Frequently, teachers of mathematics appeal to this platonic ideal of “intuition” to explain where concepts come from, or even as steps in proof-sketches. But, what really is “intuition?” What properties of this word allow it to be so incredibly powerful? Is intuition something you are born with, or does one gain intuition with experience? And, if intuition comes from experience, why do teachers rely so much on students to have experience in a field they are meant to be learning?

The following is a conversation inspired from interactions I have had with professors, teachers, and advisors of mathematics. …

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