Sunday, 14 December 2014

Talk : Maths in Society

Went to an interesting Cafe Sci talk recently in which Dr Snezana Lawrence (Senior Lecturer in Mathematics Education at Bath Spa University) discussed how mathematics was perceived in society and how it was taught to schoolchildren.

This post is based on the talk, with some added linkage thrown in.

Dr Lawrence began by describing how she had once addressed an audience of around 70 people from the London Mathematical Society to raise their hands if they were mathematicians and was surprised to find that only one person did so - it turned out that only the most "pure" mathematics researchers were actually regarded by their peers as actual mathematicians, with everyone else believing themselves to be a specialist of some sort!

The Dr continued by noting that, although mathematics was often viewed as a "universal language", there were often significant differences in how it was taught in different countries. For example, the eastern european countries are still heavily influenced by the practical style of mathematics developed by France after the revolution, in contrast to the much more theoretical work that was undertaken in next door neighbour Germany. Many of the key figures of the period, as well as the major trends, are covered in this excellent article at The Story of Mathematics.

One of the greatest awards that a mathematician can get is a "Fields Medal", which are awarded every four years. The most recent recipients, in 2014, were Artur Avila, Maryam Mirzakhani, Manoj Bhargava and Martin Hairer.

Artur Avila - top mathematician

Other mathematician who were mentioned included Paul Erdős and Andrew Wiles who discovered a proof to Fermat's Last Theorem and whose work is described here.

Andrew Wiles - aimed high, scored big time!

Dr Lawrence also played a few clips showing how mathematicians were portrayed in films (e.g. Good Will Hunting, Pi) and commented that the portrayals were generally as mathematicians being aloof, mentally on-the-edge and geniuses.

These themes were also explored in the rather awesome documentary "Dangerous Knowledge" (see also here) which looked at the lives of the great mathematians Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan Turing. The documentary describes how Europe at the end of the 19th century was moving from an age where science was all about certainty (e.g.Newtons Laws of Motion) to one that was driven by uncertainty (e.g. Brownian motion). The program shows how mathematicians such as Cantor and physicists such as Boltzmann who were grappling with ideas that involved uncertainty faced very significant resistance from their peers. Cantor's work which dealt with infinity not as an abstract idea but as a concept that could be worked with and had infinities of different sizes, led him to a nervous breakdown.

Some idea of the paradoxes involved in thinking about infinities can be seen by considering Galileo's Paradox , which goes something like this :

1) In a number line, there are fewer square numbers (4,9,16,25,36...) than there are numbers in total (e.g. 4,5,6...34,35,36...)
2) Yet for each number there is also a square (4 has 16, 5 has 25, 6 has 36 etc) - so there should be as many squares as there are numbers.

The way mathematics was portrayed in society was also discussed, with reference being made to the infamous "Maths Class is tough" Barbie and Dr Lawrence explaining that mathematics was perceived as a "high stakes" subject to study, although it did provide some kudos to those who were good at it - and that the current fascination with millionaire IT geek entrepreneurs had also raised the standing of the subject somewhat.

Governments of all colours have long been concerned about the national skills base in mathematics (as well as in other STEM subjects), with a report on the issue being issued by Prof Adrian Smith in 2004 (Government response here)

Dr Lawrence also described the work of Nicolas Bourbaki, who has published many papers, despite the fact that there is not actually a mathematician called Nicolas Bourbaki.

Winningly, Bourbaki was also the inventor of the "dangerous bend" symbol. A fact that made the talk worthwhile for NSB all by itself!

A sign from Bourbaki

A theme that recurred throughout the talk and the subsequent Q&A was that students would often ask how mathematics was relevant to them. One example of how this can be answered is the "Taking Maths Further" podcasts, which look at how mathematical concepts are practically used in science and industry.

Also, Dr Lawrence's website, has a maths timeline, list of mathematicians and a lot of other, very accessible, information.

Image Sources:
Dangerous Bend
Andrew Wiles
Artur Avila

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