A translator who has never been in a meeting translates literally, and loses half the meaning. They don't know that the boss's nod means "do it like last time," and the phrase "well, we'll see" is a polite refusal. That's how a language model that writes code from a scientific paper works: it can read the equations, but not the unspoken agreements.

The authors decided to test whether AI can be taught to extract these hidden rules from the text. They took two problems from many-body quantum physics — a field where there are so many particles that counting them one by one is pointless. For the first, simpler problem, a human and a machine together created a detailed specification: which indices go where, what sign goes before the term, in what order to multiply. After that, the program worked in all sixteen variants. Without such preparation — only in six out of thirteen.

The second problem was a tough nut to crack. It required restructuring a complex mathematical construct, and there were more hidden rules: signs, calibrations, order, size constraints. Even after jointly creating the specification, the programs worked in only eleven out of twenty-six cases. And without preparation — not a single one.

A curious detail: specifications created by one model were perfectly implemented by another, but not the other way around. This means the problem is not only in understanding the paper but also in the model's ability to write correct code. Two bottlenecks.

This approach is not just a way to get a program. It's also a diagnostic tool: it shows where exactly AI stumbles. And perhaps it will hint at how to make models smarter.