Mathematics - Quote by Dick Tahta

If certain choices about the use of the word 'same' lie at the heart of mathematical activity then mathematics starts in the cradle, for a sense of one's own identity from one moment to the next is one of the first lessons to be learnt. Mummy is quickly felt to be the same person when she comes and goes; it takes much longer for Daddy to acquire the same invariance. The rattle is seen from different positions and felt in different ways. Each perception is different but as it is explored helps to build up the idea of something permanent, something that is always the same. Later on it becomes more and more difficult to recapture the differences between our perceptions. We very rarely see a circle when we look at a penny, but that is the shape we say that we see when we are asked. In an agreed sense, a circle remains the same wherever we perceive it from; in another agreed sense it does not. In one case a circle and an ellipse are the same but in the other they are different.

Mathematics has inevitably commenced when it is decided how things are to be treated as the same. Among other issues, this raises the matter of how many different things there are. Equivalence is a choice at our disposal; but when a choice is made, counting must yield a unique answer. Here is the essence of the activity. We are free to choose bounds and may then explore the inexorable implications of our choice. But the activity must include the choice as well as the exploration.

- Dick Tahta