alt Hacker NewsI'm with @nilesh on this one, and not exactly sure how merely the existence of a solution precludes the advancement of human knowledge. If a problem is "solved" (say, symbolically verified) without any insights gained, it doesn't seem very interesting to the profession.
Navier-Stokes is a bit different (because there's a prize attached, so "scooping" matters), but almost all interesting problems don't have any prizes attached.
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Humanity is very biased for the culmination of work, considering everything that comes before and after busywork for the lower masses.
Replicating a paper is just as valuable scientifically as publishing it, but how many careers advance through replication?
If we move the goal from "find the solution" to "clear up the LLMs work" that doesn't bode well neither for the attractiveness of the problem nor for the career of the professional that takes the challenge.
More of a 'its the journey' rather than the destination type of thing.Since the insights , quirks, tricks and procedures gained along the way allows insights intoother at that moment unknown problem/domains in the future.
As far as researchers sharing their data/notes with the AI hyperscalars looks like that would be coming to an end wihth a mor guild-like structure going forward to prevent their progress being fron-run by the AI labs.
Mathematicians will be less likely to work on a problem if there is a solution - even an incomprehensible one.
Why was there a prize attached to this problem then? What does humanity get out of this being proved?
Current career structure of mathematicians works partially by looking at whether they have solved novel and interesting problems, or at least done theory-building that can help solve such problems. Many mathematicians are also motivated by being the world's first to solve such problems
Removing this measure suddenly means that academic mathematic norms need to adapt rapidly, and, even more importantly, intrinsic motivation for many mathematicians needs to change rapidly. That is understandably a sea change for the current mathematics community.
An AI-generated solution always provides two pieces of info:
Maybe the solution is pretty inscrutable, but it's almost always better than nothing.So, both of these pieces of info would be at least marginally useful for advancing human knowledge.