Reddit reviews Playing with Infinity: Mathematical Explorations and Excursions

The Number Devil is for kids, but I read it as adult and it was fun.The first part of Playing with Infinity could be accessible as well.

What is your background?

Let me recommend Rozsa Peter (1961) Playing with Infinity https://amzn.com/0486232654

To quote what is probably the best math book ever written, Peter Rozsa's Playing with Infinity http://www.amazon.com/Playing-Infinity-R%C3%B3zsa-P%C3%A9ter/dp/0486232654

> if a mathematician has proved something about points and lines, he communicates his findings to his fellows as follows: ‘I do not know what kind of pictures you have of geometrical figures. My idea is that through any two points whatever I can draw one straight line. Does this agree with your idea?’ If the answer is in the affirmative, then he can proceed thus: ‘I have proved something and during the proof I did not make use of any other property of points and straight lines apart from the ones about which we are already agreed. You can now think about your points and lines; you will still understand what I have to say.’

And

> Mathematics does not pretend to enunciate absolute truths. Mathematical theorems are always put in the more humble form: ‘If, . . . then . . .’ ‘If we can use only ruler and compass, then the circle cannot be squared. If by points and lines we mean figures with such and such properties, then the following things are true of them.’

My take on this: mathematics is a totally artificial construct and it is not even a fixed construct. There are axioms we agree on, there are rules of reasoning we agree on but Godel has proven that for every (usable) axiom system we can create two new ones (one by adding the unprovable statement and another by adding the negated statement).