Their rules PDF says they won't accept any solution until at least two years after publication in a qualifying outlet. This allows time for the mathematical community to review and accept new results.
As the OpenAI proof hasn't been officially published yet, the clock hasn't started ticking.
If the Lean initial-problem-setup/statements/assumptions/etc. aren't correct then the proof is meaningless. Lean does not know what it is that it is proving i.e. it does not have any semantic understanding but only executes formal logic.
In my opinion, I think the Clay Mathematics Institute deserves some criticism for all the drama surrounding these problems. Mathematicians know that you can make problems arbitrarily complex, and declaring problems with large prizes attached to them can lead to a lot of competition and drama. I feel that mathematics should be free from competitions and the pursuit of glory.
However, after reading the open letter signed by 25 Fields Medalists, I became quite concerned. It feels like the mathematical world is changing very rapidly, almost overnight.
I used to think that before AI, you could spend your entire lifetime working on some of the hardest problems in mathematics. If you were an introvert or someone who enjoyed solitude, all you really needed was a pencil, some paper, and an eraser. You could spend years thinking about a problem, and if you were lucky enough to make a breakthrough, it would be your own journey.
Now AI is changing that. I wonder what this means for the kind of mathematics that people have traditionally done.
Mathematics has given us so many stories of lonely geniuses and their passions, people like Andrew Wiles, Grigori Perelman, and Yitang Zhang. Their stories are interesting because they show how deeply personal mathematics can be. They spent years working on problems because they were genuinely interested in them.
I am worried that we might slowly lose some of that side of mathematics as AI becomes more powerful. I do not think change is necessarily bad, but I think it is worth thinking about what mathematics should be in the future and whether it can still remain a deeply personal pursuit of curiosity and understanding.
> In my opinion, I think the Clay Mathematics Institute deserves some criticism for all the drama surrounding these problems. Mathematicians know that you can make problems arbitrarily complex, and declaring problems with large prizes attached to them can lead to a lot of competition and drama. I feel that mathematics should be free from competitions and the pursuit of glory.
Currently 0/2 Millenium problem solvers claimed the prize money so clearly money is not their motivation for tackling the problem.
> Today, CMI shares in the excitement of the global mathematical community as we contemplate the announcement that the Navier-Stokes problem has apparently been settled. We hope to see waves of new human understanding unleashed as the innovations behind this work are analysed and interrogated.
sounds like they are providing notice that the clock has started on affirming the solution, that it IS presumptively solved, but that they are not commenting on the credit dispute nor the fields medalists open letter. seems appropriate.
"In recent years there has been an increasing sense of anticipation as breakthroughs in the surrounding field (some recognised by the Clay Research Award) have raised hopes that the Navier-Stokes problem might soon be resolved. The increasing ability of new technologies to accelerate mathematical research has heightened this sense of anticipation."
It's worth mentioning that OpenAI will not be eligible for the Millennium Prize for quite a while. Per the rules listed https://www.claymath.org/wp-content/uploads/2022/03/millenni... , Clay Mathematics Institute have some requirements to make this process deliberately slow.
1) The solution must be published in a qualifying outlet, i.e. a peer-reviewed math journal. Publishing on your own website (which is what OpenAI did) or posting arXiv does not count.
2) At least two full years must pass after publication in a qualifying journal, before CMI will even consider evaluating it. The intent is to give the maths community time to scrutinize the solution.
Realistically, they'll be eligible for a prize ~2.5 years from now, or around 2029.
> The ultimate decision as to whether a publication qualifies as a “Qualifying Outlet” shall reside in the sole and unfettered discretion of CMI. CMI may, in its discretion, relax or remove one or more of the conditions listed in Section 6(e) above if it has received advice from experts in the field of the Problem, chosen by CMI, that a published solution is likely to be correct.
Looks like even a blog post is good enough, they just need to do the review by themselves.
> The rules governing the prizes describe the process for evaluating what has been achieved and for assigning credit. The process is deliberately unhurried, but we will provide updates.
My opinion is that it is pretty clear that they’re not going to do that.
The Poincaré conjecture guy also broke that rule. They wanted to give him the prize anyway but he refused. OpenAI announced they would also not claim the prize.
As the OpenAI proof hasn't been officially published yet, the clock hasn't started ticking.
Edit: Oh, didn't see the "qualifying outlet" condition. But Poincare was ever just put on arXiv, so arXiv must count as well.
Did OpenAI Really Solve It? What the Lean Proof Proves and What It Doesn’t - https://www.youtube.com/watch?v=eu_TYYWxkgc
However, after reading the open letter signed by 25 Fields Medalists, I became quite concerned. It feels like the mathematical world is changing very rapidly, almost overnight.
I used to think that before AI, you could spend your entire lifetime working on some of the hardest problems in mathematics. If you were an introvert or someone who enjoyed solitude, all you really needed was a pencil, some paper, and an eraser. You could spend years thinking about a problem, and if you were lucky enough to make a breakthrough, it would be your own journey.
Now AI is changing that. I wonder what this means for the kind of mathematics that people have traditionally done.
Mathematics has given us so many stories of lonely geniuses and their passions, people like Andrew Wiles, Grigori Perelman, and Yitang Zhang. Their stories are interesting because they show how deeply personal mathematics can be. They spent years working on problems because they were genuinely interested in them.
I am worried that we might slowly lose some of that side of mathematics as AI becomes more powerful. I do not think change is necessarily bad, but I think it is worth thinking about what mathematics should be in the future and whether it can still remain a deeply personal pursuit of curiosity and understanding.
Currently 0/2 Millenium problem solvers claimed the prize money so clearly money is not their motivation for tackling the problem.
That “apparently” feels load-bearing
The statement is so sterile they don't even mention who solved it. The word "OpenAI" doesn't appear at all.
Keyword: New Technologies
1) The solution must be published in a qualifying outlet, i.e. a peer-reviewed math journal. Publishing on your own website (which is what OpenAI did) or posting arXiv does not count.
2) At least two full years must pass after publication in a qualifying journal, before CMI will even consider evaluating it. The intent is to give the maths community time to scrutinize the solution.
Realistically, they'll be eligible for a prize ~2.5 years from now, or around 2029.
OpenAI and Anthropic might have 3 millennium problems by December
Looks like even a blog post is good enough, they just need to do the review by themselves.
My opinion is that it is pretty clear that they’re not going to do that.
The Poincaré conjecture guy also broke that rule. They wanted to give him the prize anyway but he refused. OpenAI announced they would also not claim the prize.
Looks like no one wants this prize lol