The Millennium Prize Problems are seven mathematical conundrums first stated by the Clay Mathematics Institute (CMI) in 2000 – all of which were very old problems with no known solutions. To date, only one of the puzzles has been officially solved: the Poincaré conjecture, which concerned itself with the evolution of three-dimensional shapes. Now, a second puzzle claims to have been solved by a Nigerian professor after it has befuddled scholars for 156 years – the Riemann Hypothesis.
Reported by BBC News, Dr. Opeyemi Enoch, a mathematician from Federal University in the Nigerian city of Oye Ekiti, has announced that he’s solved the puzzle that’s been without a solution ever since it was proposed by German mathematician Bernhard Riemann in 1859. For now, the news must be treated with caution – his solution has not yet been confirmed independently to be true.
— This Is Africa (@ThisIsAfricaTIA) November 17, 2015
The Riemann Hypothesis considers the strange nature of primes. They are like the concept of atoms in physics – the smallest whole units, the building blocks of other numbers. Mathematicians use prime numbers in order to look at the underlying structure of patterns and equations. Their unique feature is that they are only divisible by themselves and the number 1.
The odd thing about prime numbers is that they do not appear to follow any sort of discernable pattern in the long run. When one prime has been found, the next one can only be found manually by someone checking each and every number as they climb the numerical ladder. Riemann, in 1859, concocted a formula that would tell you how many prime numbers there are below any given value, but calculating ascending patterns of primes eluded him – and every other mathematician in the world.
His formula calculated the coordinates of the values, providing a mathematical map showing where exactly the primes below a certain value occurred in a sequence. Taking this forward and manually checking high-value prime numbers, mathematicians have confirmed that up to the first ten trillion positions of primes all follow the patterns laid out by Riemann’s formula – the Riemann Zeta function – but there was no way of predicting future positions of primes without once again manually checking each number in a sequence.
Dr. Enoch claims to have produced a solution to this problem, which would be able to predict where prime numbers occur for any set of values, from the extremely small to the extremely large. Prime numbers are used extensively in cryptography, so a solution to this Millennium Prize would no doubt make life harder for codebreakers. If the Riemann puzzle solution by Dr. Enoch is confirmed, he’ll be the next (or perhaps first) millionaire mathematician in this very prestigious list.
Some, however, are already expressing doubt over his mathematical proof. The blog site The Aperiodical notes that links to the proof of the paper's original author – one Werner Raab – appear to be broken, and the CMI is yet to officially look at the mathematical evidence.
Only time will tell, we suppose.
— Alex Bellos (@alexbellos) November 17, 2015