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

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SUMMARY

The Seven Millennium Problems are a set of seven unsolved problems in mathematics, with a reward of one million dollars for each solution. The Poincaré Conjecture, one of these problems, was solved by Grigori Perelman using Ricci flow techniques, originally developed by Richard Hamilton. The discussion also touches on the Yang-Mills theory and the Navier-Stokes equations, highlighting the interdisciplinary nature of these problems, which involve both pure mathematics and mathematical physics.

PREREQUISITES
  • Understanding of the Poincaré Conjecture and its significance in topology.
  • Familiarity with Ricci flow and its applications in geometry.
  • Basic knowledge of Yang-Mills theory and its relevance in theoretical physics.
  • Comprehension of the Navier-Stokes equations and their role in fluid dynamics.
NEXT STEPS
  • Research the details of Ricci flow and its implications in solving the Poincaré Conjecture.
  • Study the Yang-Mills theory and its applications in quantum field theory.
  • Explore the Navier-Stokes equations and their significance in fluid mechanics.
  • Read Keith J. Devlin's "The Millennium Problems" for a comprehensive overview of all seven problems.
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Mathematicians, theoretical physicists, and students interested in advanced mathematical concepts and unsolved problems in mathematics.

Milind_shyani
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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/"
 
Last edited by a moderator:
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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