Here’s a tweet from Alex Bellos this morning:
— 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):
— 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”!