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

  • Thread starter Milind_shyani
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In summary, the conversation discusses the Seven Millennium problems and provides information on the Poincaré conjecture and the Yang Mills theory. It is suggested to read Keith J. Devlin's book on the Millennium Problems and it is mentioned that solving them can bring a reward of one million dollars. The latest problem to be solved is the Poincaré conjecture by Grigori Perelman, using surgery procedures and the Ricci flow concept. There is also a mention of a joke about the Yang Mills theorem and a question about the type of mathematician who would be most likely to solve it. The conversation ends with a humorous exchange about solving the Millennium Problems and donating proofs to charity.
  • #1
Milind_shyani
42
0
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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  • #2
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/" [Broken]
 
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  • #3
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.
 
  • #4
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.
 
  • #5
Actually he did, so the second part of my post can die.
 
  • #6
theperthvan said:
Actually he did, so the second part of my post can die.
But you are going to leave the insult?
 
  • #7
I think he said it jokingly...
 
  • #8
Yeah I did.
How about "my whole post can die".
 
  • #9
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?
 

What are the Millennium problems?

The Millennium problems, also known as the Millennium Prize Problems, are seven unsolved mathematical problems that were identified by the Clay Mathematics Institute in 2000. These problems are considered some of the most challenging and important in mathematics, and solving any of them would have a major impact on the field.

Who created the Millennium problems?

The Millennium problems were identified by the Clay Mathematics Institute, a non-profit organization based in the United States that aims to promote and advance mathematics. The institute was founded in 1998 by Landon T. Clay.

How much is the prize for solving a Millennium problem?

The Clay Mathematics Institute has offered a prize of $1 million for each of the Millennium problems. However, the prize money is not the main motivation for solving these problems, as they are considered to be extremely difficult and may require years of research and collaboration.

How many of the Millennium problems have been solved?

As of 2021, only one of the Millennium problems has been solved - the Poincaré conjecture, which was solved by Russian mathematician Grigori Perelman in 2002. However, Perelman declined the prize money and the Clay Mathematics Institute has not awarded the prize to anyone else.

Why are the Millennium problems important?

The Millennium problems are important because they represent some of the most fundamental and challenging questions in mathematics. Solving these problems would not only advance our understanding of mathematics but also have implications in other fields such as physics and computer science. Additionally, the prize money serves as a way to encourage and motivate mathematicians to tackle these difficult problems.

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