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What is mathematics you may ask yourself - and particularly as you approach new school year or you have just finished one. Some people think that mathematics is a science of numbers - but they usually mistake maths for arithmetic. Knowing how to do sums does not mean that you are a mathematician, and very often the reverse is true as well - being mathematician doesn't necessarily mean that you will be good at sums!

So what is the difference between mathematics and arithmetic? Well, to put it simply, arithmetic is part of mathematics, but mathematics is not part of arithmetic. Arithmetic is knowing how to use basic operations and being what some call 'numerate'. Seeing and understanding some of the wonderful patterns, being able to describe them and to apply your general understanding to other similar things means that you are on the way of becoming a mathematician.

We now know that certain animals can recognise numbers of things, form and measure. Magpies recognise the difference between groups of five or six objects and chimpanzees know that five is more than four.

Counting horse

Wilhelm von Osten and his mathematical horse Hans

At the beginning of the 20 th century a certain Wilhelm von Osten claimed that he had a horse who knew how to do arithmetic. Hans, as the horse's name was, was apparently able to add whole numbers and fractions. In a 1904 a committee was set up made of experts to investigate the phenomenon. They agreed that Hans was indeed able to do all that von Osten claimed. However, a psychologist Oskar Pfungst proved later that the horse's boss was doing the maths, and Hans the horse was only very apt at reading the unconsciously given signs by his master.

Chimpanzee

There have been numerous researches to show how much arithmetic chimpanzees can do. Here is photograph of one such attempt.

This, however, does not mean that animals can do mathematics. Some animals can recognise groups of objects, and can be taught to be better at this. If we think back to the proposition that arithmetic is not really mathematics, but only a part of it, then we can see that humans are that much different from other known species - we can recognise the patterns, describe them, and apply them to any situation. Next time you try some algebra algebraic problem and are frustrated by it just think that you are that much better than Hans - you can generalise what you see, write up a formula and apply it to any situation, and not only add or subtract apples or pears...

Because we can do this, we can also experience beauty through generalisation, description and application of this knowledge.

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