Can bitcoins be traced by pool workers?
When a miner in a pool finds a valid block, the pool receives a reward (currently ~50 BTC) in a special generation transaction in the block. The address receiving the generation reward in a given block is known, and pools publish statistics on which blocks they found (and even if not, the miner who found it can in theory know which blocks he himself found if his mining software keeps a record of it), so the generation rewards can be tracked (to the same extent that any other Bitcoin transaction can be tracked).

The mathematical operation done when mining is calculating SHA-256 hashes of variants of a block header. You can learn more about mining for example at What exactly is mining?