As a youth entering the sixth form to study Mathematics, Further Mathematics and Physics I enjoyed the riches of the school's mathematics library and in particular three books which appealed to me, A mathematician's apology [1], A book of curves [2] and On growth and form [3].

Hardy's book [1] is one that an impressionable, young mathematician should not read unguided. It left me with the impression that the proper pursuit of mathematics was as a pure subject, of no use or application, to be studied for its own sake; to my regret, I held to this view for several years before finally being able to shake it off through teaching Newtonian mechanics. Looking across mathematics teaching today I seem to observe great interest in geometry, number and algebra ‘curiosities’ that are rooted entirely in mathematics. This in itself is no bad thing, since it clearly draws us and our students into the fascinating world of mathematics. But what of the applications of mathematics? Might they be equally fascinating? Surely we do not want to lure our students into Hardy's trap?

The Independent [1], prior to the 1996 Wimbledon tournament, carried a story to the effect that Tennis had a problem. Rackets were getting longer and, so the International Tennis Federation (ITF) claimed, rallies were getting shorter as the serve dominated. The story provided some surprising figures. The current limit to the length of a racket is 32 inches, but the longer rackets which are the cause of the problem are 29 inches, 2 inches longer than the standard racket. The article claimed that such rackets 'give players up to 14 per cent more power than standard models'. The article went further,

John Branfield’s request [1] for the mathematics of bowls was too tempting to resist. What follows comprises a simple model for the curve upon which the bowls move, an explanation of how and why they move as they do and an attempt to refine the model of the curve. The search for a model proved to be addictive and effectively displaced many other activities. One of the reasons for this was the way in which the investigation involved so many people with interesting contributions to make. In order to give a flavour of the investigation, I have taken the liberty of giving a somewhat personal rather than strictly mathematical account, the mathematics being no less important.

If the above phrase appeared in an A-level paper the Board responsible would receive many protests: “a contradiction in terms”, “impossible”. But is it? Our attention was drawn to this via this A-level problem from the J.M.B.

(Further Maths, Paper II, 1988)

A number of recently published articles have dealt with aspects of mathematics as applied to the motion of the human body, [1, 2, 3], some with special regard to the modelling process. There seems to be a growing interest in the application of mathematics to this area and the recent introduction of A-level “Sports Studies” into some schools and sixth form colleges must help this trend. At a talk I gave recently to a branch of the Mathematical Association on “Mechanics and gymnastics”, five out of an audience of twenty-five were P.E. specialists looking for ideas to enable them to teach the mathematical/mechanical part of this A-level syllabus.