Scott Armstrong

Scott Armstrong

@scottnarmstrong · Twitter ·

I disagree with this. Obviously the openAI construction of the Navier-Stokes blow up is a huge, huge contribution to the field. It will take us PDE analysts some time to understand it well. (Longer than a week, but perhaps less than a month.) Soon some of us will understand it, and hopefully rewrite it in a way that others can follow. When this is done, our human understanding of these important equations will be past the bottleneck we've been stuck at for 100 years since Leray. What is weird is that, up until now, proofs like this have always emerged AFTER human understanding. But that is not the case any more. From now onwards, human understanding will typically lag the proofs, which will first be written by our machines. The understanding however WILL follow closely behind. The reason people are upset has nothing to do with the fact that this process is inverted. They are simply upset that the machines are going to be much smarter and more capable than us. (They are also upset that the humans who got the machine to produce the proof don't understand it, and this feels very unfair to them.)

Itai Sher

Itai Sher

Imagine that I taught a class and I said, “what matters is truth. So we are not going to waste time with explanations in this class. Instead we will use the semester to list everything that is known in the field.” This is what some of the discourse about AI in math is like.