I lifted the title of this post from the related discussion on Slashdot.org. Xian-Jin Li's proof has been reviewed and apparently there are some things wrong with it. Apparently Alain Connes, (I have no idea who he is but he won a Fields Medal in 1982) took a look at it and instantly saw a problem with it. On his blog he made some comments at the end of one of his posts about it and why it was wrong (scroll down to the comments and he talks about it).

As Dr. Connes explains it, "The "proof" is that of Theorem 7.3 page 29 in Li's paper, but I stopped reading it when I saw that he is extending the test function h from ideles to adeles by 0 outside ideles and then using Fourier transform (see page 31). This cannot work and ideles form a set of measure 0 inside adeles (unlike what happens when one only deals with finitely many places)."

Well that obviously clears it up. No wonder it's wrong! I should have seen that! So for those of you who missed it, someone else posted a comment after Dr. Connes to clairfy their take on the problem.

"it seems to me an elliptic curve functional on the closed measure 0 inside adeles would provide the requisite metric space for an extended test function h; the associated omega-consistent Goedel-zeta function transform would then serve as an adequate ring Hecke for a 1-0 Lie group functional connective space"

Man! If you didn't understand Dr. Connes' comment then that last one surely cleared things up for you!

Anyway, on a serious note, it doesn't seem like Xian-Jin Li's proof will be good enough. I have to give him credit for trying. He obviuosly understands more about it than I do. Even though he may have made a mistake it was a very technical one, a mistake that could only have been made by someone who understands what they are doing. Congratulations Dr. Li!

Yeah, its too bad it didn't turn out. I was routing for him.

ReplyDeleteBy the way, not only is Alain Connes a big mathematician, is has done great things for theoretical physics since he is a major father of non-commutative geometry and has done a lot with other areas very helpful in physics.

He is like the inverse of Ed Witten. A mathematician but has done just as much for theoretical physics as math! :)