Mostly they teach various theorems and their proofs, so that you can “stand on the shoulders of giants”, and they try to train your “intuition” (incommunicable heuristics) by exercise in proving simple theorems.
More advanced math courses teach explicit heuristics (in the form of “proof strategies”: general patterns that are often found in proofs), which can be programmed in an automated theorem prover to some extent, but they are not good enough to make up for the lack of human-level intuition.
On the other hand we know excellent heuristics for chess, in the form of position evaluation functions that give an higher score to positions which are more likely to lead to a victory. The chess piece relative value heuristic, for instance, is extremely simple and yet very effective. High-level computer chess programs use much more complicated evaluation functions, but chess piece relative value is usually the dominant component of it.
Mostly they teach various theorems and their proofs, so that you can “stand on the shoulders of giants”, and they try to train your “intuition” (incommunicable heuristics) by exercise in proving simple theorems.
More advanced math courses teach explicit heuristics (in the form of “proof strategies”: general patterns that are often found in proofs), which can be programmed in an automated theorem prover to some extent, but they are not good enough to make up for the lack of human-level intuition.
On the other hand we know excellent heuristics for chess, in the form of position evaluation functions that give an higher score to positions which are more likely to lead to a victory. The chess piece relative value heuristic, for instance, is extremely simple and yet very effective. High-level computer chess programs use much more complicated evaluation functions, but chess piece relative value is usually the dominant component of it.