alt Hacker NewsThis is great.
But how incremental are these advancements?
I picked one at random (B.2 -- the second autocorrelation inequality). Then, I looked up the paper that produced the previous state of the art (https://arxiv.org/pdf/0907.1379). It turns out that the authors had themselves found the upper bound by performing a numerical search using "Mathematica 6" (p.4). Not only did the authors consider this as a secondary contribution (p.2), but they also argued that finding something better was very doable, but not worth the pain:
"We remark that all this could be done rigorously, but one needs to control the error arising from the discretization, and the sheer documentation of it is simply not worth the effort, in view of the minimal gain." (p.5)
So at least in this case it looks like the advancement produced by AlphaEvolve was quite incremental (still cool!).
Replies
Yeah for the kissing number stuff people can find slight improvements if they want. It usually isn't worth it because it provides no insight. But maybe when you generate a lot of them one or some family will turn out to be interesting.
not worth the time for a human, but if you can throw AI at all of those "opportunities" it adds up substantially because all the chores can be automated.
If this is not the beginning of the take off I don’t know what is.
Merely from your telling, it seems it is no longer "not worth the effort", as "the effort" has been reduced drastically. This is itself significant.