11
$\begingroup$

I am making a presentation about Millennium Problems. There are 7 Millennium Problems but a lot of unsolved mathematics problems are also waiting to be solved. I know that these problems are much more important than many others but I need a more detailed explanation. Why these 7? Who decided? Are they really the most important ones in mathematics? For example, one question comes to mind is why 3n+1 conjecture is not in this list, maybe solving it will provide us great mathematical devices like FLT. I will be really glad if you can provide some reliable links or a detailed explanation.

Thank you,

TT

$\endgroup$
5
$\begingroup$

The website of the Clay Mathematical Institute writes the following:

The focus [...] was on important classic questions that have resisted solution for many years.

Arthur M. Jaffe, once director of the Clay Mathematical Insitute, wrote on the history of conceiving the Millennium Prize Problems (emphasis mine).

As a first step, I requested that each SAB member submit a personal list of top questions. Each of these questions should be difficult and important — a time-tested challenge on which mathematicians had worked without success. [...] We added questions to the list one by one. With each new question we asked whether the list should be expanded or whether it might be improved by substituting a new question. [...] While each problem on the list was central and important, I want to stress that the SAB did not envisage making a definitive list, nor even a representative set of famous unsolved problems. Rather, personal taste entered our choices; a different scientific advisory board undoubtedly would have come up with a different list. The persons we consulted were experts, but they were chosen under pressure of time. However, the spirit of the selection transcends these decisions: the resulting list represents an honest attempt to convey some excitement about mathematics. We do not wish to address the question, “Why is Problem A not on your list?” Rather we say that the list highlights seven historic, important, and difficult open questions in mathematics.

The source of the above article also describes in more detail the actual process of creating the final list of $7$ problems.

For reference, the seven problems are:

  1. The Birch-Swinnerton-Dyer conjecture (Andrew Wiles)
  2. The Hodge conjecture (Pierre Deligne)
  3. The Navier-Stokes equation has smooth solutions (Charles Fefferman)
  4. P is not NP (Stephen Cook)
  5. The Poincaré conjecture (John Milnor)
  6. Quantum Yang-Mills theory exists with a mass gap (Arthur Jaffe and Edward Witten)
  7. The Riemann hypothesis (Enrico Bombieri)
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.