Out of the millennium prize problems, what one do you think is the most interesting/important?
I think the Riemann hypothesis, but P = NP is a close second.
I hope stokes doesnt get any strokes from this (well he can't, he must be dead), but i voted for RH, although possibly because it's the most popular one.
I don't know or understand many of them. I can't really vote on which is interesting.
Why not? I think the existence of turbulence on multiple scales is neat. Other interesting questions that arise from it is the idea of deterministic chaos.
I personally think that yang-mills theory is the interesting, but on a purely mathematical side i think the poincaré conjecture was also interesting
I think PvsNP is the most likely problem to inspire new mathematics.
It is also interesting from a practical point of view since all e commerce depends it being true (RSA public key encryption)
riemann hypothesis, no mathematician can deny this.
What about the hodge conjecture?
Which one of these millennium problems is the hardest one? From Hardest to Easiest?
How does one rank the difficulty of unsolved problems?
One does this by looking at what one has to do and the level of this mathematics. For example, hodge conjecture is from algebraic geometry, riemann hypothesis is from number theory, Yang-mills is a combination of quite alot and some of the mathematics does not exist, so that might rank more difficult because there is a very vague starting point.
The mathematics which described Fermat's last theorem looked simple but yet the math used to solve it was not simple.
touché, then in that matter, list it in order of most important/interesting. Also, how important/hard do you reckon the hodge conjecture is?
Without question the Riemann Hypothesis, especially considering all the useful results and theorems have been established provided that the Riemann Hypothesis is in fact true!
It is so stupid about how we all talk about these problems, pretending to ourselves we any idea what they really mean. The Riemann Hypothesis is the most famous and easiest to understand/state out of the problems (of course, just because the problem is easy to understand doesn't mean its easy to prove). Believe it or not, but the other problems are lead to interesting results.
I enjoy the P vs NP. Doing graph theory lately, and P vs NP comes up rather often and we naturally assume it's true, or as my professor says, "well, most of us feel it's P NP but hey who knows I can be teaching you bs for all you'll know."
the riemann hypothesis can eat the P versus NP
Good luck explaining the importance of RH to anyone who's not well versed in math. It is much easier to do so for P vs NP.
my question is why there isnt even one foundational (i.e metamathemtical) open problem worthy of claymath's money?
I have a somewhat layman question. Why are there not in the list the usual crackpot-attracting, simple-to-state problems in number theory? The 3n+1 conjecture, the twin prime conjecture, ... a closed form for primes? Are these considered less important than the Riemann hypothesis or the others?
(Personally, I'd love to see someone finding a way of adding two integers using only their prime factorization representation. One can dream.)
The 3n+1 problem can restated in terms of proving whether the "function" is partial recursive or total recursive, right? Is this connected to the halting problem in some way? Can we decide in general whether a recursive function is total? I'm still learning the recursion theory lingo.
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