality of the actual inferential steps by ~39%, so the model reaches right answers by post-hoc rationalization instead of real reasoning, and ordinary metrics never notice Does supervised fine-tuning improve reasoning or just answers?. The corrective is to inject knowledge *through* reasoning: RL-from-augmented-generation rewards both the correct answer and a coherent explanation, internalizing facts as reasoned structure rather than memorized tokens, and outperforms SFT precisely because it refuses to separate the two Can reinforcement learning embed domain knowledge more effectively than supervised fine-tuning?.

Which reframes the original either/or. Reasoning-focused RL used to be confined to domains with checkable answers (math, code), but verifier-free methods now extend it to open knowledge domains by scoring how well reasoning predicts a reference answer Can reasoning improvement work without answer verification? — so even fact-heavy fields can get reasoning training. The real caution isn't the injection-vs-reasoning split; it's that reasoning models still wander unsystematically and collapse on deep problems Why do reasoning LLMs fail at deeper problem solving?, and that every adaptation method has a narrow domain-specific sweet spot with hidden costs outside it How do domain training techniques actually reshape model behavior?. The competent move is to diagnose first — is the domain short on facts or short on inference? — and then, wherever possible, inject the facts in a form that trains the reasoning at the same time.