Data centers use evaporative cooling, not closed loop. You can't really scale up in a closed loop system. Evaporative utilizes a ton of water.
As for point 3, supercomputers have been assisting with scientific problems for decades now. This isn't new, just new tech applied. Your article is actually the best way to use AI, imo. It will be better at finding patterns in data than humans will ever be.
But my point is to say would it have been able to discover that those math problems existed in the first place?
No. The answer is no.