Has Someone Actually Solved the Riemann Hypothesis

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.

 Prime Numbers
Predicting Prime Numbers

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

Should We Follow Japanese Maths Teaching?

Improving mathematics standards in the US has been a common goal since the Common Core State Standards were introduced. Unfortunately if we use the National Assessment of Educational Progress figures there have been no improvements in maths at all during the last few years.

This has pushed American educational experts to look overseas for some inspiration, and they think they’ve found some answers in the way the Japanese teach maths. Unlike the traditional US strategies which focus on memorizing, the Japanese method will focus on solving mathematical problems.The method is Sansu arithmetic and it actually aligns quite neatly with the US Common Core so it wouldn’t actually be that difficult.

It’s actually somewhat ironic that the method adopted by the Japanese was actually first identified in the USA. The National Council of Teachers of Mathematics investigated this method in the 1980s however it was never officially adopted.And so, some 40 years on our children are still learning mathematics by memorising from simple sheets.

The Japanese instantly recognized the benefits to students of being able to create their own solutions and methods for solving problems.  It means that in classes, you can create a context and student will learn much more easily than simply learning by rote from a sheet of paper.  A similar method has been tried in some European countries including in Germany, article on BBC about German education on BBC iPlayer, access here.  The focus is to learn and interest students by a concept called hatsumon (addressing a concept through questioning). If it taught well, students will see their learning benefit them in real life situations.Which also helps promote elements of self confidence and some enthusiasm for the subject.

Lessons are created by individual teachers who then try the lesson in front of students and other teachers including a professor. The lesson is then discussed with the teacher so that feedback can be given and modifications made if necessary.If there is no feedback teachers are forced to make their own decisions on the quality of their own lessons.

These might seem like simple, common sense steps but unfortunately they are missing in many Western classrooms.There are many critics of the Common Core standards despite being endorsed by most educational organisations in the United States. One of the issues though is that teachers are given very limited training in the method.

A shortcoming which we’ve seen before. In the 1960s, there was a big push to introduce ‘new maths’ to push onto the space age. There was much enthusiasm but little change simply because nothing was invested in training the teachers in new methods.

There is a feeling that maths teaching in the US should change but a lack of direction and funding to implement this change. Japanese teachers get much more support whenever new methods are implemented across any area of education.Which in turn is usually reflected in the scores of students in international comparison tables.

There is no reason to accept that American students should be worse at maths. However, the fact is that a global economy demands certain skills and mathematics is at the top of that list.

Further Reading