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Prominent Mathematicians Rebuke Recent Riemann Hypothesis Proof
Bryan writes "Xian-Jin Li's purported proof of the Riemann Hypothesis (reported on recently) has been rebuked by Fields Medalist Terence Tao. Fortunately, Dr. Li's proof fails alongside a respectable graveyard of previous attempts." Relatedly, jim.shilliday writes "The proof cites and appears to be based in part on the work of the leading French theorist Alain Connes. A few hours ago, Connes posted a comment on his blog stating that the purported proof is so badly flawed that he stopped reading it."
From the summary:
Fortunately, Dr. Li's proof fails alongside a respectable graveyard of previous attempts
Why? I'm probably missing something obvious, I'm not even a mathematician to start with, but...
I mean, we (the world) do want to prove it right (or wrong) one day or another, don't we?
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).
The proof, and the rebuke, only proved my theory that there is a distinct surge in advil usage when something like this is posted on /. or digged.
Feed the need: Digitaladdiction.net
Well duh this is what we have been saying - this is a preprint and is likely to have errors. Whether or not they can be repaired is open to question.
Wiles' proof of Fermat's last theorem took a long time to go through the review and repair process. And there was at least one pretty hard problem that had to be fixed.
Slashdot's "journalistic" process really suxors when it comes to this sort of stuff.
Well it doesn't have any piratical applications, but the ninjas will definitely find a use for it
Oh come on, you were almost there! How about:
"Renowned Researchers Rebuke Recent Riemann Reasoning"
The submitter used stronger language to describe the comment than the comment itself. Connes just said "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... "
There are a lot of results based on assuming the conjecture is true, including a variety of factoring and root finding algorithms that are computationally very useful.
Until it is proven you really don't know if these algorithms are giving correct answers.
This is why it is so important and has a big prize associated to it.
My husband is a mathematician, and he gets emails weekly from crackpots claiming to have disproved the proof of Fermat's Last Theorem or having proven the Riemann hypothesis or whatever. You can submit anything to the ArXiv, this shouldn't have even been news in the first place until it was confirmed.
Warning: Apple/Nintendo fangirl. Likes her electronics cute & cuddly. May be rabid.
Yes, why don't you tell the Fields medalist how to make himself look good? I'm sure he needs your help desperately. Jeebus, you know that a Fields medal is objectively harder to get than a damned Nobel prize, right?
He did critique the 'proof' objectively. The claim was that by looking at the function on a certain domain ("ideles" whatever those are), one could look out from there and see how it would have to behave elsewhere ("adeles"). However, the "ideles" aren't big enough to give a good viewpoint of what's going on (i.e. the function at the ideles is not necessarily representative of the rest of the function). If you only look at multiples of 2pi, you could "prove" that sin(x)==0. Just because you or I couldn't notice the obvious problem in the RH proof, doesn't mean that it doesn't merit quick dismissal. Sometimes obvious mistakes are made in math (some would say that only obvious mistakes are made - but they are only obvious once they are pointed out).
"They were pure niggers." – Noam Chomsky
Since the work based on the assumption that the hypothesis is true is in itself valuable, it will still be used.
It's just that a proof, if found, will elevate who-ever finds it to the status of mathematical superstar.
Consider this, we are still finding proof of various of Einstein's theories, but work based on his has been of real value for decades.
Here's another example that makes me sound all clever because I know it.
Newtons equations, and his entire body of work, completely failed to explain how it is that the moon can orbit the earth while the earth orbits the sun, and we *still* don't have the equation to explain that bugger.
There are specific n-body solutions, I've written one myself, but a solution for the general case? Nope, never been done.
Louis Pasteur spent most of his life on that particular problem, as have many other prominent scientists, all to no avail. We found a use for Newtons work regardless, and Einstein extended it successfully, even with that glaring hole.
A learning experience is one of those things that say, 'You know that thing you just did? Don't do that.' - D. Adams
Why? Li is stating "I base my proof on X". Connes says "I see you've based your proof on X. I'm quite content that X doesn't work." Game over. If the fundamental assumption is wrong, what is gained from going on? If you read a paper that started "assume the square root of 9 was 3.1", do you *really* need to read all of it before you decide "this fellow might be off track."?
Nope. We can do calculations that involve n-bodies, of which obviously 3-body is part, but they involve using the 2-body solution of Newton for all unique pairs in a simulation.
A separate general three body solution probably does exist, but no-ones found it.
If found, it would quite possibly revolutionise n-body modelling, and prove useful to space science (if, and only if, it sped up calculations), but I doubt astronomers would care much.
A learning experience is one of those things that say, 'You know that thing you just did? Don't do that.' - D. Adams
Just wanted to point out that Professor Connes is also a Fields medalist (1982).
I guess it is a testament to Xian-Jin Li excellent reputation and the importance of the topic that these two mathematical superstars took the time to look at his proof.
The proof was a legitimate effort by a non-crackpot, but the ideas in it were well known to specialists in the field and were generally understood to not be powerful enough to crack the problem. So the errors were found fairly quickly. Scott Aaronson's post Ten Signs that a claimed mathematical breakthrough is wrong item #10 may be helpful in understanding what happened.
You are mixing the basic tenants of physics and mathematics, not a good thing to do. Science is a mix of inductive and deductive logic, math has a higher standard and doesn't admit inductive proofs.
Three guys were vacationing in Scotland. One was an astronomer, one a physicist and one a mathematician.
In their travels they chance on a black sheep grazing in a field.
Astronomer: All sheep in Scotland are black
Physicist: Some sheep in Scotland are black
Mathematician: There is one sheep in a field in Scotland that is black on at least one side.