Mathematics is much more than just calculations
A PERSON who can perform lightning-quick calculations is often called a maths wizard, mathematician or a "human computer" ("India's 'Human Computer' dies, aged 83"; last Tuesday).
These could be misnomers. Such a person is no human computer, for a computer can do much more than just calculations. The ability to perform phenomenal mental calculations alone, though it is an undeniable talent, does not qualify anyone to be a mathematician.
That skill, by itself, makes him only a "human calculator" and no more. He is not a mathematician any more than a quick typist is a writer and a pianist who can play with lightning speed is a musician or virtuoso.
It is a common misconception that maths consists only of studying and calculating numbers. A mathematician is one who can detect similarities and relations in many situations, devise rules and form structures that summarise and organise these situations, make logical conclusions from these rules and by reasoning, enlarge such structures so that they can include more and more situations.
Any student should know that many maths topics have nothing to do with calculation. Geometrical proofs, algebraic proofs and set theories are some examples.
I once asked my students to evaluate 999,999,999 multiplied by 999,999,999, without using a calculator. Most gave up. One went through the laborious chore of multiplication and got it right. Still, he was only a successful "calculator". Those who, without having been taught, used 999,999,999 multiplied by (1,000,000,000 - 1), were budding mathematicians.
A computer that can perform complex calculations quickly should not be honoured as a mathematician. The programmer who devises the computer program through reasoning is one. A student who passes maths examinations by repeating exactly what he has been taught may not be a mathematician, even if he scores excellent grades.
A mathematician must have an organised set of mental repertoire, be skilful in both deductive and inductive reasoning and devises creative procedures which are often shorter or more elegant than those found in textbooks. To him, maths is a mental game of fun.
It is my hope that our maths teachers will produce not just mere calculators, but more mathematicians for Singapore.
Ee Teck Ee