When a large language model solves a math problem, it turns out the model is not thinking in terms of "algebra" or "geometry." It is thinking in terms of technique.
Researchers tested eight open math-capable models against five reasoning benchmarks using a generation-replay protocol: have a model solve a problem, replay its own prompt-plus-solution trajectory, then extract activation-importance signatures from the reasoning tokens. Clustering those signatures without supervision produced groups that beat random baselines in all 40 model-source combinations tested. Two independent frontier-LLM judges rated 77 to 82 percent of the resulting clusters as coherent by approach, versus just 6 to 11 percent for control clusters built from the same topic. When researchers explicitly asked models to use a different reasoning approach, cluster assignment shifted in seven of eight model conditions, while simply rephrasing a question left it unchanged.
This matters because nearly every math benchmark in wide use, from GSM8K to MATH, is organized by topic: algebra, geometry, word problems. If models are actually routing computation by method instead, a benchmark or training set that is carefully balanced across topics can still be badly skewed across reasoning approaches without anyone noticing. That is a blind spot baked into how the field measures and trains math ability.
It is a reminder that the categories humans find intuitive for organizing a subject are not necessarily the categories a model builds for itself.