SPEED DATING is a relatively new phenomen where single men and women meet and each person gets to spend a few minutes talking, one at a time, to all the people of the opposite sex; for example, if 10 men and 10 women took part, each man would get perhaps 5 minutes to talk to one of the women and then after his 5 minutes was done he would move over to start talking to the next women for 5 minutes, and so on until he had spoken to all 10 women. The idea is that, hopefully, one of the people you speak to is someone you really like – and if they like you too, then you might go on a proper date!

But the problem is this; if, whilst speed dating, you are talking to someone you really like – and let’s say it is the 4th person you have talked to that night – should you ask them out? You see, there are 6 more people to see and you might like one of them even more! And what if you ask them out and they say no? Well then you could move on and see the next 6 people and maybe you’ll really like one of them and want to ask them out! But if they have seen that you’ve been declined they might think that they were only your second choice and decline you too! A useful and very similar example appears in the famous Russell Crowe film ‘A Beautiful Mind’ about the life of the game theorist John Nash. In the film, Russell Crowe’s character (Nash) recounts an example where a group of women walk into a bar in which there is already a group of men. All the women are pretty but one in particular is especially attractive; and, in turn, each of the men approaches the most attractive women but is rebuffed. They then turn their attention to the other, less attractive but nonetheless very pretty, women only to be rebuffed by them too – because they think the men are only seeing them as their second choice. The result? All the men and all the women stay single. But, as John Nash subsequently argues, if the men had approached the other women first they would have accepted their invitation and all the men and women would have coupled up, with the exception of the most attractive women!

Now this is clearly a gross simplification of what would happen in real-life; and I have no idea whether the real John Nash ever used this example – after all, Hollywood films are allowed to apply a little poetic licence in order to create a more vivid image! But the central idea is valid; in certain circumstances it is better to settle for something less than the best, just to ensure that you do achieve something you’re happy with – after all, I would love for my football team to win 10-0 in their next game (incidentally, I support Spurs and our next game is against Blackpool – so please join me in wishing Spurs good luck!) but, if I’m honest, I would be very happy if we just won our game; in this situation it is the winning which matters to me, not how comprehensively we win. And the same idea is often used in FINANCE where a large number of financial transactions that are carried out are designed to be ones which produce a very small but very safe profit – rather than risky but very profitable deals. Now obviously not all financial transactions are safe ones that make a small profit – otherwise we might not be in the current dismal financial environment we find ourselves – but a lot of them are, and a very large number of small but safe profit-making deals, when added together, can a produce a very large income for the company or investor in question. On the other hand, when it comes to matters of love surely you don’t want to settle for a safe option, someone you merely like? Don’t you want to go for your one true love; the man or woman who is that special someone for you?

In life we sometimes settle for the safe option – like in some forms of financial trading – and sometimes we go all out for what we want – like in love. And it is these ideas which lie behind this year’s challenge. Rather than students having to decide which man or woman they wanted to ask on a date, to simplify things students just had to pick the highest number (as opposed to the most attractive man or woman) from 6 numbers selected at random – the trick was that they would be shown one number at a time and had to decide, before seeing the next number, if they wanted to pick the number they’ve just seen (just as when speed dating you see each person one at at time). Let me illustrate this with an example. Suppose I produce a number at random – say 57 – you immediately have to decide whether you want to pick that number; if you say yes then you cannot change your mind and if a number greater than 57 is subsequently selected, you lose. If you don’t select 57 then when I show you another number – say 138 – you have to decide whether you want to pick that number or not. And so on until we reach the sixth, and final, number. If the number you picked was the highest of the 6 numbers, you win; if not then you lose! Students could play as many rounds of this game as they like, with the two students from each class that finished with the highest average number of wins, making it through to the grand final – which was won by one of my A-level students, Sephy from China!

Clearly, because you don’t know what numbers are going to be drawn next, you cannot guarantee to win at this game. However, the idea of this game – and other GAME THEORY games – is to decide whether or not there is a strategy you can play that gives you a good chance of success. And there is. But I will save that for another blog!

Ripple Dissolve:  Saturday 15th January 2011

I think there were a few sore heads the next morning, but the atmosphere was still remarkably buzzy.  Our IT support chaps manned their post at reception with reassurance and efficiency.  It’s one of the major nightmares presenters have these days – will the tech work?  It did.  Very well.  Yay!

As you can see, we were spoilt for choice in terms of electives this year.

Last minute sign-ups for sessions completed, we all peeled into the banqueting hall exam hall for the plenary session.  Due to illness, the programmed session was cancelled, so Nik Peachey stepped into the breach and gave us a fantastic session on  how to build up our PLNs (Personal Learning Networks) using social networking & internet based technology.

Judging from the people sitting behind me, I think this session was a bit like Marmite.  Love it or Hate it.  While I sat in rapt attention there were mutterings behind me of “Why would I want to do that?” and “Doesn’t he have a life?”

I think the potential for networks of any kind for information overload is off-putting for some.  However, as Nik went to great pains to explain, he does all his filtering in a nifty 30 mins a day before he starts work.  Not so daunting, surely?

At lunch I endeavoured to explain to some of the non-believers that perhaps younger, less experienced teachers would be used to using these types of tool, and, more importantly, now that we certainly do not live in a ‘jobs for life environment’, there is a heavier pressure on us to constantly acquire new skills and extend our areas of expertise.

As I said, Marmite.

Nik set up a live backchat site for the conference, for those of us who could access the wireless (one of the only IT glitches of the day) If you’d like to read his presentation click here.

So, onto the first sesssion:

This was given by Peter Ryley & Jennifer Wain over at the University of Sussex ISC.

They were here to talk about their  ELPP class blog project – choc full of cultural reflection and some really great content.  With over 100 students blogging, this was a perfect example of how thinking outside the box sometimes can produce bounteous rewards.

The presentation was great, with some really good discussion about being realistic about the time you need to set aside for a project like this, as well as a knowledge swap of practical technical issues.

You should go and have a look here.

There were a couple of really great resource links on their handout, too:

icons – this site has links to info and photos of typical British icons – everything from phone boxes to chicken tikka masala!

project britain – a fantastic web resource of all things British -  a fantastic cultural gallimauffry suitable for so many activities.

My next two sessions were with Dr Wolfram Just, from Queen Mary’s in London.

Adrian Underhill and Dr Wolfram Just ponder the dynamics of the pointy stick

The first “Time Delay Dynamics – Why Drunk People Cannot Walk” was a fantastically mega-nerdy maths exploration of how we go about solving problems – we looked at the simple question of how to balance a pointer stick on the palm of your hand and how you would go about putting that into some kind of mathematical framework.

We looked at a reverse idea – the pendulum – and then worked our way on from there, visiting latency, rocket engineering and biophysics on the way.

Now, to be honest, I have no idea what the maths was about – not my strongest subject – but it is credit to Wolfram that I can still remember every part of this presentation.  I do know that we looked at transcendental equations and their “infinitely many solutions”.

I’ve never been so inspired (or laughed so much) in what was, to all intents and purposes, a deeply nerdy maths class.  Wolfram was quite simply superb; an eccentric German maths professor.

Inspiring how?  Because it just goes to show that if you know your subject inside out and are enthusiastic about it, then a high level of eccentricity in the delivery can melt even the iciest heart and engage even the most sluggish of brains.

Bliss.  Total.  Bliss.

Our second session, “Fractals – the mathematics of a paper strip” had us all folding paper strips, predicting the right angles and then seeing how something so simple and kinaesthetic could be used to demonstrate something as complex and mind-blowing as fractals.

images taken from here

Again, this was an inspiring and memorable presentation. I know this is so because I can still repeat it pretty much verbatim now, a month later.

He left us with this amazing landscape.  Not a photograph, but a piece of fractal art.  You can see more here

My final session was a two hander – the first with Peter Jenkins on “Helping students to answer exam questions effectively” where he invited comment on a new video to help students look at questions in a more focused way.

I have to admit that I was a bit late for this, having been cornered by a publisher from Macmillan, so I missed most of it – sorry Peter!  I still managed to put my usual ha’pence worth in though!

The second part was an introduction to Bellerbys’ role in the world of social media, with Stephen Whitehead.

This was very interesting, I had no idea that Bellerbys took such an active role – and if you want to know more about it email socialmedia AT bellerbys DOT com or visit www.bellerbys.com/socialmedia

This session over-ran so I missed the closing plenary and hovered outside until the end, to say my goodbyes for another year to some really great delegates.

So, that about wraps it up for another year!  I feel as if it’s taken me longer to blog about the conference than to actually attend, but I hope it’s given you some idea of the diversity of content and the consistent level of expertise.

As ever, the conference committee comprising David Rowson, Julie Waller, Adrian Underhill, Vic Richardson and Barbara Gardner deserve a huge thank you for all their organisational prowess.

Wojciech Cieszynski  co-ordinated all the techie nerdy stuff and I’m sure there are plenty of unsung others to thank, including the APs and especially our specific centre coordinators, so a big thank you to John Gardiner, here in Brighton, too.

Roll on 2012!

Another slice of terrine, anyone?

Sarah Witherby teaches CIT on the Foundation programme and is AP for Bellerbys Brighton.

Friday 14th January

To kick off the evening the Bellerbys & Embassy APs (Advanced Practitioners) met up with Barbara Gardner for a quick snifter in the Sussex Yeoman pub – a fantastic foodie pub, if you’re ever in search of somewhere close to the station.  We never usually have time to meet up, unless we’re training, so it was a lovely breather before the concentration and intensity of the next day!

(Jo Timerick and David Watson were scuppered by our magnificent train service so joined us the next day)

	top R to L: Agata Biernat, Mary Henderson, Luke Fletcher, Rolf Tynan, bottom: Claire Chapman, Rui da Silva, Barbara Gardner, Emma Procter-Legg
L to R: Rui da Silva, Luke Fletcher, Rolf Tynan, Barbara Gardner	L to R: Janet Smith, Stephen Whitehead (SG social media boffin), Penny Humm

…  but alas, the time passed very fast, so we moved on to the Brighton Centre …

… where we were greeted by Brighton Principal Nigel Addison, given our badges and urged to buy tickets for a mystery raffle!

I love the night before conferences start for real – people from the centres and ISCs gather to greet and gossip and there’s an air of anticipation of what’s to come.  This, coupled with the tangible tension of those who will present the next day, all adds up to a buzzy atmosphere. And this year, for the first time, I wasn’t presenting, so I just enjoyed that collective buzz.

At 8.30 we were seated for dinner in our exam hall banqueting area, and welcomed by Vic Richardson and Adrian Underhill, the conference organisers.

James Pitman, MD of Study Group’s Higher Education Division, also greeted us warmly, but with the added sting of a cautionary message for us to actively participate in reacting to the UK Border Agency’s proposed changes to the Tier 4 Visa entry requirements.

You can read more about the potentially devastating impact these changes could have on our jobs, students and universities here and here … and you can certainly do your bit by responding directly, online, here at the UKBA website.   Deadline is 31st January, so don’t just bookmark it, DO IT!

Then, the serious business of dinner got underway, starting with a touch of game terrine and home made piccalilli …  as Mrs Hoover said: (more of her later)  “That’s got to be some home for the numbers eating here tonight”…

Dinner was good, the wine flowed (water in my case, New Year’s resolutions and all that!) and conversation filled the usually silent exam-stress ridden hall.

Towards the end of dinner we were entertained by Mrs Hoover, a host mother residing at 179 Davigdor Road (for those of us Brightonians in the know that was funny …  It’s the address of Hove Police Station!)

A bit hit and miss, but there were some great one-liners and then the raffle … That’s Paul Lovegrove (Principal, SG ISCs) acting as Mrs Hoover’s glamorous assistant …

I made a D.E. (discreet exit) as everyone peeled off to the bar at Jury’s Inn.  Wise move.

Read all about my day at the Conference in the next post …

Sarah Witherby teaches CIT on the Foundation programme and is AP for Bellerbys Brighton.

Bellerbys London STMC Team

The first round of the British Maths Olympiad (BMO1) is a very important milestone in the year for ambitious maths students as it is used to help select the UK team for the International Maths Olympiad (IMO); and although Bellerbys College students are not usually eligible to represent the UK at the IMO, it is a great opportunity for our students to compete against other talented students and pit their wits against genuine challenging maths problems!

The first round of the British Maths Olympiad consists of an exam paper containing six complex mathematical questions, with students having three and a half hours in which to answer them; which presented quite a logistical challenge for us this year – the BMO1 had to take place on Thursday 2nd December, which was one of the days that London was blanketed by heavy snow!

Fortunately, both students were able to make the competition – it certainly helps when students live on-site in our halls of residence! It wasn’t so easy for staff to make it into school that day; I only live twenty minutes walk from Bellerbys London but even I found it difficult to get into school that day! But fortunately my colleague Clive Cubitt and our principal’s new P.A., Sheila Clewley were able to make it in that day to help me invigilate the students; although we try to ensure that our students enjoy themselves when taking part in these competitions, we also have to follow the strict rules and guidelines the UKMT insist on!

Although Daniyar will have moved on from Bellerbys by the time of next year’s competition – by then he will be studying Mathematics at university – I hope Xirui will take part again!

by Dr John McDarby

Maths Teacher at Bellerbys College London

And for me, it has been a very special year; in April my first child Lily was born! Hence, irrespective of anything else that might have occurred this year, 2010 will be guaranteed to be a memorable year for me and one that I shall always look back on with fondness. But does the year 2010 have any mathematical significance? Will 2010 be looked back on as a special year by mathematicians? The answer is, possibly, yes! You see, 2010 is the year in which two very special mathematical research papers were published.

The first of these research papers was the long-awaited ‘Turbulent Interactions for Rotating Blades and Wakes‘ by John M. McDarby (yes, that’s me!) and Frank T. Smith, the hugely anticipated sequel to the best-selling ‘Turbulent Flow on a Planar Moving Belt and a Rotating Disk’ by McDarby and Smith!

As with all sequels, it is very difficult to live up to the success of the original and our paper was no different; we were at times beset by technical difficulties, artistic differences and inevitable delays but finally, our paper was released – and is available at all good Journal of Engineering Mathematics stockists!

Okay, time for me to be honest; although I’m very proud of having my paper published by such a prestigious journal and whilst it has been an absolute honour to have worked with such a brilliant mathematician as Professor Frank Smith of University College London, I very much doubt that my paper will be so successful that everyone will remember 2010 as the year in which my research was published!

But there was a paper published this year which may well be remembered for many years to come and 2010 may indeed be a very important year in the history of mathematics. The paper in question, by Vinay Deolalikar of Hewlett Packard, concerns the rather cryptic statement ‘does P = NP?’.

The question ‘does P = NP?‘ has a relatively straightforward explanation; if P = NP then it means that, for a given mathematical problem, if it is easy to verify that a particular answer is a genuine solution then it should also be easy to find a solution to that problem.

Let me explain that idea further with an example.

If I asked you to find a factor of the number 8051 (a factor of N is any whole number that divides N exactly; for example, 2 is a factor of 6 but 5 is not; and 3 is a factor of 21 but 4 is not) then that should take you quite a while; the answer is not obvious. But instead, if I asked you to show that 83 is a factor of 8051 then that is very easy; just divide 8051 by 83 and if the answer is a whole number (it is, 8051/83 = 97) then 83 is indeed a factor. Hence, finding a solution is difficult but verifying that a particular answer works is easy. And this is the idea at the heart of the ‘P = NP’ problem; if there is a problem for which it is easy to verify its answers, does this mean that there is guaranteed to be an easy way to find those answers or could it be the case that even though it is easy to verify answers, finding them is difficult?

The problem of whether P = NP or not is one of the great outstanding problems of mathematics; but why does this problem matter so much? Well the answer to that lies partly in the fact that the author of the paper claiming to have solved this problem, works for Hewlett Packard, a very large and famous computer company; or to put the question in different ways, why should Hewlett Packard employ someone with the mathematical ability to even attempt such a challenge? And why should someone with such an interest in mathematics work for a computer company? The answer to all these questions lies at the heart of the computer industry; in essence, a computer is a machine that can be programmed to solve specific tasks and a good computer is one that can do such tasks quickly – and a supercomputer is one that can do such tasks very very quickly!

Computers rely on algorithms which are a list of explicit, simple instructions that, when followed correctly, solve the problem that particular algorithm has been written for. And this is why the ‘P = NP’ problem is so important; if it is true then it tells you that there is an efficient way to solve certain problems and hence it is worth searching for an efficient algorithm for solving those problems; but if it is not true then at least you know that there is no easy way to solve the problem! And this is a deceptively important point. If you know that a solution exists to a problem then it is a great motivating factor in finding that solution; conversely, if you don’t know that a solution exists then it is easy to get dispirited and disheartened, and maybe give up.

Personally, I have no idea whether Dr Deolalikar’s proof is correct (incidentally, his paper claimed that P does not equal NP) as this is not my specialist branch of mathematics and his work was too advanced for me to follow properly and so I have to rely on the judgement of professional mathematicians; and as yet I have not heard any conclusive opinion yet as to the validity of this paper. However, his work does hold out the prospect that this famous unsolved problem may have been resolved – in 2010!

In a previous blog I set one of the questions that I’d given to my students as part of our series of weekly maths challenges. This particular challenge was to answer the question ‘What is the number 3?’ without referring to other numbers (hence you couldn’t just say 3 is the next whole number after 2 or 3 is one more than 2, etc).

The answer to this problem lies with the idea of a SET. In mathematics a SET is just a collection of objects; for example, the names of my four nieces are Bernadette, Katherine, Maria and Niamh and so I can form a set that it is made up of four nieces, which I would write as S = {Bernadette, Katherine, Maria, Niamh}. Similarly, I could define a set to be made up of all the objects in my pocket – which in this case would be the set S = {coins, keys, mobile phone}. And I could define a set to be made up of the days of the week – which would give me the set S = {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}.

Now to answer the challenge I set my students we will need to consider the following sets:

S1 = {x, y, z}
S2 = {apple, pear, banana}
S3 = {red, blue, green}
S4 = {x, y}
S5 = {Maria, Kamilla}
S6 = {x, y, z, w, u, v}

It should be straightforward to see that sets S1, S2 & S3 are the same size. Likewise sets S4 & S5 are the same size but sets S1, S4 & S6 are all different sizes. In maths we define the number 3 to be the size of any set which is the same size as the set {x, y, z} (or {apple, pear, banana} or {red, blue, green} …). Similarly, we define the number 2 to be size of the set {x, y}, the number 4 to be the size of the set {Bernadette, Katherine, Maria, Niamh}, the number 7 to be the size of the set {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}, and so on. In fact this is how we define all the whole numbers!

This achievement is even more impressive when you realise that our team only had a few days to prepare for the competition!

The competition, which is made up of three different rounds, took place on Wednesday 24th November at Ravens Wood School which is several miles away from Bellerbys College London and so our principal Andy Quin genorously arranged for a taxi to pick our team up from Bellerbys College and take our students to the competition in style! Our team was accompanied by Maths teacher Clive Cubitt who, along with fellow teacher Faissal Taheri, had worked very hard to prepare Daniyar, Sunghee, Mimi and Cindy before the big day. None of the students had taken part in this competition before so it was a very new experience for them but one they all enjoyed and I’m very proud of how well they have all done!

Although next year Daniyar and Sunghee will have moved on to university, Mimi and Cindy will still be with us and so hopefully they will be able to take part again in 2011 and with their experience maybe we’ll do even better next year!

Maths challenge

Image by: http://www.flickr.com/photos/acidwashphotography / CC BY 2.0

********

Dr John McDarby is a Maths teacher at Bellerbys College London, a university preparation college for international students.

The exam, which is set and organised by the United Kingdom Mathematics Trust (UKMT), is composed of interesting and challenging questions which are designed to test students’ analytical and problem-solving skills and is therefore a great way for our talented students to stretch themselves! For the 5th consecutive year Bellerbys College London has participated in the SMC and this year we had 33 students take part – the highest number of participants yet!

The exams are marked by the UKMT with the results sent out to schools later in the term. Students who do sufficiently well will be awarded certificates (either Bronze, Silver or Gold; depending on how well they did!) and students who do very very well will be able to take part in the 1st round of the British Maths Olympiad (BMO1), another very prestigious competition – which is even more demanding than the SMC!

As usual, I’m far too impatient to wait for the official results so I’ve marked our students’ exams already and although I won’t mention any names yet, suffice to say some of our students appear to have done very well indeed!

Students at Bellerbys London sitting the SMC

The success of this event is thanks to the much appreciated efforts of many members of staff at Bellerbys College London, without which our students would not be able to benefit from taking part in the SMC or have as much fun taking part as they do. Firstly, I would like to thank Donald Sweeney and his kitchen staff for the wonderful spread of food they provided for us! The SMC has to take place on a specific date (which this year was 4th November) and with students from many different classes wishing to take part, the exam has to be sat after lessons finish that day – in other words, during dinner time!

Therefore, so that our students don’t get too hungry or miss dinner, we serve them food whilst they take the exam! This year Donald and his team provided us with home-made pizza (which was very popular!), fish cakes, wedges, sandwiches, canapes, goujons, quiche and much, much more! And with classes finishing at 4.45 and the SMC starting at 5.15, there is also a great logistical challenge to overcome – in just half an hour our maintainance officer Joseph Carvalho has to turn three classrooms into an exam room complete with rows of desks and chairs arranged for an exam – and then have the three rooms turned back into classrooms in time for the lessons taking place there the next morning – so, thank you and well done Joseph!

Thanks are also owed to our principal Andy Quin for his support for our involvement in the SMC. Each year Andy agrees to pay the entry costs for the SMC and the British Maths Olympiad so that we can offer these events to our students for free. Andy also funds a prize each year for our highest-scoring student so that we can reward their success. I am also very grateful to my colleague Christine Barit for volunteering to stay late after school to help me run the SMC this year – her help made everything a lot easier!

But, as ever, the real star is my fellow maths teacher Clive Cubitt who has been the inspiration and mastermind behind our recent stunning success in the SMC and British Maths Olympiad, working late to help students prepare for this competition and sharing his great experience and insight into maths challenges! This year he was supported by one of our new teachers, Faissal Taheri, and between them the support they provided made a big difference to how our students performed in this competition and ensured that our recent success has continued!

Me, Dr John McD (left) and Clive Cubbitt (right)

Study at Bellerbys College

In addition to enjoying and being successful in their studies, I hope that my new students will be genuinely happy at Bellerbys College London and that they’ll enjoy all of their experiences here; and although I intend to work my students hard as usual, I hope that many of them will find time to also take part in some of the extra-curricular activities offered to them at Bellerbys College London. So far the signs have been very promising, our weekly Maths Challenge has returned after a summer break and has proven to be even more popular than ever!

This term in particular sees a hectic schedule of extra-curricular maths activities, run by the Maths Department here in London. Very soon our students will be taking part in the UK Mathematics Trust’s Senior Maths Challenge and any students who do well in this competition will have the chance to compete in the British Maths Olympiad, in which we hope to build on the success we have enjoyed in previous years.

And we will also be looking to recruit some new students to our team for this year’s Senior Team Maths Challenge – we came a very pleasing third place in last year’s regional heat but most of last year’s team has since left Bellerbys London so we need to find some new team-mates to take part this year. It’s always interesting to see which of our new students will emerge as our new maths stars over the coming years!

And it is particularly interesting to meet and get to know my new A Level students whilst, at the same time, my former students are starting at university and settling in to their new lives as undergraduates. I’ve also had the pleasure of meeting some of my old students as they return to England and it’s been lovely to see how excited and enthusiastic they are about starting university. I’d like to take this opportunity to wish them all good luck for their future – especially those studying Maths!

Of course there’s another group of students who mustn’t be overlooked, those students returning for their second year at A Level – and it’s always nice to see these students again after their long summer holiday! Teaching my second year students this term has been particularly fun for me, as the group that I taught last year has merged with a class taught by my colleague Clive Cubitt and a few other students have also decided to join the combined group – so that they can study some extra maths modules. As a result I have a nice big group of enthusiastic and eager second-year students to teach – and I’m thoroughly enjoying it!

So to end this blog I’d just like to wish “Good luck” to all three generations of my students – the new students who are just starting their studies at Bellerbys London, my returning A Level students and all my ex-students now starting at university!

Cover via Amazon

In my previous blog I championed Gregory Chaitin’s excellent book , ‘Meta-Maths’, a unique and very personal maths book. In this blog I want to encourage you to read a very different style of maths book; ‘The Music of the Primes‘ by Marcus du Sautoy.

In many ways ‘The Music of the Primes’ and ‘Meta-Maths’ are very different books; they are written in very different styles and their content – mathematically speaking – is also very different. But what unites these two books is that they both convey the passion that mathematicians feel for mathematics. In the case of ‘Meta-Maths’ this was achieved through a very personal account of one mathematician’s work; in ‘The Music of the Primes’ it is achieved through a wonderful historical journey through mathematicians obsession with prime numbers.

Reading ‘The Music of the Primes’ reminded me why I love mathematics. I simply could not put the book down and did not want it to end. Yet ‘The Music of the Primes’ also inspired me and made me want to stop reading and actually do some new maths myself.

As the name suggests, ‘The Music of the Primes’ is about PRIME NUMBERS. A number is described as PRIME if it can only be divided by itself and 1; so, for example, the number 3 is prime because it can only be divided by 3 and 1, whereas 6 is not prime because it can be divided by 6, 3, 2 and 1 (Read my previous blog on Prime Numbers).

Mathematicians have proven that there are infinitely many prime numbers (incidentally, the first fifteen prime numbers are 2, 3, 5, 7, 11, 13, 17, 23, 29, 31, 37, 41, 43, 47, 53) and many other facts about these numbers but there is still a lot more which we don’t yet know or understand about prime numbers. And the most important of these is the RIEMANN HYPOTHESIS (Read my previous blog on the Riemann hypothesis).

What makes ‘The Music of the Primes’ so brilliant is that it describes the RIEMANN HYPOTHESIS – one of the most important problems of modern mathematics – and is able to explain why this problem is important, why it has fascinated mathematicians since its conception and the progress mathematics has made in solving it, all in a manner which is enlightening, inspiring and accessible; and this is not an easy thing to achieve.

For some time now I have thought about writing a blog on the topic of the Riemann hypothesis but each time I have sat down and tried writing a blog about it I have found that it is simply impossible because there is just so much that needs to be said. And despite my best efforts, I have never been able to explain the Riemann Hypothesis to anyone successfully. And so I am relieved to have discovered this brilliant book which explains the Riemann hypothesis in a manner that is far more lucid, eloquent and engaging than I could ever have achieved!

The concept of a prime number is relatively easy to understand and most people will encounter prime numbers at a very early age; in contrast, the mathematics involved in Riemann’s hypothesis is much more advanced, and involves maths that you would normally only see if you studied mathematics at university. This in itself tells us something about prime numbers; they are easy to define but their existence and behaviour is deceptively complex. And this is why it was so challenging for me to write a blog about the Riemann hypothesis; the mathematics and the history of this problem are just too great. 

This is why de Sautoy’s book is so good. Firstly, he is able to explain why prime numbers have fascinated mathematicians for so long and ‘The Music of the Primes’ does an excellent job explaining why prime numbers are important, especially to mathematicians, and how they have captured the fascination of some of the greatest minds mathematics has ever produced. Marcus de Sautoy then takes us on a historical voyage explaining the many contributions that have been made by some of the greatest mathematicians ever – people such as Euler, Fermat, Gauss, Hilbert, Hardy, Littlewood, Riemann, etc – to our understanding of the prime numbers; including Riemann’s postulation of his hypothesis, it’s historical background and the endeavours of many great minds to proving it. Reading this book has given me a much richer understanding of mathematics in general and is an inspiring work that conveys the passion and love that mathematics engenders in mathematicians. As such I would strongly recommend this book to anyone with an interest in any aspect of mathematics.

Incidentally, I read this book after noticing it in a second-hand book shop for just £1. And what a bargain it has turned out to be – ‘The Music of the Primes’ is a fantastic book and one of the best books I have read in years! I must also confess that despite Professor de Sautoy being a very famous mathematician and author I had never read any of his books until now; however he is one of the few authors that I can boast that I have met and even spoken to! My friend Dr Tim (who told me about the egg-dropping problem! ) once worked as an assistant to Professor de Sautoy when he presented the prestigious Royal Institute Christmas Lectures  and, as part of their tour around the country, I had the pleasure of meeting Professor de Sautoy (and my friend Dr Tim) accidentally in Greenwich one day after work! And I wish then I had gone straight into a bookshop and bought a copy of his book rather than wait several years before reading it!

Dr John McDarby is Maths Teacher at Bellerbys College London