Mathematics

Beauty There is a beauty to mathematics in two senses of the word.  There is the obvious visual beauty of fractals.  The wallpaper to this page was generated from the equation  .   But there is also the beauty of an elegant mathematical proof.  I am tempted to show a few, but mathematicians know them and most non mathematicians would not take the time to see their beauty.  To them I would only say ask any mathematician to show that the root of 2 is irrational, or there is an infinite number of primes, or that there are ‘more’ points between 0 and one than there are integers (1,2,3,4,      ). Of course they are both infinite, but one infinity is ‘bigger’ than the other!

Applicability  I can imagine some people reading the last sentence and mutter something like “its like arguing about how many angels can stand on the point of a needle”, or less politely “sad gits”.  Before anyone dismisses mathematics so lightly they should consider this.  As part of widening participation we visit schools to encourage them to think about taking up a degree in mathematics.  We spend about half an hour asking them to list a subject that does not use mathematics.   When we have a reasonable sized list, we take each item in turn and give examples of mathematics from each.  For example if they say ‘Art’ we can point out, the beauty of abstract fractals, the use of perspectives and focal points in many pictures, and the whole industry that is generated around computer graphics.  If they say ‘Music’ we can point ort that the scales are mathematical, the sounds of an instrument can only be objectively described using the language of mathematics, we could talk about Fourier Analysis and so on.  That is even before we get on to the finance of an orchestra, mathematics of crowd behaviour and so on.  Mathematics is even creeping into sociology.  Robert Axelrod’s work on the iterated prisoner’s dilemma and human cooperation is fascinating.  I, myself, have written a mathematical essay on corruption.  Only once were we stumped by the school students.    One asked us to show the mathematics of wine tasting.  At that time we could not think of an answer!

Popularising Our group at Sheffield Hallam University has launched a number of initiatives to popularise mathematics.  We had a successful day conference called “One that went well.”  We invited teachers to bring one lesson plan on one mathematical topic the students liked.  Each teacher gave a 10 minute talk on the subject, the approach, the materials used, and why they think it went well.  Each teacher brought one good lesson and walked away with many.It is a good idea but needed support to allow teachers to participate.  Sadly the support was not forthcoming.  We like many other university groups give master classes.  Our most successful initiative is Popmaths.

Personal Interests For the last few years I have been teaching Game theory, (what is the best strategy to take a penalty, and much much more), Genetic Algorithms (There is a creationist website called evolutionofideas. com.  They argue that you cannot get order by random changes and selection.  Lesson one of a Genetic Algorithm course shows that they are wrong.  They believe God designed their magnificent brains.  It is a shame they don’t use them.) I also teach about Cellular Automata.