17. The importance of mathematics.

The minimal objective in schools in most countries is to ensure that leavers, somewhere in their  teens, are both literate and numerate. And while teaching methods have changed and in some ways advanced in recent decades, where the traditional approach has been totally abandoned, far too many pupils leave school innumerate. Numeracy may be defined as the ability to carry out elementary tasks under the three headings-arithmetic, geometry and algebra. Of these, arithmetic is the most valuable for ordinary purposes.

If that is true, it is something of an irony that electronics, which helps mathematical processes in so many directions, have had an adverse effect in pupil's ability to do mental arithmetic. Pocket calculators give immediate solutions to virtually all mathematical problems. In no way do they exercise the brain. So, the use of logarithms and the slide-rule has disappeared. The ideal situation is the teaching of mathematics by the old methods and the use of calculators for checking purposes only. Given the basics, a pupil can then use the calculator to great effect in the outside world.

So, what are the uses of mathematics to the ordinary person? As a wage-earner, it is an obvious advantage to be able to check one's wage slip and bring any discrepancies in deductions for tax, insurance, union dues etc to notice. Secondly, it is essential to be able to work out a personal budget, and if possible to allow for savings to cover holiday expenses, other luxuries, and unforeseen calls on the pocket. As a professional, selfemployed or business person, further advantages emerge. Assume you wish to start a small business and you approach your bank manager for a starting loan. He or she will expect a realistic breakdown of initial costs, wage bills, if any, expected returns, with provision made for taxation, VAT if applicable, rent, leasehold or mortgage repayments, and of course the pre-parathion and auditing of accounts. None of this is possible without at least an elementary knowledge of mathematics, and your manager will show no sympathy if you expect him to pay somebody else to do the work.

All of the scientific, engineering and technological professions demand the application of pure mathematics to physical problems, and this then becomes applied mathematics. A bridge-builder must work out all the stresses and strains to which the bridge will, or may be subjected, taking every factor into account; maximum load, wind pressure, storms and floods being obvious examples, in order to comply with safety standards. Mathematics provides the essential preliminary to this or any other major

ronstruction, such as a tower block, or an oil rig, and indeed to every minor building project.

Apart from mechanical engineering, applied mathematics is crucial to the generation and use of electricity, and to the sciences of astronomy, optics, thermodynamics, aeronautics, ship-building and virtually every other practical aspect of modern life. The manifold uses of electronics and computers are all mathematically-based. It is no exaggeration to say that life as we know it would be impossible were it not for this fundamental study.

In fact, every past generation since history began could say the same thing. It is true that there have been significant advances in the past few decades. However, counting and measuring date back to the early civilisations of the Chinese, the Hindus, the Babylonians and the Egyptians. Thales of Miletus and Pythagoras invented theoretical geometry, and in the 4th and 3rd Centuries BC, Euclid and Archimedes added to this knowledge. Western numerals are Hindu-Arabic in origin, reaching the West by about
1000 AD. However, significant developments came later, from the 15th Century  onwards, and one needs only to mention Descartes, Napier, Leibniz, Lobachevski and Einstein, and what the application of their discoveries achieved, to underline the fact that mathematics has always been crucial to man's material progress.

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