The Millennium Prize is $1,000,000 for solving the problem briefly described below (more details at the link), or any of the other 5 problems described in the links at the end of this article - the Poincare Conjecture has been solved. You just have to solve one of them to claim the prize.
An excerpt:
...
The case of interest in the Millennium Problem “Yang-Mills theory and Mass-Gap” is Yang-Mills gauge theory, a non-abelian theory which we expect to describe quarks and the strong force that binds the nucleus and powers the sun. Here we encounter a contradiction between the classical and quantum theories.
The classical theory predicts massless particles and long-range forces. The quantum theory has to match the real world with short-range forces and massive particles. Physicists expect various mathematical properties such as the “mass gap” and “asymptotic freedom” to explain the non-existence of massless particles in observations of the strong interactions.
As these properties are not visible in the classical theory and arise only in the quantum theory, understanding them means we need a rigorous approach to “quantum Yang-Mills theory”. Currently we do not have the mathematics to do this, although various approximations and simplifications can be done which suggest the quantum theory has the required properties.
The Millennium Problem seeks to establish by rigorous mathematics the existence of the “mass gap” – that is, the non-existence of massless particles in Yang-Mills theory. The solution of the problem would involve an approach to quantum field theory in four dimensions that is sophisticated enough to explain at least this feature of quantum non-abelian Yang-Mills gauge theory.
more ...
Printer-friendly format
Email this thread to a friend
Bookmark this thread
(1000+ posts)
Send PM |
Profile |
Ignore
