In 2000, the Clay Mathematics Institute of Cambridge, Mass., identified seven math problems it deemed the most "important classic questions that have resisted solution over the years." Several of them had in fact resisted solution for more than a century—the Rieman Hypothesis, for example, has confounded mathematicians since its formulation in 1859.
To create a bit of frisson among the public for the so-called Millennium Prize Problems, the Clay Institute announced it would offer a one-million-dollar reward apiece for solutions to the problems.
The general rules are: the proof must be published in a qualifying outlet, two years must have passed since publication and the solution must have general acceptance from the global mathematics community.
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While a layperson might have a tough time penetrating the quantum physics behind the Yang-Mills and Mass Gap problem, they have no difficulty understanding the meaning of the number 1 followed by 6 zeros and preceded by a dollar sign.
Seven years after the Clay Institute announced its challenge, the century-old Poincaré Conjecture, one of the thorniest of the millennium problems, has been solved.Poincaré's Conjecture deals with the branch of math called topology, which is the study of shapes, spaces, and surfaces.The Clay Institute offers this deceptively friendly-sounding doughnut-and-apple explication of the bedeviling problem: If we stretch a rubber band around the surface of an apple, then we can shrink it down to a point by moving it slowly, without tearing it and without allowing it to leave the surface.Kind of like the prognosis on the ABC conjecture proof stuff.From what I understand he's still revising his paper.There will still be a wait to see if Atiyah has truly solved the hypothesis.The rules on being awarded the prize money is posted on CMI’s website.Here's a brief overview of the recent progress on the BSD conjecture.In particular, at least 66.48% of elliptic curves satisfy the rank part of the BSD conjecture and have finite Tate–Shafarevich group.Georg Friedrich Bernhard Riemann first came up with the Riemann Hypothesis 160 years ago.The reason people do not agree with Atiyah’s T(s) is because Atiyah says it has to have certain properties.