| This 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!). |