Sometimes a paper comes along which can breath new life into a subject or problem long thought unsolvable. This year a trio of mathematicians looks like they’ve done just that in offering a new tactic to solve the ‘greatest unsolved problem in mathematics – the Riemann Hypothesis.
This paper has just been published in a maths journal called Physical Review and suggests that the analysis is proven correct then it can also be used to prove the Riemann Hypothesis.
For those whose lives are not centred around mathematics this might sound a little obscure.However for mathematicians it represents fame, success and of course cash.The solution to the Riemann hypothesis is one of the seven Millennium Prize problems which cover the most difficult problems in maths. For more information on this prize have a look on BBC iPlayer where there was a recent maths documentary, this link shows how to access it from outside the UK. Every one of these problems comes with a one million dollar prize for a solution.
This hypothesis is names after the German born mathematician Bernhard Riemann.It’s such an important problem because it offers a method to understand the distribution of prime numbers. If a method was found it would completely revolutionise mathematics.Being able to work out how may prime exist in any given situation would make many branches of the science much, much easier.
So where is this solution hidden, well it is suggested it lies in quantum mechanics.
An amazing statement from this paper proposes that quantum mechanics could solve the Riemann Hypothesis. This difficult area of physics usually used to try and make sense of some of the smaller scales in nature.
So what’s in the paper? Well the authors have suggested that the existence of a quantum system of energy corresponds to the proposed conditions in the Riemann Hypothesis.They have also defined a specific variable called the Hamiltonian Operator as the crucial part of this system.
If this all works out then the method effectively reduces the huge problem of the Riemann Hypothesis down to the level of the Hamiltonian Operator. A mythical problem that was almost deemed impossible to solve suddenly becomes much closer.The paper is only in the first stages though and peer review is next which could take some time.
But it certainly has created some excitement for anyone who has even a passing interest in mathematics.
Further Information: BBC News Streaming