The incentives to mine are: newly created coins and the transaction fees. Even when all coins are mined, the transaction fees still belong to the miner.
mskryxz: the algorithm behind Bitcoin (SHA256) is useless for "genome, dna, ai, weather modeling". ASICs are not reprogrammable, the algorithm in them cannot be changed.
I am asking when all 21 million coins are found though....who's going to mine then?