Mathreader's Blog

I found the following quote from John von Neumann in a book as a motto (I don’t remember which one, maybe David Joyner’s Adventures in Group Theory, but need to check):

Young man, in mathematics you don’t understand things. You just get used to them.

I liked this very much. My girlfriend (she’s a math teacher and also doing a PhD on teaching math) liked it too. So we were happy to see that quote…

…Then few months later the quote came up again in a discussion, and I realized that we had two different interpretations of it. Her take:

• This is how (rather badly) math is taught nowadays. We teach mechanistic algorithms and the pupils do not need to know why do the recipes work as long as they can carry out the calculation, they get good marks.

My take:

• As you dig deeper into math or go higher into the thin air of extreme abstraction (choose your favourite metaphor) the mathematical objects are no longer directly grounded in our everyday 3D physical bodily experience. You can understand number 3, just 3 sheeps or 3 fingers, easy, but how about generalised reciprocities in number theory? No matter how abstract the objects are, if you meet them regularly, they become good friends and you don’t care about their ontological status, they become part of your world.

So who is right? What did the old master mean?

Little investigation reveals that it was said to a young physicist who complained when having difficulties understanding a mathematical method… Still, both explanations seem possible.