https://www.claymath.org/millennium-problems

1 was solved - the Poincare conjecture - by Grigori Perelman. There are 6 remaining.

There are 17ish years left before this market closes.

Apr 4, 1:51am: ~~Will at least 4 of the 7 Millennium Problems by solved by 2040?~~ → Will at least 4 of the 7 Millennium Problems be solved by 2040?

## Related questions

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.

@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.