Even artists appreciate sunsets and the ocean waves and the march of the stars across the heavens... as we look into these things we get an aesthetic pleasure from them directly on observation. There is a rhythm and a pattern between the phenomena of nature which is not apparent to the eye, but only to the eye of analysis, and it is these rhythms and patterns which we call Physical Laws. "
So wrote Richard Feynman, Nobel-winning physicist, in The Character of Physical Law (1965), explaining how a "deep understanding of mathematics" is crucial to grasping the laws that govern the natural world.
Yet all too often, says Simon Carson, head of science at Norton College, north Yorkshire, pupils are encouraged by their experiences at GCSE science to believe that they can do A-level physics with little feel for or knowledge of maths. Links between maths and science departments are frequently weak; and the approach to maths in science at GCSE tends to dodge straight mathematical knowledge. For instance, GCSE physics teachers will avoid using an equation to talk about the relationship of speed, distance and time, preferring to use a triangle. Students can thus get to A-level believing that they are "good at science" and that physics is not mathematical. What a shock when they suddenly have to manipulate algebraic equations, analyse graphs and describe functions.
The challenge, says Simon Carson, is to find ways "of making maths a part of physics that is interesting in its own right". Two projects being run by the Institute of Physics - the post-16 Initiative and Advancing Physics - are developing syllabuses that will "teach maths in context as it arises in a physics course". For example, creative use of software such as the Modellus package will enable students or teachers to play with graphical modelling and get a feel not just for how to construct a graph but how to read it, how to grasp the story behind a mathematical model such as a graph - or an equation. Then, perhaps, sixth-formers will agree with the mathematician Eugene Wigner who wrote, in Communications in Pure and Applied Mathematics (1960), "the miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift".
Simon Carson is editing a booklet - 'Maths and Physics' - for the Institute of Physics, which will be published after a debate at the ASE annual meeting. Details from the Institute of Physics' education department, tel: 0171 470 4800