Monday 28 January 2013

Become Millionaire by solving problem



If you know lot of maths, a Professor in Maths or a PHD student who wants a topic to research on, then this post is for you. And you will get a prize if you successfully solve the Unsolved problem in Mathematics. 
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  • P versus NP problem
  • Hodge conjecture
  • PoincarĂ© conjecture (solved)
  • Riemann hypothesis
  • Yang–Mills existence and mass gap
  • Navier–Stokes existence and smoothness
  • Birch and Swinnerton-Dyer conjecture
  • See the 3rd problem has already been solved by  Grigori Perelman in 2003; ; its review was completed in August 2006. Perelman was officially awarded the Millennium Prize on March 18, 2010. But he declined the money prize, I don’t know why.
    But still the 6 problems are waiting to be solved. A brief Summary of Six Problems:

    P versus NP

    The question is whether, for all problems for which an algorithm can verify a given solution quickly (that is, in polynomial time), an algorithm can also find that solution quickly. The former describes the class of problems termed NP, whilst the latter describes P. The question is whether or not all problems in NP are also in P. This is generally considered one of the most important open questions in mathematics and theoretical computer science as it has far-reaching consequences to other problems in mathematics, and to biology, philosophy[1] and cryptography.

    The Hodge conjecture

    The Hodge conjecture is that for projective algebraic varieties, Hodge cycles are rational linear combinations of algebraic cycles.
    The official statement of the problem was given by Pierre Deligne.

    The Riemann hypothesis

    The Riemann hypothesis is that all nontrivial zeros of the analytical continuation of the Riemann zeta function have a real part of 1/2. A proof or disproof of this would have far-reaching implications in number theory, especially for the distribution of prime numbers. This was Hilbert’s eighth problem, and is still considered an important open problem a century later.
    The official statement of the problem was given by Enrico Bombieri.

    Yang–Mills existence and mass gap

    In physics, classical Yang–Mills theory is a generalization of the Maxwell theory of electromagnetism where the chromo-electromagnetic field itself carries charges. As a classical field theory it has solutions which travel at the speed of light so that its quantum version should describe massless particles (gluons). However, the postulated phenomenon of color confinement permits only bound states of gluons, forming massive particles. This is the mass gap. Another aspect of confinement is asymptotic freedom which makes it conceivable that quantum Yang-Mills theory exists without restriction to low energy scales. The problem is to establish rigorously the existence of the quantum Yang-Mills theory and a mass gap.
    The official statement of the problem was given by Arthur Jaffe and Edward Witten & recent status by Michael R. Douglas

    Navier–Stokes existence and smoothness

    The Navier–Stokes equations describe the motion of fluids. Although they were found in the 19th century, they still are not well understood. The problem is to make progress toward a mathematical theory that will give insight into these equations.
    The official statement of the problem was given by Charles Fefferman.

    The Birch and Swinnerton-Dyer conjecture

    The Birch and Swinnerton-Dyer conjecture deals with a certain type of equation, those defining elliptic curves over the rational numbers. The conjecture is that there is a simple way to tell whether such equations have a finite or infinite number of rational solutions. Hilbert’s tenth problem dealt with a more general type of equation, and in that case it was proven that there is no way to decide whether a given equation even has any solutions.
    The official statement of the problem was given by Andrew Wiles. --> 

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