I was recently reminded of this anecdote from Junaid Mubeen, originally in Bright Magazine. Juniad recalls a time where he assisted his 12-year old nephew on a math homework problem. As it turns out, the problem had no solution, Junaid could elegantly prove it, and the nephew excitedly accepted their reasoning. Then:
What happened next was revealing. My sister told me that my nephew devoted the rest of the evening to searching for a solution. That’s a strange commitment to make when you’ve just been convinced that no such solution exists.
My nephew was in a state of cognitive dissonance. He understood that this problem has no solution. And yet, this was his maths homework. From all his years of schooling, every maths question always had an answer. Why should this time be any different?
My nephew’s deference towards school maths, with closed questions and prescribed answers, betrayed his mathematical reasoning.
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