There is a genre of jokes about engineers, physicists and mathematicians. They play on the viewpoint of each of these when tasked with certain problems. A particular one I’ve remembered (though many versions exist) is one where the three are asked to fence some sheep with as little fencing as possible.

The engineer carefully manoeuvers the sheep into a neat circle and attempts to build a fence round them. It works. But the physicist notices that he can make the circle smaller. So he builds a fence of infinite radius then draws it in and makes it as small as possible with the sheep inside. Satisfied he challenges the mathematician to do better.

The mathematician sighs and puts a fence round himself and declares "I am outside". He wins.

That’s what mathematicians learn. We have conventions that we make without really realising. Why is the centre of the circle thought to be on the inside? Why is there no square root of a minus number? Why is there only one infinity? If you can’t answer those questions then keep an open mind, and you’re half way to being a mathematician.

Of course, you’re also half way to madness.

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See I agree with this completely.