Show a chess master a position from a real game for five seconds, take the board away, and ask for it back. Most of the pieces will come back correctly. A beginner given the same five seconds will place four or five.
The obvious explanation is memory, and the obvious explanation is wrong. In an experiment first run in the nineteen seventies, the same masters were shown boards with the pieces randomly scattered — positions that could never occur in a game. Their advantage almost entirely disappeared. They placed about as many pieces as the beginners did.
What the master has is not a bigger memory. It is a vocabulary of familiar chunks — a castled king with its three pawns, a knight and bishop working together. Where the beginner is holding twenty-five separate facts, the master is holding five or six familiar shapes. Take the shapes away and there is nothing left to hold.
The same thing happens on a page of algebra. A beginner reads a long expression symbol by symbol and runs out of room. Somebody who has met the shapes before sees three or four recognisable groups and works with those. That is not talent. It is exposure — the same shapes, met often enough that the eye stops spelling them out.