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Well we get into the complicated question of what mathematics is about which is very difficult. If it is about some abstract realm of abstract objects - some version of Plato's idealised concepts - then we need a good explanation of how we actually know or learn anything about this realm. On the other hand, if it is just, some kind of notational convenience, symbols pushed around a piece of paper according to certain rules, then we need to explain why it has such predictive power and in particular why concepts like imaginary number and infinity which, in this interpretation, really are just squiggles on paper, are so damn useful.

However, I very much doubt that the teacher wanted to open a discussion of the nature of mathematical reality when he asserted that I was wrong. In some ways I was more irritated that, having successfully got the children excited and interested about some (quite advanced and abstract) feature of mathematics the teacher's reaction was obviously to make them feel ignorant and stupid. Moreover, as a teacher of mathematics, he really shouldn't be asserting that such a cornerstone of large areas of mathematics doesn't exist without explaining the philosophical standpoint behind it. I mean, I've lost touch with the A level syllabus, but I assume they still teach integration and differentiation which is difficult without coming to terms with some concept of infinity.

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purplecat

May 2025

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