What should one do who discovers after prayer that he prayed without ablution?

You must perform ablution and repeat the prayer if you prayed without purification, because purity is a condition for the validity of prayer. Scholars have reached a consensus on this, based on the Prophet's (peace be upon him) saying: "Allah does not accept the prayer of anyone of you if he passes wind until he performs ablution," and his saying: "No prayer is accepted without purification."