Scrying is staring hard at one thing, in order to try to find out about another. In the occult origins, it’s often a mirror or glass, viewed under darkened conditions to inspire hallucination.
I like this framing, but there’s some detail that I see as key here. When famous math problems are stated, usually what’s really going on is a bet that solving the problem will require working out a theory that lets you understand an area better. The problem is then meant to focus your efforts in a way that you hope will necessarily increase your general abilities.
This isn’t just a math thing, by the way. When learning new skills, it’s often useful to give yourself a specific goal (like “I am reading this physics textbook so that I can code up a physics simulation”), even when the goal is not the real point. If you were trying to build a rocket before modern science, “Let’s have a third of you figure out how to predict the motion of objects, a third to build a really tall tower, and the rest will make really big explosions” is a plausible plan to figure out the requisite physics/materials science/chemistry.
The bet can be a bad one, for example if a conjecture can be disproven by using standard techniques applied in standard ways then you haven’t really learned what you wanted to.
I suspect that the recent AI proofs have a higher number of cases like this, and I’ve seen some mathematicians say that this is what happened. However, I’m wary of trusting them, because many seem biased enough that they’d downplay the results.
I like this framing, but there’s some detail that I see as key here. When famous math problems are stated, usually what’s really going on is a bet that solving the problem will require working out a theory that lets you understand an area better. The problem is then meant to focus your efforts in a way that you hope will necessarily increase your general abilities.
This isn’t just a math thing, by the way. When learning new skills, it’s often useful to give yourself a specific goal (like “I am reading this physics textbook so that I can code up a physics simulation”), even when the goal is not the real point. If you were trying to build a rocket before modern science, “Let’s have a third of you figure out how to predict the motion of objects, a third to build a really tall tower, and the rest will make really big explosions” is a plausible plan to figure out the requisite physics/materials science/chemistry.
The bet can be a bad one, for example if a conjecture can be disproven by using standard techniques applied in standard ways then you haven’t really learned what you wanted to.
I suspect that the recent AI proofs have a higher number of cases like this, and I’ve seen some mathematicians say that this is what happened. However, I’m wary of trusting them, because many seem biased enough that they’d downplay the results.