My friend’s wisdom was a type of abstraction, abstracting heartbreak down to its very essence. Abstraction can appear to take you further and further away from reality, but really you’re getting closer and closer to the heart of the matter. To get to the heart, you have to strip away clothes and skin and flesh and bone.

Mathematics is the study of anything that obeys the rules of logic, using the rules of logic.

The key in maths, and with maps, is to find the most appropriate level of abstraction for the given moment.

In maths the technique we use is logic. We only want to use sheer logical reasoning. Not experiments, not physical evidence, not blind faith or hope or democracy or violence. Just logic. So what are the things we study? We study anything that obeys the rules of logic.

Choosing what features to ignore should depend heavily on what context we’re thinking about.

There’s a subtle difference between something that’s ‘simple’ and something that’s ‘simplistic’;

‘It’s very simple really. You’ve lost something you loved.’

feeling stupid for not having understood something before just shows that you are now cleverer than you were then.

This can seem frustrating (there simply are diagonal highways in Chicago) but the point is to shed light on something rather than to model it precisely.