Uranium actually does not require mining. Most uranium is extracted using underground wells where water is pumped underground and the Uranium is extracted from the water. Also extracting Uranium from sea water (which would be basically unlimited) is close to being commercially viable and has received a lot of lab-scale research.
Also, Uranium is only recyclable once with light water reactors. With breeder reactors (which have been built in the past) it can be recycled a hundred times.
Also, Uranium is only recyclable once with light water reactors. With breeder reactors (which have been built in the past) it can be recycled a hundred times.