A Mathematician Lurking in the TechUnderWorld

A Mathematician Lurking in the TechUnderWorld

Stop ruining your job with LLMs, do this instead

Three cognitive lanes, one factor analysis on hundreds of professional cases, and clean rules for picking your winner among GPT-5, Claude, or Gemini

Jose Crespo PhD's avatar
Jose Crespo PhD
Apr 30, 2026
∙ Paid
The first cognitive-lane classification of LLMs.Figures, animations, diagrams, and plots were created by the author using Stable Diffusion, Blender, and Python libraries.

Oh no, another LLM guide?

I can understand that reaction. By now, everyone has seen too many of them, and you probably expect to find here another crowded table, another pointless ranking propped up by whichever benchmark fits the headline.

No. Forget it. Here you will not see another childish contest pretending to decide which LLM is the smartest, which is the cheapest, which writes the best code, or which sounds the most human. Most of that is BS when it comes to the thing that really matters to you: getting the damn job done in the best possible way.

So yes, you are lucky. Your frustration is welcome here, and what you are about to read is the first cognitive map of the frontier, the one built from your real work rather than from leaderboards.

The Cards on the Table

Pay attention now, please, because this is where we are saying bye-bye to the non-scientific LLM classifications you see most of the time.

First, mathematics separates the chaff from the grain. Then the real work begins: I take 24 related LLM skill variables extracted in turn from hundreds of cases in professional environments with LLMs (the details of this first varimax are not shown here), run the rotation, and extract the three cognitive factors that actually predict which LLM is best suited to the task you need to solve. The animation below shows what came out.

Watch 24 LLM skills collapse into 3 cognitive factors.What you are seeing is the math doing its work. The varimax rotation turns the three axes through the cloud until each one lines up with a natural direction already present in the data, while the cloud itself stays fixed. As that happens, the messy bundle of LLM skills, verbal ability, reasoning, mathematics, and the rest, condenses into three explanatory cogntive factors or lanes that account for nearly 63% of the variance in the full set of variables..

You have the diagnosis. The cure is behind the paywall: the decision rules, the routing patterns, and the multi-model sequences that turn the three lanes into countless hours saved and a lot of unnecessary pain avoided. Subscribe to unlock the rest.

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