This common complaint has an adult version, “Why do we need mathematicians if we have (statistics) software?” Apart from the notoriously wrong political polls of last year, the following story may provide a partial answer:

In 1943, at the peak of World War II, the American military assigned Columbia University to study air bomber damage with the intention of reinforcing any defects. The duly performed statistical analysis on the vast amount of data that the Air Force had accumulated showed clearly that the statistically most likely place of an airplane to get “hit’’ was the fuselage. The committee was expecting to recommend reinforcing it. “Not so fast!’’ cried Abraham Wald, a Hungarian refugee and mathematician, “what you should really do is add armour to the engines! The aircraft that are most damaged there don’t return. You don’t see them. Since we see far less damage to the motors than randomness would produce, it indicates that they are the weak point”.

The point of mathematics is not calculating but solving problems generically and correctly. No matter how sophisticated a program may be, it uses set models with (hidden) assumptions. Experienced mathematicians know that changing the conditions even slightly may alter the conclusions. The following website is a very readable introduction to the mathematical approach to problem solving: http://worrydream.com/LadderOfAbstraction/

Teaser problems

‘O’-level: Two satellites orbit the earth at a height equal to R/4 where R is earth’s radius. How far apart can they possibly be for them to still communicate with each other directly? (Ans: 3R/2.)

‘A’-level: Among all (right) cones that fit inside a sphere, show that the unique one which has the largest curved area also has the largest volume.

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