What are the Seven Millennium Problems and Their Significance in Mathematics?

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The discussion revolves around the Seven Millennium Problems in mathematics, highlighting the Yang-Mills theory, Navier-Stokes equations, and the Poincaré conjecture. The Poincaré conjecture was recently solved by Grigori Perelman using techniques involving Ricci flow, originally developed by Richard Hamilton. Participants express skepticism about explaining these complex theories in detail, with some humorously suggesting that a book would be a better resource. There is also a light-hearted exchange about solving the problems and the qualifications of mathematicians likely to tackle them. Overall, the thread emphasizes the significance of these unsolved problems in mathematics and the community's engagement with them.
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Hi,
Does anyone know about the Seven Millennium problems, if yes can anyone explain to me the yang mills theory, navier stokes equation and the poincare conjucture in great detail:smile:
 
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I recommend you read: Keith J. Devlin - The Millennium Problems

Some of them are pretty much taken but if you solve the other ones it's a million a pop. :smile:

The latest one solved is the Poincaré conjecture using surgery procedures with a difference on Ricci flows. Grigori Perelman came up with that, but Ricci flow came from Richard Hamilton.

See also the http://www.claymath.org/millennium/"
 
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Milind_shyani said:
Hi,
Does anyone know about the Seven Millennium problems, if yes can anyone explain to me the yang mills theory, navier stokes equation and the poincare conjucture in great detail:smile:

Yes get a book. Explain those is great detail to you? I swear this is some kind of joke lol.
 
Gib Z said:
Yes get a book. Explain those is great detail to you? I swear this is some kind of joke lol.

I swear you are some kind of a joke. He didn't say in detail, so it's a fair call.
 
Actually he did, so the second part of my post can die.
 
theperthvan said:
Actually he did, so the second part of my post can die.
But you are going to leave the insult?
 
I think he said it jokingly...
 
Yeah I did.
How about "my whole post can die".
 
yangs mill theorem:

Given a paper mill that prints ying yang water-marked rice paper with a water wheel that has radius r, paddle size x by y, in a river whose flow is described by a differential equation of third order wrt position in the river, how many pieces of paper can it churn out an hour?
 
  • #10
Office_Shredder said:
yangs mill theorem:

Given a paper mill that prints ying yang water-marked rice paper with a water wheel that has radius r, paddle size x by y, in a river whose flow is described by a differential equation of third order wrt position in the river, how many pieces of paper can it churn out an hour?

None. The mill didn't comply with the city's Feng Shui code, so it was closed down. :biggrin:
 
  • #11
Actually I have a slightly more serious question regarding the Yang Mills problem. What type of mathematician will most likely solve it? i.e. a pure mathematician or a mathematical physicist? If the former an analyst, topologist or an algebracist?
 
  • #12
Well, who can say really, but it is a problem in mathematical physics...
 
  • #13
actually i have solved 5 of them, but the word length limit here prohibits me from posting the solutions. And since I care nothing for fame, I also decline to submit them for refereeing. I may include them in coded form in my next comic book.
 
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  • #14
mathwonk said:
actually i have solved 5 of them, but the word length limit here prohibits me from posting the solutions. And since I care nothing for fame, I also decline to submit them for refereeing. I may include them in coded form in my next comic book.

Have you considered donating the proofs to charity? There are mathematicians around the world starving for theorems, adopt a mathematician.
 
  • #15
mathwonk said:
actually i have solved 5 of them, but the word length limit here prohibits me from posting the solutions.

This reminds me of the ship that didn't sink with Hardy :wink:
 
  • #16
mathwonk, I looked through your comic book, and only three of those proofs are correct. In particular, you twice state the Miller-CoorsTheorem with incorrect hypothesis
 
  • #17
yes, i keep forgetting, is it less taste? or more filling?
 
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