That's some really bad wording indeed. But it may vary from one source to another.
The more intriguing point of your comment is about assumptions. Can you provide a relevant example?
It's hard for me to provide a specific example because (for me) it applies to many different fields of advanced math. It seems like people who are good at math have some preconceived idea in their heads about what the purpose of a math concept is going to be and that helps them to make sense of new concepts faster. Maybe that's what people refer to as a 'mathematical intuition'?
To me (who is not naturally gifted at math), it often seems like math has no specific direction; it appears to explore almost every direction arbitrarily. I can't usually tell which part is supposed to be interesting or potentially meaningful so I don't know what to focus on or what to look for when I'm learning it.
It's like if someone gives you a confusing and vague instruction or question, it helps if you know what the reason is. Like if someone asks you "what day is it?", it helps if you know the intention behind the question or else you can't know for sure if you should answer with "27th of September" or "Wednesday". You don't fully understand the question without knowing the intention behind it. To me, learning math presents a much more extreme variant of that effect.
jongjong|2 years ago
To me (who is not naturally gifted at math), it often seems like math has no specific direction; it appears to explore almost every direction arbitrarily. I can't usually tell which part is supposed to be interesting or potentially meaningful so I don't know what to focus on or what to look for when I'm learning it.
It's like if someone gives you a confusing and vague instruction or question, it helps if you know what the reason is. Like if someone asks you "what day is it?", it helps if you know the intention behind the question or else you can't know for sure if you should answer with "27th of September" or "Wednesday". You don't fully understand the question without knowing the intention behind it. To me, learning math presents a much more extreme variant of that effect.