Could you say something about why your subjective probability distribution for the difficulty is so tight? I think it is very hard to predict in advance how difficult these problems are; witness the distribution of solution times for Hilbert’s problems.
Even if you’re right, I think that says that we should try to quickly get to the point with a serious large programme. It’s not clear that the route to that means doing focusing on direct work at the margin now. It will involve some, but mostly because of the instrumental benefits in helping increase the growth of people working on it, and because it’s hard to scale up later overnight.
My distribution isn’t tight, I’m just saying there is a significant probability of large serial depth. You are right that much of the benefit of current work is “instrumental”: interesting results will convince other people to join the effort.
Could you say something about why your subjective probability distribution for the difficulty is so tight? I think it is very hard to predict in advance how difficult these problems are; witness the distribution of solution times for Hilbert’s problems.
Even if you’re right, I think that says that we should try to quickly get to the point with a serious large programme. It’s not clear that the route to that means doing focusing on direct work at the margin now. It will involve some, but mostly because of the instrumental benefits in helping increase the growth of people working on it, and because it’s hard to scale up later overnight.
My distribution isn’t tight, I’m just saying there is a significant probability of large serial depth. You are right that much of the benefit of current work is “instrumental”: interesting results will convince other people to join the effort.