Also according to Bill Gates. But that calculation is wrong in an important way. In fact (AFAICT) it currently costs something on the order of $1000 x N to save some large number of lives N via any single method whose efficacy has low variance in the number of lives saved.

If you're willing to use a lot of different methods and only fund them up to some relatively low limit, you can save a lot more expected lives per dollar - but the cheap methods aren't always scalable due to (e.g.) not enough people with an easily cured fatal disease, and if you're spending enough money the costs of finding all of the cheap unscalable methods may be fairly high.

If you're willing to accept a high variance, like p=0.9 of saving no one and p=0.1 of saving tons of people, you can save a lot more expected lives per dollar - but you're a lot more susceptible to error here, since these methods often don't have nearly as many data points that show p is really 0.1 and not 0.001.