Has OpenAI shared any new interesting _problems_? I.e. do more than strip-mine mathematics, as said in the article, but said: "Here is a question I cannot answer, it's interesting for this and that reason, I believe it's true for this and that reason, it's beyond me though, have at it." Has that happened yet?
I'm in this boat too and I find it a bit strange that this hasn't been more emphasized by mathematicians themselves.
So far, a lot of the hullabaloo has been around solving legacy problems, but more interesting and more important for actually progressing mathematics is the generation of new insight and new problems. Someone had to pose all those problems OAI is solving in the first place, in some cases, ages ago.
The collective letter response to navier strokes, sort of touched on this, but still didn't really emphasize the epistemic value of problem generation explicitly. I find it sort of strange that this has been so underemphasized.
I think their expectation is that “problems” as we’ve understood them just won’t be nearly as important to mathematical research going forwards. The field will look more like e.g. economics, where progress sounds more like “developed our understanding of the microeconomic foundations of macro” than “breakthrough on the Coase transaction cost problem in five dimensions”.
I've never heard a particular reason why the Millennium Problems were of special interest. They had resisted solution despite significant effort, but I don't know if Riemann or Navier and Stokes had ever singled those out as especially high priorities. They started as ordinary problems and became known for their durability.
So I'm not sure if it's something we should expect from a machine, just because we don't expect it from mathematics either. Maybe the machines will interrupt that process because we've changed how we go about looking, but perhaps not because old problems are solved.
In order to celebrate mathematics in the new millennium, The Clay Mathematics Institute of Cambridge, Massachusetts (CMI) established seven Prize Problems. The Prizes were conceived to record some of the most difficult problems with which mathematicians were grappling at the turn of the second millennium; to elevate in the consciousness of the general public the fact that in mathematics, the frontier is still open and abounds in important unsolved problems; to emphasize the importance of working towards a solution of the deepest, most difficult problems; and to recognize achievement in mathematics of historical magnitude.
It then goes into details in each of the chosen problems.
Considering that this is where the mathematician excels over machine wouldn’t that only offer a new view from such a mathematician that “OpenAI has rapaciously stolen from mathematics that last dignity: of choosing worthy problems”? Perhaps with sufficient effort the community of mathematicians may yet forestall such an effort.
