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

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Discussion Overview

The discussion revolves around the Seven Millennium Problems in mathematics, specifically focusing on the Yang-Mills theory, Navier-Stokes equations, and the Poincaré conjecture. Participants explore the significance of these problems, share resources, and engage in both serious and humorous exchanges regarding their complexity and the nature of mathematical inquiry.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant requests detailed explanations of the Yang-Mills theory, Navier-Stokes equations, and the Poincaré conjecture.
  • Another participant suggests reading Keith J. Devlin's book on the Millennium Problems and mentions the Poincaré conjecture has been solved by Grigori Perelman.
  • Some participants engage in a humorous exchange about the request for detailed explanations, questioning the seriousness of the initial inquiry.
  • A participant humorously presents a fictional scenario involving a paper mill and the Yang-Mills theorem, indicating a playful approach to the topic.
  • Another participant raises a more serious question about the type of mathematician likely to solve the Yang-Mills problem, speculating on whether a pure mathematician or a mathematical physicist would be more suited.
  • One participant claims to have solved five of the Millennium Problems but expresses reluctance to share the solutions due to word limits and a lack of interest in fame.
  • Another participant humorously suggests donating proofs to charity, highlighting the competitive nature of mathematical discovery.
  • A later reply challenges the correctness of some claimed solutions, indicating ongoing debate about the validity of certain proofs presented in a comic book format.

Areas of Agreement / Disagreement

The discussion features multiple competing views, particularly regarding the seriousness of the initial request for explanations, the nature of the Millennium Problems, and the validity of claimed solutions. No consensus is reached on these points.

Contextual Notes

Participants express varying degrees of seriousness and humor, which may affect the interpretation of claims made about the Millennium Problems. The discussion includes speculative questions about the types of mathematicians involved in solving these problems.

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:
 
Mathematics news on Phys.org
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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