Imagine that careful examination of the mineshaft helps determine where the most profitable place to dig next might be... And then imagine a machine that only p

Imagine that careful examination of the mineshaft helps determine where the most profitable place to dig next might be... And then imagine a machine that only produced mine shafts that tell you nothing. Sometimes the machine might be very useful! It would allow scaling up solutions for downstream users. For example, if you have more people who want solutions to many slightly-different complicated integrals that we don't have a good overarching theory to solve. But in other cases, knowing /where/ to dig is much more important than how fast you dig.