assuming no AGI/ASI, almost certainly P vs NP won't be solved by 2040. RH probably has the most thought put into it, but hasn't really budged and still lacks lots of crucial ingredients to attempt a proof.

Birch and Swinnerton-Dyer and Navier-Stokes have good partial results and probably the closest to be solved, still terribly difficult. Hodge and YM are also very unlikely

IMO unless AI deeply, deeply improves pedagogy in the next few years that gives everyone the ability to be some timelord super mathematician i dont see 3 of these being solved, and I'm not too convinced that current paradigm AIs will lead to a solution to any of these (admittedly 15 years is a long time for someone to find some new paradigm and make some supermachine)

P vs NP is almost universally considered the hardest of the 7. Next to zero chance it's solved by 2040. That means we need 3 out of the remaining 5

Navier-Stokes: most likely candidate. If it's false as many physicists suspect, I would expect we're able to find a counterexample before 2040. Otherwise it may remain unsolved

Birch and Swinnerton-Dyer: mathematicians have built up a good bit of the framework here, so it's possible but I'd give it a <50% chance.

Yang-Mills: the harder of the physics problems. Physicists have been at it for 50 years with little progress. Unlikely.

Riemann: the most famous of the 7. Results have come along the way which could be useful, but the workhorse of the proof has not been established. Unlikely

Hodge: I don't have the mathematics background to even understand the problem statement but I've heard it's the hardest of the pure math problems.

I know an online betting site is going to full of people that think AGI is coming tomorrow but AI is not going to be our savior here. It can do casework quite well but the millennium problems are not that type of problem. My credence is ~8% that this resolves YES. I'd put 2 out of 7 around ~50% and 7 out of 7 at essentially 0%

@SentientTree So what I'm seeing is:
- 1 already solved + 2 on average solved "naturally"
- I think AGI is coming >50% by ~2029/2031
- AGI can make ASI and/or improve math/physics progress a LOT in almost a decade
- AGI/ASI only needs to solve 1 "unnaturally" in that decade-ish
- This only whole chain only needs to occur slightly more than 50% of the time for a bet to be worthwhile

I believe in math ai

If any are proven to be something like axiom independent, or there exists a formal proof that the proof can't be known, do they count as "solved"

@Shahara Surely yes

This should be single digits at most.

@JureSmolar This website is full of people who think an AI eschaton is about to occur

Do you want any more shares at 40% @AdamK?

@Arky I put a 5k limit order up

@Arky Yup, thanks!

Ok i forgot to link the related markets but here they are:

I'm curious which problems the YES-betters here think have any significant chance of being solved within this timeframe. Personally, I'd put Navier-Stokes at probability ~30% and the rest at ~5% each, independently, which would put this market at <1%. I can see how one might put the probability at 5-10% with some slightly more optimistic estimates, but to bet on 40-50% you would have to believe in some kind of magic.

@sbares 5% I can fathom, but 5% independently? Hell no. There happens to be a pretty salient story for how the relative capacity for skilled mathematical research will shoot up by several orders of magnitude, in which case we'll get to watch these puppies fall ~simultaneously.

@AdamK There is a story, but not a believable one. I know it is a quite popular idea in the supposedly-rational-ist community that a magical piece of technology will in the near future attain essentially every capability you can think of, but I for one don't think that reifying such a hypothetical deity with a three-letter acronym name makes magic any more likely to exist. At any rate, it is certainly not ~40% likely to exist, which is what would be required to justify the level of discrepancy on this market.

@sbares You’ll make your bet, I’ll make mine. Let the sharper worldview win

@sbares Btw the market for at least 2/7 being solved is at 85%

@AdamK Nah, this is madness. Yang Mills isn't just a math problem, it requires fundamental advances in entire fields of theoretical physics that everyone agrees will take decades. You truly need an acausal robot god to emerge in the next 16 years for this to be true.

@Najawin Point taken on Yang Mills, but for the other problems, I put decent weight on a narrow system succeeding

I don't think there is necessarily a good reason to believe that Yang-Mills will require significantly more "theory building" than other unsolved Millennium problems. They're all so "hard" / still unsolved because they fall out of reach of existing methods and require significantly new insights and methods — new "theory". (Would bet in this direction if we worked to define "theory building" sufficiently to quantify it.)

@AdamK (And in particular, I'm at >83% that the system that solves all the other Millennium problems will also be capable of solving Yang-Mills, i.e. I don't think Yang-Mills has disproportionate chance of being the hardest one.)

@Lovre Those two things aren't synonymous. It can both be true that Yang Mills is easier than another one of the problems and that a system that solves all the other millennium prize problems is incapable of solving Yang Mills.