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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."
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.
They're just being polite by pointing out there's no shame in failing to prove the Riemann Hypothesis, since it has frustrated the attempts of many a prominent mathematician so far.
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... "
It's called "Proof by Intimidation":
using the formula:
[ some formula ]
it is trivial to see that:
[ some other formula out of nowhere ]
therefore, combining the above, we can arrive at the easily obtained answer:
[ some MATLAB result ]
Don't forget, it works both ways; the people marking your assignment don't want to admit that they can't see the so-called "trivial" derivation.
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ECHELON is a government program to find words like bomb, jihad, plutonium, assassinate, and anarchy.
Use the "Star Trek" filter:
he is extending the test function h from [ tech ] to [ tech2 ] by [ tech 3 ] and then using Fourier transform ... This cannot work and [ tech ] form a set of measure 0 [ tech 4 ] (unlike what happens when one only deals with finitely many places).
When he moved from one set to another and did the Fourier transform, he forgot that he ended up with an empty set instead of a finite number of points because that's apparently a property of whatever the hell he was talking about.
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ECHELON is a government program to find words like bomb, jihad, plutonium, assassinate, and anarchy.
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
Unless it says the number is prime (you have to trust there are no factors) or gives factors that aren't primes.
Having said that, Li is no crank. I had not heard of him, but that's no surprise since I'm not a number theorist. But he has published several refereed papers in this area, has a position at BYU, and really ought to have known better than to explode on the scene like this.
I've gotten communications from genuine crackpots, wanting my comments on their work. Early in my career, I wrote back, gently pointing out the mistake. To my horror, friends then received slightly modified but still absurd drafts, listing me as a collaborator! Li is a real mathematician, probably with poor social skills, and a bad proof.
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."?
Don't forget, it works both ways; the people marking your assignment don't want to admit that they can't see the so-called "trivial" derivation.
UNCLEAR. NOT CONVINCED.
When marking a proof, it's your job to convince me, not my job to figure it out.
No shit. I took a minor in math, really loved and grokked things, up to a certain level. Beyond that I suddenly have no fscking clue what they're even talking about. When looking at similar levels of, say, biology, I at least have a faint idea of what it's about. High-level math is weird.
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.
For the record, most people don't know what P or NP is ;)
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.
Yeah, this is becoming a real problem with the preprint journals. Media groups like New Scientist will run a hyped-up story on some "ground-breaking new development" which will have propagated through the blog echo-chamber before other scientists have even had a chance to review it. It's not enough for the media to completely butcher the science they do present, now they have to present results which haven't even had cursory review. It's no wonder the public doesn't trust science considering what is is being presented to them.
It also creates unnecessary drama within the science community by means of the Leonardo DiCaprio affect - the more people hype a star the more everyone else hates them. The author of these papers are usually legitimate scientists who just made an honest mistake, whose only crime was submitting their preprint to ArXiv just like thousands of other scientists. But now they are suddenly being framed as "genius underdog" / "cocky attention whore" by the media and scientists.
The only reason that the preprint journals exist is as a loophole to get around normal journals posting rules. I'm really hoping that preprint journals will fade away as more reviewed papers are published for free X months after their journal publication date.
Mathematician: There is one sheep in a field in Scotland that is black on at least one side.
I thought he was going to say all sheep in Scotland are grey?
Anyhow, what's with there's no inductive proof in Mathematics? There are many many inductive proofs, even at high-school you write "proof by induction" quite a lot. Google it, all the top hits are mathematical.
http://en.wikipedia.org/wiki/Mathematical_induction