In reviewing The Code I should note that this is a TV programme not aimed at me. Nonetheless as a mathematician I do like to see the portrayal of my subject in the number one mass medium. Actually, I’m unsure who the target audience is. At one point pi is introduced slowly over a number of minutes which would indicate that the producers thought that even the most basic ideas could not be assumed. Leaving that minor criticism aside (after all it’s a problem with TV output rather than a specific fault of this programme), what was the programme like? What’s it about? Well, the intro said that it was about answering the question Why is the world the way it is? The precise definition of ‘The Code’ was a bit obscure but we all know they’re talking about maths. The programme began with Marcus du Sautoy pacing around a cathedral at night with an echoing voiceover from a girl. We had fancy graphics, moody lighting, long shadows, strange camera angles and occasional uses of black and white. Hidden in the cathedral was a code, said du Sautoy, and then showed how mathematics showed up in its design. In particular the relation with harmonious combinations of notes. For example the altar divides the nave into a ratio of 8 to 5 which is a minor sixth in music. This episode was about numbers, so primes, pi, i, acceleration due to gravity and a constant associated with a nautilus shell were explored. See the video below for a clip about this last constant. To exemplify the appearance of pi the normal distribution was used. Unfortunately, the idea was to get the daily catch from a fisherman and weigh the fishes. From the mean and variance...

In a change to my scheduled post I’ll advertise The Code. This is a new TV series presented by Marcus du Sautoy. Judging by the trailer I saw last night the BBC has spent decent amounts of money on it. Leaving aside that it is scheduled in the summer rather than more prestigious autumn time it is good to see a maths/science programme on BBC2 rather than BBC Four. The series starts on Wednesday 29th July, 9pm and will be available later on the iPlayer. The website, http://www.bbc.co.uk/tv/features/code/, contains clips, competitions and other interactive treats. My favourite bit so far is an interesting clip with...

I recently received a request for help with an exercise in a text book (I guess this happens when your profile suddenly becomes higher). The exercise was a dressed up version of a children’s game. The idea is to take one word and transform it into another by changing one letter at a time. For example, to change DOG to CAT we can do the following: DOG COG COT CAT Obviously longer words make the game more complicated but my interest in this is that it is a great way to get students talking about proof and doesn’t involve any new mathematics getting in the way of their understanding. I got the idea from Ian Stewart’s Nature’s Numbers. In Chapter 3 he talks of the necessity of proof in mathematics and to show this uses the above game played with changing SHIP to DOCK. (How this game is connected to proof is given at the bottom of this post.) You can try this yourself. One possible answer, given by Stewart, is SHIP, SLIP, SLOP, SLOT, SOOT, LOOT, LOOK, LOCK, DOCK. One year I set the problem of getting the SHIP to DOCK to my group of six tutees during their first tutorial in their first week of university and left them to play with it while I located some chalk. When I returned some of them had done nothing – not one letter had been changed and progress had not even been attempted. The reason given by one of the students has stuck in my mind ever since. He shrugged in bewilderment as if I had asked him to perform brain surgery and said “But I’ve never seen this before”. He honestly could not see how he could solve such a problem without having...

I was reading Alex’s Adventures in Numberland and was inspired to find some Martin Gardner on video. I managed to locate a TV programme from 1996 which I had never seen before. And it is great! It features Max Maven, John Conway, Scott Kim, Persi Diaconis, Ron Graham, Michael Webber, Jay Marshall, Donald Coxeter, James Randi and Meir Yedid (the guy with or rather “without” the fingers!). Also, a young Gardner is seen performing magic (although the secret of one of my favourite card rise tricks is revealed). There is a section (at about 25:30) involving perfect shuffles. You can find out more in my video on the subject. The Nature of Things / Martin Gardner from Wagner Brenner on...

I am always interested in simple/elegant/cool proofs of mathematical facts. I’m also interested to know their origins. Does anyone know who came up with the following rather elegant proof of ? It’s likely that the origins are lost in time but I thought I would ask anyway. Proof: I like this because of the use of 2-1=1. Another situation where the use of 1 gives a cool proof is the following from complex analysis. Does anyone know the origin of the proof? Theorem: If is complex Riemann integrable and is Riemann integrable, then . Proof: If the left-hand side is zero, then the statement is trivial. Hence, assume that the left-hand side is non-zero. Define the complex number by We have, Do you have any cool proofs? (With or without clever use of...