The trouble with this is that nothing behaves logically. — Eugenia Cheng

"Maths... as its taught in school is often... boring, pointless, painful, beside the point, and doesnt show people the things that... are the most beautiful about abstract math, and what the point of it is..."

"[I]n order to study anything logically, we have to ignore all the pesky details that prevent it from behaving logically, and... move into the idealized world... rather than the real world of things... [T]his... is what... abstraction... is..."

"Infinity is a Loch Ness monster, capturing the imagination with its awe-inspiring size but elusive nature. Infinity is a dream, a vast fantasy world of endless time and space. Infinity is a dark forest with unexpected creatures, tangled thickets and sudden rays of light breaking through. Infinity is a loop that springs open to reveal an endless spiral."

"If youre only presented with... things you dont care about... then you wont care about having those things made easier, and so if all the problems... given are dumb... problems that dont... have anything to do with real life, then everyone.., especially young people... will immediately see that were just talking a load of rubbish..."

"Id like to talk about abstract mathematics and my experience of making it... palatable to people who may have had very bad experiences of it..."

"We will never be able to encompass everything by rationality alone... [T]his is a necessary and beautiful aspect of human existence."