[personal profile] mathphysicist
Now that Grisha Perelman became the First Clay Prize Awardee, what about the rest of the Millenium Problems?

[Poll #1540339][Poll #1540339]

Date: Mar. 22nd, 2010 01:47 (UTC)
From: [identity profile] akitrom.livejournal.com
The honest answer is 90% "who knows?" because I have next to no information about who's doing what to try to solve these. When we do get a solution, it'll come out of left field for everyone except the team that does the solving.

But the other 10% puts smart money on the Hodge Conjecture, because there's so much of algebraic topology that already does heavy lifting in one branch, only to do even greater work once it's transformed and understood in a different context. There are a lot of very powerful tools in AT, and I get the feeling that we just needs to bring the right combination of them to bear on the Hodge conjecture.

As opposed to, say, the Mass Gap problem or the Navier-Stokes equations, which (a) don't have the same kind of mathematics flinging about, and (b) require more real-world applications. (Heck, with the Navier-Stokes equations, I don't even know what a proof would look like.)

Date: Mar. 22nd, 2010 22:11 (UTC)
From: [identity profile] eigenvalue.livejournal.com
The Hodge Conjecture is mainly a problem in algebraic geometry.

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