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We all deserve to see it…

…the secret garden of maths.

Romanesco Fractal Broccoli

Romanesco "Fractal" Broccoli


Dear reader,

My name is Micky Bullock and I am, amongst other things, a concerned mathematician.  My paranoia is rooted in the average person’s contemptible indifference to maths and their assumption that mathematical elegance is incompatible with their interests.  There is an infinite world of fascination at our fingertips, yet only those lucky enough to have found the key to this secret garden can freely explore it.  I believe the rigidity of the National Curriculum is heavily to blame for this woeful situation, that those mathematicians who have decided to teach, to attempt to instil enthusiasm for maths in our younger generations, have barely been afforded the time or resources to impart anything more than boring repetitive sums.

As a mathematician, I like to solve stuff.  And due to the complexities of the problems I take it upon myself to solve, I like to keep my brain clear of information, which is why I strictly maintain a calendar and write everything down, rather like the way a computer uses RAM, to get all the noise out and keep the central processing unit running at maximum efficiency.  It is not uncommon for me to discover fascinating mathematical patterns in apparently simple systems, patterns that are often too exciting to keep to myself.  Therefore, both to share these findings with those who need or seek inspiration in maths, and to prepare my mind for those findings which succeed, I have created this blog to serve as an exhibition for these mathematical curiosities. 

A quarter of a century ago,
maths teachers were more or less free to teach whatever they believed appropriate and in whatever manner they chose.  The revolutionary introduction of the National Curriculum in 1988 began to standardise education across the country and elevate it to a red hot topic, a priority in any political campaign.  Two decades later we should have reached the zenith; the UK should be the global forerunner in secondary maths education.  But are we really inspiring our children or just frying their fragile brains?

Today, 16-year-olds’ enthusiasm for mathematics remains abysmally low.  It is not surprising; there is only so much a person can be bombarded with abstract sums.  It’s obvious to us how useful it is to have a solid grounding in arithmetic, so it is our responsibility and goal to equip every child with the mental tools they require to lead a successful life. The theory is sound, but the kids aren’t interested.  Why not?

I was once performing some vacation work as a secretary for an estate agent when a flustered young student on work experience came rushing over to me with four huge piles of info packs.  “My boss needs exactly 150 of each of these immediately!” she cried, and dumped the pamphlets on my desk.  “You’re good at maths,” she continued, “Count these!”

Of course I indignantly refused.  However such events illustrate how people have confused the sacred art of mathematics with counting and repetitive sums.  I didn’t take a degree in maths to be really good at adding up!  Comparatively few people ever realise that mathematics is actually something far more exciting, creative and imaginative, that it could be defined as the technical exploration of the universe.  Maths is the engine of life and it runs seductively beneath the surface of everything we ever do.

Perhaps once it was easy for children to concentrate on their algebraic skills in school for it was fairly obvious to them how these tools were going to be used.  But in today’s information deluge the human mind has been forced to become far more selective in the information it chooses to retain and skills it chooses to learn.  There is plenty of evidence of this, not least in the explosion in popularity of Twitter which is effectively a personalised news channel. 

Indeed, if ever we need technical information about an unfamiliar subject we can usually find the right person to speak to, often via ones Facebook friends which would in most cases satisfy the vast majority of conceivable occupations.  As a classic example I was recently asked by a friend in the energy assessment industry how to find the length of the diagonal of a rectangular room; I texted back, “Google Pythagoras” which was all he needed to hear.  The point is, with the Internet now in our pockets, what is it important for people to know and understand anymore?

A Rendering of a Riemann Sphere
A Rendering of a Riemann Sphere

Recent expressions from the education sector have highlighted the repressed attitude that teachers – arguably the real education professionals – need more freedom in the classroom to promote their subjects.  This suggests a potential shift away from rigid utilitarian lesson schedules toward the more liberal approach.  But with propositions like the “Use of Mathematics” A-Level, an initiative supposedly to increase post-16 numeracy, heavily denounced by academics to further reduce creativity and pattern recognition to the simple memorising of algorithmic procedures[1], one would be forgiven for showing a lack of optimism.

In English, things are different; we study the technicalities in “Language” and are exposed to the great artistic works in “Literature”.  It wouldn’t take much restructuring to have a second, more qualitative and exploratory,  maths GCSE in which children would be exposed to the great historic and contemporary works of mathematics, for example the discovery that π is encoded into the Great Pyramids or how, for example, in music, Ghanaian and Indian rhythms exploit the indivisibility of the primes[2].  And if even that sounds boring, what about studying the fractal patterns in the Romanesco Broccoli?  Everyone likes fractal vegetables!  Marcus Du Sautoy, professor of mathematics at the University of Oxford, said, “We are not frightened to throw Richard III at 13-year-olds. Let’s be more brave and throw Riemann at them, too.”[2] 

Don’t get me wrong; I’m not against sums – it is of course in the interest of society, the economy and the individual to be proficient in arithmetic – but teaching sums without showing their potential is abstract and absurd, and the modern learner is switching off.

One thing is clear: Our children must experience the beauty of mathematics before our reckless curriculum paralyses their interest forever.  Give them the key to the secret garden – inspire them – and watch the sums follow.

“A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas. The mathematician’s patterns, like the painter’s or the poet’s, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.”[3]

GH Hardy


Giza Plateau, Egypt 2007

Micky at the Giza Plateau, Egypt 2007


1. “Academics denounce maths A-level” – UK BBC News – 9 July 2009

2. “The secret life of numbers” – Guardian.co.uk – 23 June 2009

3. From “A Mathematician’s Apology” – a 1940 essay by British mathematician G. H. Hardy. It concerns the aesthetics of mathematics with some personal content, and gives the layman an insight into the mind of a mathematician.

  1. tagesgeldkonto
    November 19th, 2010 at 08:43 | #1

    Lovely sharp post. Never thought that it was this easy. Extolment to you!

  2. bukmacher
    September 19th, 2010 at 20:55 | #2

    You post great articles, i have bookmarked for future reference!

  3. paul
    June 18th, 2010 at 10:31 | #3

    Rotation of earth .

    24hrs to take one rotation ,earth itself so.
    24=360deegree angle to reach same possition.
    the round shape of rotation around the sun,
    1hr=15*12 =180, 2*180=360,
    365 days round , rotation around the sun.
    speed=s,distance=x , to reach the same possition but verying possition due to hexagen rotation in 3D
    delta x,
    to the same possition it take (delta y ,years) at same
    point calculate.

    applying to calculas 0 to infinity integration.
    delta y , with distance to sun.

    applying intial to infinity timing below
    delta y*365 ,zero to infinity.
    ie, 1year=365,half of 1year=356/2 =182.5 (182days 12hours)
    year 182 to next 365 days ,(273days,12hours)full rotation.
    182.5+182.5=365 days, calculating 0 to infinity.
    365,year 0 to 2*182.5,365+1/2 to,2*182.5 infinity.
    applying calculas , can determin the path of earth rotating
    spins like electric 3d circle ,can also calculate no: circles.sun is still in motion

  4. Barbara Bullock
    August 21st, 2009 at 12:15 | #4

    School used to be amazingly creative place for both pupils and teachers before the national curriculum came along! truancy was low and children were excited and enthusuastic about school. Now teachers are bogged down with paperwork. Most of which doesn’t actually get read or used! A large majority of pupils are dissatified and turnedoff by school. Something needs to change! Schools are full of creativity among its inmates. Let it be!

  5. Harri Deo
    July 28th, 2009 at 22:24 | #5

    I for one was an enthusiastic maths student, but when it came to GCSE’s we were the first “guinea pigs” to the new curriuculum which you refer to in this artice. It did not leave any room for creativity as you were left with the immense task of memorising an enormous amount of theory with no understanding of its use. I applaud you in highlighting this and bringing about a new perspective on maths and its relevance on our every day lives.

  6. Lawrence
    July 27th, 2009 at 23:53 | #6

    nice. will follow this with interest.

  7. Geoff
    July 27th, 2009 at 21:08 | #7

    good article

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