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..."

"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..."

"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..."

"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."

"[A]bstract theory often comes from wanting to be lazy, or... conserving brain power, conserving energy, because if you do the same thing over and over again, wouldnt you rather not... and just do it once... [T]hats what abstract theory is there for... [T]hat applies to all sorts of aspects of life, not just sciences and programming"

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

"The point is to help us. Its not there to cause people pain. The point of abstraction is to clear out the fluff in order... to see more clearly whats actually going on."

"I make it my business to help everybody understand these things a bit more, because... theyre very misunderstood..."

"I believe very strongly in helping other people understand things. Theres no point knowing things if you dont help other people know..."

"Now, if you imagine drawing a circle in the air with a , the surface you make is a over a circle. The idea is that for each point in the circle, you now have an entire vector, that is, a line given by the lightsaber at that instant."

"[S]omething is easy if it is attainable by logical thought processes.... without having to resort to imagination, guesswork, luck, gut feeling, convoluted interpretation, leaps of faith... drugs, violence... [etc.]"