I'll respond/comment on the parts I hope are relevant to you, in no particular order: Yes, a proof is a proof regardless how you get there. We however don't he

I'll respond/comment on the parts I hope are relevant to you, in no particular order: Yes, a proof is a proof regardless how you get there. We however don't hear about when they fail, and I doubt their 10000 agents (from their own statement) would necessarily reach another solution/proof (this by leaning towards using user data after finding out others were close). They could as well have attacked another Millenium problem, but they didn't. In whichever case, we will have to wait and see if they (either company) can reach novel solutions/proofs without significant amount of human provided data for the LLM to bridge the gaps. Further, and this is more of a policy opinion/prediction: If the numerable obtainable (albeit very hard) problems are solved, assuming training data is needed, will it push out future researchers from entering the field due to lack of reachable goals, thus cutting off future training data? LLMs have been great at replacing gateway jobs. But those jobs are what leads to frontier training data (be it maths, physics, chemistry, economics, graphics, prose, etc).