An example would be my Matrix Multiplication example (https://youtu.be/5DDdBHsDI-Y). Here, a series of 4 key insights turn the problem from requiring a decade, to a year, to a day, to a second.

In fact Strassen’s algorithm is worse than textbook matrix multiplication for most reasonably sized matrices, including all matrices that could be multiplied in the 70s. Even many decades later the gains are still pretty small (and it’s only worth doing for unusually giant matrix multiplies). As far as I am aware nothing more complicated than Strassen’s algorithm is ever used in practice. So it doesn’t seem like an example of a key insight enabling a problem to be solved.

We could imagine an alternate reality in which large matrix multiplications became possible only after we discovered Strassen’s algorithm. But I think there is a reason that reality is alternate.

Overall I think difficult theory and clever insights are sometimes critical, perhaps often enough to more than justify our society’s tiny investment in them, but it’s worth having a sense of how exceptional these cases are.

I’m imagining the first marginal unit of effort, which you’d apply to the most likely possibility. Its expected impact is reduced by that highest probability.

If you get unlucky, then your actual impact might be radically lower than if you had known what to work on.