Wednesday, 19 September 2012

Everything is Mathematical

The set of Everything is Mathematical books.
I've recently been involved with a new mathematical project called Everything is Mathematical. A group of Spanish Mathematicians have written a comprehensive set of popular maths books, which have proved so successful that they're being translated into other languages, including English. The team behind the series have joined up with The Times newspaper and Marcus du Sautoy to present the series to the British audience.

But where do I fit it? Well, to generate some interest in the series they're producing a number of maths challenges that can be found on their website (mine is below).
Some of the challenges are fairly standard and well known, however, there are a couple of gems in there that I had never seen before! Keep a look out on the website for the weekly challenges. If you do solve one of the problems there is a competition you can enter. The winners receive a free subscription to the entire set of books.

Now since there are 40 in the set and each one is £10, you may need come convincing before you part with your cash. To get you interested I thought I would review one of the books. Of course since I'm working with these guys you'll have to weight my review with the fact that I'm biased :) (although I'll try to remain neutral).

Who are they for?
Based on what I've read I think these books are more suitable for an older audience. It could certainly appeal to those who were educated in numerical subjects and then left due to career decisions, but never lost their interest, as well as those who never really got on with mathematics but realise its importance. Having said that I could also also see parents buying a set to enhance their children's education as school as well as benefit their own interests.

The first thing I noticed about the series is the sheer comprehensiveness of the books. To be honest, I'd be hard pressed to even name 40 different mathematical fields! The books cover all the standard aspects such as geometry, symmetry, probability, etc. but then goes further with books on the mathematics of our senses and perception, artificial intelligence and, of course (my favourite) mathematical biology.

You may think (as I did) that, by spanning so many subjects, each one would be a pamphlet in size. Here, again, I am pleased to say I was surprised. Each book I've seen is a really nice hard back spanning over 100 pages in length. They contain: nice clear diagrams; formulas; anecdotes about the history; fact boxes and even problems to challenge you.

Book number 1.
What about the content? 
Well here is my first admission: I haven't actually read the first book. The first one is all about the golden ratio and its geometry and to be honest, I've never been a fan of the golden ratio because even though it has some extremely nice mathematical properties I find that discussions quickly descend into numerology [Rant 1]. So, instead of starting with The Golden Ratio, I jumped straight in with "When Straight Lines Meet" a book all about non-Euclidean geometry.

Now I would've expected the book to have started with easy stuff, y'know setting up the cartesian coordinates and linear geometry leading on to hyperbolic and elliptic geometry later. How wrong could I have been? The first chapter drops you straight in by explaining the taxi cab metric, using the city of el Ensanche as an illustration.

el Ensanche's very regular city set up.
This is certainly one of the strengths of the books. They use of definite, tangible examples allowing them to discuss complex ideas and very quickly outstrip even my knowledge! For example I had never heard of Girolamo Saccheri's contribution to non-Euclidean geometry.

Each chapter is completely different and could potentially be read independently. For getting a deep overview about a specific aspect (history of geometry, curved space in relativity, uses in computing, etc.) then this format is very appealing. However, it lacks an overarching sense of story that will keep you reading all the way through like the best popular science books can.

What is good to see is they're not afraid of displaying mathematical functions and formulas and then challenging you to calculations that actually mean something, e.g. why calculate the length of a line of a sphere when you can calculate the distance between New York and Sydney on the Earth?
£400 is a steep price for a comprehensive set of popular maths books, although calling them "popular" perhaps does not do them credit. Think of them more as a set of encyclopaedias of the mathematical world, but with each chapter being eminently more readable than a fact driven summary of events.

There is no better set that will give you the range and depth of subjects available. Due to their diverse nature you will discover topics that interest, entertain and even surprise you. Thus, if you have want to see what mathematics can really do outside of the classroom then these books are you.

[Rant 1] Of course you're going to find things in the golden ratio if you look for it. Any ratio can be found in nature if you look hard enough. I freely admit that in certain cases you can attribute inspiration to the golden ratio, e.g. Le Corbusier's architecture or Dali's and Da Vinci's paintings. However, these are explicit uses. Stating that certain natural phenomena occur in the golden ratio is much dodgier.

To really believe that the ratio is there I would want to understand WHY it is there. This is the essence of mathematical biology. Biologists observe phenomena, mathematicians try to understand its cause. For instance, there are reasons why the golden ratio/ Fibonacci's sequence should appear in sunflower seed packing as it is the optimal packing ratio. Compare this to the claim that your fingers are in the golden ratio and the suggestion that beautiful people are more in the golden ratio than not. Not only are you left asking why but you're suggesting that people who don't fit your rigid proportions are ugly!

The golden ratio supposedly appearing in the human body.


  1. Am reading Prime Numbers and am not sure whether I have misunderstood the statement on page 46 concerning 504 being divisible by 8 which is "a" in the equation. Shouldn't this be "504 is divisible by 3" as this is the "p" in the equation?

  2. Sorry for the large delay in getting back to you. I didn't spot your post until just now.

    I've looked at the page you mention and the are quite correct. The mistake is clear because 8^3-8 is clearly divisible by 8. However, it is not clear that it is divisible by 3. Which is why Fermat's theorem is important.

  3. this is a really interesting post. love the golden ratio supposedly appearing in human body, this just amazed me and started looking at my hand as soon as i read this post :-D

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  4. My Maths Department are finding major errors in the books and lots of grammatical mistakes. We are very worried.

    1. That is disappointing to hear. If you can email me some specific examples I'll forward them on to the publishers.

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  6. Thanks for the post. I can't find who are the authors of the series. Do you have any extra info on that? A link to the original spanish edition?

    1. Hi Marco, apologies about the late reply. To answer your question, I'm only able to give you the authors of four of the books as they're the only I have. Outside of that, I can tell you no more.

      Joan Gomez wrote When straight lines curve. Non Euclidean geometry
      Mathematicians, spies and hackers. Coding and encryption.

      Fernando Corbalan wrote The golden ratio. The beautiful language of mathematics.

      Enrique Gracian wrote Prime numbers. An unpredictable series.

      I hope that helps.

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  8. The picture of the arm is laughable indeed. How about making the forearm with proper proportions. If you did, you would see the golden ratio

    1. I fully agree that the picture is not to scale, it is merely a schematic. My point is that the idea that the human body is in the golden ratio is dodgy at bet as there is no real reason for it to be there.

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  10. Have you had a look at the recent relaunch from National Geographic? Wondering if it fixes the mathematical and grammatical errors mentioned in these comments

    1. Good question Matthew. I had seen it in WH Smiths earlier this week. Unfortunately, I didn't have my original set to hand so I couldn't compare. All I can say is that I forwarded all corrections sent to me to the publishers. I cannot say what they did with them. Please do keep me updated if you do by the first issue.

    2. I have subscribed but don't know when it'll arrive, will update when it does. The series has been extended by 20 issues but the content seems to be fairly similar in a slightly different order.

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  12. Hi, I'm student from Greece and I would like to buy this series of books but I can't find them here .I want to ask you if you sell these books or if you don't then is it possible to tell me if you know stores or publishing houses in Europe that I can buy these books? Thanks for your time.

    1. Hi Thomas, I'm not affiliated with them at all. Also I don't think this series exists as shown above. However, it appears that National Geographic are selling a version. More details can be found here: