Here’s a tweet from Alex Bellos this morning:
BBC claims Nigerian solves Riemann Hypothesis, most famous problem in maths. Surely a hoax! https://t.co/Wkltfkh2P3 https://t.co/UHGy9W8shC
— Alex Bellos (@alexbellos) November 17, 2015
He’s right to be surprised – as reported in Vanguard, a Nigerian newspaper:
The 156-year old Riemann Hypothesis, one of the most important problems in Mathematics, has been successfully resolved by Nigeria Scholar, Dr. Opeyemi Enoch.
Suspicion levels are raised, as the paper also reports:
Three of the [Clay Millenium Prize] problems had been solved and the prizes given to the winners. This makes it the fourth to be solved of all the seven problems.
Unless we missed something, that’s not massively true – the only Millennium Prize problem solved so far is the Poincaré conjecture.
So who is this Nigerian mathematician? Dr Opeyemi Enoch is a professor with the Federal University in Oye Ekiti, Nigeria. The article says:
Dr. Enoch had previously designed a Prototype of a silo for peasant farmers and also discovered a scientific technique for detecting and tracking someone on an evil mission.
So he straddles the disciplines, at least. This story is made more interesting by the presence of a serious interview with the BBC World Service (shocking behaviour) in which he’s even asked ‘What will you do with the $1 million?’.
Unfortunately, it looks like in this case it’s not a real proof of the Riemann Hypothesis, and this post on a Nigerian discussion forum says emphatically he has not solved it. As mentioned in that post, there’s a paper on academia.edu under his name, which is actually a copy of a paper by someone called Werner Raab (retired). Raab’s website – http://www.raab-math.at/ is empty, and has a single broken link to “the truth of the Riemann hypothesis”. Some digging reveals that that URL has never worked. Confusingly, Enoch seems to be gathering papers about the Riemann Hypothesis on academia.edu under his own name.
The “proof” was presented at this legitimate academic conference (yes, the URL is “computer.conference-site.com”) which does appear to have taken place – although the photos don’t seem to show the kind of turnout you’d expect for presenting a result of this magnitude. Here’s the proceedings of the conference (Enoch’s presentation is “A matrix that generates the point spectral of the Riemann Zeta function”). It also looks like the local organiser of the conference is quite a character. (What’s the deal with fuzzy logic and definitely legitimate academic proceedings?)
There’s another article denying the truth of the claim in Nigerian newspaper The Herald. Marcus du Sautoy has also been consulted, naturally (and taken the opportunity to plug his book, well done):
Has Riemann been proved? Check out my interview @BBCr4today Verdict: Music of the Primes doesn't need updating yet https://t.co/eKRWvVA3R2
— Marcus du Sautoy (@MarcusduSautoy) November 17, 2015
As a last-minute addition to the show, Marcus’ bit isn’t listed in the schedule, but you can listen to the whole episode on the BBC website.
So sadly, nobody’s cracked this 156-year old problem, although the method Enoch might be trying to use is one approach that is currently being tried by more well-known researchers – here’s some serious info about attempts to prove the Riemann hypothesis by looking at the zeros as eigenvalues of a Hermitian operator on a Hilbert space. Alain Connes also recently wrote a paper about how you might (and might not) go about actually solving it.
As always with such long-standing results, there are plenty of incorrect proof attempts – although the arXiv seems to have done a good job keeping out crank proofs of the Riemann Hypothesis recently (or, the cranks are on holiday). All our roving reporter CLP can find is this from August.
The last word on the subject should probably go to the Clay Mathematics Institute website, which at time of publication still says:
Update 19/11/2015: Coverage continues in “Riemann hypothesis not proved, part 2”!
Nice update! BTW Matthew Secrets-of-Creation Watkins has very nice FAQ entry: I think have a proof of the RH! What do I do now? which links to a list of failed proofs. I don’t know if he’ll bother to add this one…
I downloaded the Raab paper. It was originally uploaded in 2013 to the site Bundlr which is a file-sharing site, not an academic journal. The paper looks to be quite old (I’m guessing late 60s based on the citations), and it is possible that Raab simply uploaded it as a curiosity. He doesn’t seem to have ever claimed it was a “proof”.
Manning, what paper are you talking about? The “Truth about Riemann hypothesis” one (here: http://www.raab-math.at/true.pdf) cites a 1988 paper and a Wikipedia article…
Good work, Aperiodicalians-who-aren’t-me!
Re. “The last word on the subject should probably…” I wouldn’t rely on the Clay Institute announcing a Prize for breaking news. I think they awarded Perelman’s 2003 proof the Prize in 2010, after leaving a suitable amount of time to be really sure.
But I would rely on the Clay Institute for announcing whether the prize has actually been awarded, which is what the BBC claimed.
Can someone indicate when in the Today programme the Marcus du Sautoy bit was? I can’t bear to listen to the whole 2.5 hours.
Marcus has posted the clip on SoundCloud.
There’s a typo and the URL http://www.raab-math.at/hypothesis.html actually exists and links to the following paper: http://www.raab-math.at/true.pdf
Aha! Thanks for that.
Raab’s paper was apparently published in the journal “Open Science Repository Mathematics”:
–Dr. Enoch had previously designed a Prototype of a silo for peasant farmers and also discovered a scientific technique for ” detecting and tracking someone on an evil mission.”–
All forces to discredit this *black* guy are already full power in motion, to make it looks like he hasn’t prove it.
I reject that completely. We laid out all the reasons we don’t believe he’s solved the problem, and none of them were to do with the colour of his skin.
Christian, with all due respect your point is irrelevant in response to Gerald’s. his point was not that there are no good reasons to reject that he has solved the problem, just that there is racism at work when it is announced that a (black) Nigerian professor has solved a maths problem and is met with disproportionate scepticism, indeed, much greater scepticism than a white professor would’ve received. it doesn’t even need to be taken as solely directed at your blog-post here, but in the general response to the ‘news’. you can see this already at work in the first tweet from ‘Alex Bellos’ above, which strongly implies it is unbelievable that a Nigerian of all people could solve a century-plus old maths problem.
Not true. When a Kazakh recently claimed to have solved the Millennium problem on Navier-Stokes, there was doubt and debate. There were two major differences though: 1. news agencies in the West, who, let’s face it, don’t have a clue about how maths research works, didn’t pick it up, so there was no hysteria and the wording was more cautious to start with (“the problem MAY be solved”), 2. Otelbaev’s proof was made available for review, and knows that it is for others to recognise if it is correct (as said in this article’s update). Mr. Enoch, on the other hand, claims, without releasing a paper AFAIK, or at least no-one can clearly source one, to have solved the problem.
We only have this obscure conference, which I’ve found is linked to the publisher, “International Scientific Journal”. It’s an open-access publisher, and Nina Ringo is on its editorial board. Now I’m not Jeffrey Beall, but it looks to me as if it enters the scope of his blacklist. I’ll query him on the topic today.
Speaking as a Black Mathematician, I wish to agree with Christian Lawson-Perfect. There is a time honoured fashion of scrutinizing mathematical proof. The mathematics community need to see the paper and go through it with a fine tooth comb before we accept that the logical argument is true. It is Dr Enoch’s responsibility to defend his work. Christian has simply raised some concerns that need answering and this is not a racist thing to do. Any mathematician would welcome such questioning, because if the maths is correct and true, they have nothing to hide.
So, when a “black” man’s claims are proven wrong, with genuine references to verifiable information, it’s only because he is “black”. I bet the verifaible sources of information are created specifically to discredit “black” people.
“Proven?” where are they? Did you read them at all?
Or you just ended up stereotyping him and went along with what was written above.
The black race will surely prevail from this sense of doubt and stereotypes. SMH!
Don’t let evidence uproot your deeply-set prejudices and biases.
I reject that sentiment too. Why must we scream racism all the time? Im a Nigerian btw. I first heard of the “news” and my first instinct was to Google. The Riemann hypothesis is HUGE! (I have read the music of the primes so I had some idea) How was the mathematical community reacting to this?
But you know what I found? All the results were from Nigerian blogs and a couple of newspapers. All with similar wording and obviously plagiarised. That surely wont happen if it was true! I went further to search for the paper with the supposed proof, nothing! On academia.edu, the papers there didnt even have his name attached. I couldn’t even find evidence for a paper not to talk of if it was true or not . That was damning! (I later found the paper he presented at a conference but it isnt confirmed true so no basis for the scandalous headlines)
I am a Nigerian passionate about making great contributions to the world just like solving this problem. But this was a blow. It is blow to every Nigerian. It serves to discredit us and enforce the 419 narrative. I am still angry about this. Even more skepticism would be met next time a Nigerian actually does something of note. Make no mistake, the headlines marketed it as “Nigerian professor SOLVES the Riemann hypothesis” . It was Nigeria’s glory if true and her shame if it wasn’t.
I am even more particularly annoyed by the the News agencies. This shouldn’t have got this badly out of hand if they had bothered to fact check. To google. To ask for independent confirmation. All of the news was based on just one man was claiming. I didn’t even see any evidence that the Nigerian mathematical society or the African one supported him. It makes you wonder about other stories they write. That includes the Telegraph and the BBC.. shame. They made it seem credible. People would say it must be True since the BBC said so.
It is sad.
Your Comment here…It’ll have been far better if you’re more logical than emotional !
Ope’s comment was the best possible comment. Your criticism is without foundation.
Nonsense. I am black and have lived in Africa. Nothing would please me more than to have the story being true. What a great role model this would be for many on the African continent. However, when someone claims to have discovered a scientific technique for ” detecting and tracking someone on an evil mission.”, I know that I am dealing with a Quack!
If that “invention” was real, this man would be a billionaire. I can just see his invention at every airport in the world to detect “evil doers”. Every country would want to build his invention.
Please, give me a break!
Wow, that lady’s written some terrible poetry.
I think I got a new theorem in mathematics. Can post it here for a review? Just need your help because I am a student.
Only 1 (not 4) of the 7 millinium problems has in fact been solved, and the winner rejected the 1mill dollars.
So there are still some problems to be solved? Wow… how much can we say the Mathematic is reliable to describe and solve the greatest Concerns and Questions of the Humanity? That’s disappointing!
I mean, it’s disappointing to think that a thousand years weren’t enough to present any solution, but only ONE… I say, Mathematic seems to be no longer a reliable language to answer the Greatest Concerns of the Humanity, not even in thousand years… With all the respect to those most erudite than me, the Holy Scriptures are still the best way to answer problems… even the Mathematical ones.
The Millennium Prize problems were enumerated at the millennium — the year 2000. That’s only 19 years ago. Your comments display a great deal of misunderstanding, and religious fairy tales don’t solve math problems.
Looking closely, there’s another typo (no, the URL isn’t “computer–conference-site.com”).
It’s amazing to see this: a 150 years old Mathematical Problem claims for a solution, and in the sense of all here, there are still NO solution given… it makes me understand that “nicht alles” has maybe a real solution; Things which can be manipulated and verified as true or false through Mathematical Equations has alot of times given to explain the Universe Origins… so as the Riemann’s Problem, are they speaking the truth? It causes a miscredit in the scientists who had tried to do this, as sure as in the Nigerian Professor, if we can say an opinion. Some Mathematical Problems will never be solved… and it means that Matheatics are no longer a appropriate Language to describe the Universe Problems… I am sad… I’d rather that someone had appeared with a slution to the Life’s Origin proved by some of these Mathematical Problems… but I miserably found that the problem s greater than the minds which has created them! No use on answering a Mathematical Problem and keep unknown Life’s Origin. And this is true for all kind of Men.
Sorry… but God still is the only solution to these questions, despite who don’t believe Him …
Gildasio, it sounds as if you have finally found the solution to all the problems that might or have ever confronted man. Congratulations! In fact, you’ve found the solution for problem-solving in general. There’s no sense thinking any longer, is there? I guess it’s time to just give up solving any problems on our own, and trust to the priests to tell us, the helpless and ignorant, what to do.
You’re not sad at all … you’re thrilled to troll this page with your silly proselytizing.
I am a female Nigerian trying to study engineering at coventry university! it hasn’t been easy because all the boys give me the u’re a girl look! I sense the his just an African mentality of the writers. I read that he struggled 7 years to come up with something! wrong or right he should be FIRST AND FOREMOST BE ENCOURAGED! LIFE IS NOT A COMPETITION!
“I read that he struggled 7 years to come up with something!”
You read wrong.
Seeing that this is a mathematics blog, I have a question that has posed a challenge to me for more than 21 years! Here is the question:
If X^X + Y^Y = 31
and X + Y = 5
Find X and Y
Some of the answers are: X, Y = (2, 3) and (3, 2), but I don’t know how to solve it mathematically! Your help will be greatly appreciated. Thanks
While I think the Nigerian newspaper and BBC might have made a muddle of the story of the proof by claiming Dr. Enoch has been paid, the post in this blog has also not done due diligence in refuting the proof. If the evidence the blog provides is from “nairaland” and a purported refutation by Herald newspaper. Nairaland is not a credible source while Herald just reported CMI‘s position, which is in line with their policy to subject proofs to test and acceptance over time. This blog couldn’t even get URLs right.
You claim Enoch has been gathering papers about the Reimann Hypothesis under his name, how is this a crime?, as long as he doesn’t claim to have written them. The only inkling of noticeable proof you provide is a hunch about the method Dr. Enoch “might” be trying to use. This is publicity-mongering blogging at best. No valid proof whatsoever.
Dr. Enoch has not done himself any good too by not submitting a paper prior to the claims. Of course I think there will some paper at some point, but till then I would give him the benefit of the doubt. Lastly, yes I do think there is tacit racism at play since the news broke out.
He solved it. Why are u beefing!!!!????
A black person doesn’t get an Oscar nom, there’s racism! A not-so-smart-afterall (in my opinion) black professor claims to have cracked the Riemann code and is discredited, racism! Guys help me out here…Is there any scientific and/or mathematical equation of a sort in use today without dozens of peer reviewed papers backing it? This academia for God’s sake! It ain’t about color. We black people should really work on our thought processes. “It’s nothing personal, just business.” BTW, I’m Ghanaian.
He has not solved it!