Polynomials

[flexibeast]

This just popped up on arXiv.org:

A Polynomial Time Algorithm for The Traveling Salesman Problem

Which, if verified, would be rather impressive. The problem this paper purports to solve is one of the seven Millenium Prize Problems; one of the other problems, the Poincaré Conjecture, was solved earlier this year.

If anyone can tell me if and why this paper falls down, i'd be most appreciative. :-)
 

Comments

[annie-lyne.livejournal.com]

I'm giving it a quick read. The grammar isn't the best, but that doesn't necessarily mean that the mathematics is wrong.

It does however imply the counterintuitive result that P == NP, whereas it is "commonly" thought that P != NP. I tend to lean towards the former, though ;)

[ubiquity.livejournal.com]

I'm skeptical, but I can't follow the math well enough to find the flaw I suspect is there.

[noteris.livejournal.com]

i can't follow it but P versus NP page (http://www.win.tue.nl/~gwoegi/P-versus-NP.htm) item 28 near bottom of page links to comments that claim to be a refutation of version 1 of that paper. i did not notice a reference to the refutation in version 2.

there's a depressingly long list of such announcements at above link and also a link to this parody (http://geomblog.blogspot.com/2004/04/meta-proof.html).