Competition - post a photo you've taken of nature >>

Proof of the Riemann Hypothesis

Scroll to see replies

Link to paper: https://www.youtube.com/watch?v=Qwygzmx8NkE

So what? I highly doubt the proof holds, but where would the flaw be...

Reply 21

Olive Kitteridge

Didn’t watch it. Anyone able to give an overview of what went down? Someone said something about it all relying on two self-referenced papers?

Reply 22

AngryJellyfish

Chat Forum Helper, Entertainment Forum Helper

Original post by Olive Kitteridge

Didn’t watch it. Anyone able to give an overview of what went down? Someone said something about it all relying on two self-referenced papers?

TL;DW version:

[video="youtube;UBVy0oOYczQ"]https://www.youtube.com/watch?v=UBVy0oOYczQ[/video]

Reply 23

DFranklin

Original post by Chris Cao

Link to paper: https://www.youtube.com/watch?v=Qwygzmx8NkE

So what? I highly doubt the proof holds, but where would the flaw be...

Original post by Olive Kitteridge

Didn’t watch it. Anyone able to give an overview of what went down? Someone said something about it all relying on two self-referenced papers?

So, key to the whole thing is "the Todd function", which he defines in this paper: https://drive.google.com/file/d/17NBICP6OcUSucrXKNWvzLmrQpfUrEKuY/view

I say define, but the paper is rambling and incoherent, and if I'm honest reads like it's written by a crank . I admit I've not spent very long trying to decide if there's something "real" there, but life is too short, and I'll trust the proper experts who say there isn't.

That said, he says various things about the Todd function in the RH paper, and undergraduate understanding of complex analysis is enough to say "well, if that's all true, the Todd function equals 1 everywhere". (*)

This is particularly telling when you consider that his actual RH proof involves showing that the function

F(s) = T(1+\zeta(s+b)) - 1

is identically zero, which is obviously both (a) true, and (b) tells us nothing about the behaviour of

\zeta

if T is identically equal to 1. To be completely clear here: his deductions are invalid if it turns out T = 1 everywhere.

(*) The one nagging doubt has to be that there's something more complex going on with this "Todd function" that everyone is missing. However, I don't see anything ruling out the Occam's Razor explanation that T equals 1 everywhere (and its claimed properties seem to prove this must be the case).

It should be noted that there are various other red flags - some I can comment on directly:

(1) The proof seems to make no use whatsoever of the known properties of the Zeta function - you could replace it with any other (analytic) function, in particular with ones for which the result is obviously false.

(2) When he explains the miraculous properties of the Todd function, there are multiple "oddities" where what he says things that don't really make sense. (if a function is a polynomial on any compact set, it must be a polynomial everywhere, for example).

(3) There are various asides/comments that are completely out of place in an essentially analytic proof (e.g. digressing to say "this is a proof by contradiction, so not valid in ZF", noting that

\mathbb{C}

doesn't have characteristic 2).

But basically point (1) and the fact that the whole thing sounds like it's written by a crank is enough to make me confident there's no proof here.

(edited 5 years ago)

Reply 24

Chris Cao

Original post by DFranklin

S
(2) When he explains the miraculous properties of the Todd function, there are multiple "oddities" where what he says things that don't really make sense. (if a function is a polynomial on any compact set, it must be a polynomial everywhere, for example).

Do you mean “if an analytic function is a polynomial on any compact set, it must be a polynomial everywhere”?

Reply 25

DFranklin

Original post by Chris Cao

Do you mean “if an analytic function is a polynomial on any compact set, it must be a polynomial everywhere”?

Not really. The "true for all compact sets" claim is so strong that it covers everything in one go. I think there's a feeling that's not what he actually meant, in which case appeals to identity theorems for polynomials/analytic functions becomes more important, but it's pointless to try to go into detail when any such argument would be based on trying to guess what was actually meant.

Unfortunately, the whole thing is like that.