The obvious mathematical breakthrough would be development of an easy way to factor large prime numbers.
Bill GatesYou wish that you could move more rapidly and you have setbacks. You know, the AIDS epidemic was a huge setback for Africa, and it's only through generosity that we've avoided that just completely crippling an entire generation there.
Bill GatesThe most straightforward path would be if we could bring the cost of solar electric and wind down by another factor of say, three, and then have some miraculous storage solution, so that not only over the 24-hour day but over long periods of time where the wind doesn't blow, you have reliable energy. That's a path. But energy storage is hard. That's not a guaranteed path.
Bill Gates